id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,116 | OWR-10252930-028 | Induced Four-Cycle Profiles Above Half Density | Among $n$-vertex graphs with edge density $\xi$, determine asymptotically the maximum number of induced copies of $C_4$. For $\xi>1/2$, is the maximum asymptotically attained by the extremal construction for the triangle-density problem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-028",
"literature-status:partially-solved",
"owr-year:2022"
] | The induced C4 profile conjecture is proved at the densities one minus one over k and has general upper bounds, but the claimed formula for every density above one half remains open. | [
{
"url": "https://doi.org/10.1016/j.jctb.2022.09.003",
"label": "Liu, Mubayi, and Reiher, The feasible region of induced graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Among $n$-vertex graphs with edge density $\xi$, determine asymptotically the maximum number of induced copies of $C_4$. For $\xi>1/2$, is the maximum asymptotically attained by the extremal construction for the triangle-density problem? | We have the following conjecture of Liu, Mubayi, and Reiher [1]. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,117 | OWR-10252930-029 | Petersen-Graph Counts in Sparse Pseudorandom Graphs | Let $G$ be an $n$-vertex, $C_4$-free graph with edge density $p\gtrsim n^{-1/2}$ such that $$|e_G(A,B)-p|A||B||=o(pn^2)$$ for all $A,B\subseteq[n]$. Is the number of copies of the Petersen graph in $G$, up to a constant factor, at least its expected number in $G(n,p)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-029",
"literature-status:open",
"owr-year:2022"
] | Under the stated C4-free and discrepancy hypotheses, whether the Petersen count is bounded below by the corresponding random-graph count is posed as an open sparse pseudorandom counting problem; no proof or counterexample was found. | [
{
"url": "https://doi.org/10.1112/jlms.12500",
"label": "Conlon, Fox, Sudakov, and Zhao, sparse regularity"
},
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Let $G$ be an $n$-vertex, $C_4$-free graph with edge density $p\gtrsim n^{-1/2}$ such that $$|e_G(A,B)-p|A||B||=o(pn^2)$$ for all $A,B\subseteq[n]$. Is the number of copies of the Petersen graph in $G$, up to a constant factor, at least its expected number in $G(n,p)$? | Is it true that the number of copies of the Peterson graph in G is at least (up to a constant factor) the number of copies of the Peterson graph in Gpn, pq? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,118 | OWR-10252930-031 | Efficient Recognition of Cyclic Sumsets | Given $B\subseteq\mathbb Z/n\mathbb Z$, is there an efficient algorithm that decides whether some $A\subseteq\mathbb Z/n\mathbb Z$ satisfies $B=A+A$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "scope_correction",
"evidence": "source_correction"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-031",
"literature-status:open",
"owr-year:2022"
] | The original extracted text included an adjacent, unrelated source item. The source report confirms the existing clean statement; the original_statement field is now restricted to this problem. No theorem about the neighbouring item is treated as a solution here.
**What remains.** The clean problem retains its existin... | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
},
{
"url": "https://doi.org/10.4171/owr/2022/22",
"label": "Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. ... | 2026-09-28T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Given $B\subseteq\mathbb Z/n\mathbb Z$, is there an efficient algorithm that decides whether some $A\subseteq\mathbb Z/n\mathbb Z$ satisfies $B=A+A$? | Can one find an efficient algorithm such that given B Ď Z\{nZ determine whether or not B “ A ` A for A Ď Z\{nZ?} | corrected_verified | Removed material belonging to a neighbouring source item after checking the original report. The clean mathematical statement is unchanged. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,119 | OWR-10252930-032 | Uncommon Pairs of Linear Equations | For even $k\geq 6$, if the common solution space of $\sum_{i=1}^k a_ix_i=0$ and $\sum_{i=1}^k b_ix_i=0$ has dimension $k-2$, is the pair of equations uncommon over every sufficiently large finite field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-032",
"literature-status:partially-solved",
"owr-year:2022"
] | Several broad subclasses of even-variable rank-two systems are now proved uncommon, including generic systems and systems of girth k minus one, but the full conjecture for every rank-two pair remains unresolved. | [
{
"url": "https://doi.org/10.1112/blms.70135",
"label": "Altman and Liebenau, minimal rank-two systems"
},
{
"url": "https://arxiv.org/abs/2404.17005",
"label": "Dong, Li, and Zhao, uncommon linear systems"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For even $k\geq 6$, if the common solution space of $\sum_{i=1}^k a_ix_i=0$ and $\sum_{i=1}^k b_ix_i=0$ has dimension $k-2$, is the pair of equations uncommon over every sufficiently large finite field? | Conjecture 16. For all k ě 6, k even, such that the dimension of the solution space of a1 x1 ` . . . ` ak xk “ 0, b1 x1 ` . . . ` bk xk “ 0 is k ´ 2, and q sufficiently large, we have that the pair of equations is uncommon. Natasha Morrison Fix a pair of equations a1 x1 ` . . . ` ak xk “ 0 b1 x1 ` . . . ` bk xk “ 0. We... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,120 | OWR-10252930-033 | Sharp Concentration of Random-Graph Chromatic Number | For $n^{-1/2+\delta}\ll p\leq1-\delta$, is the $\widetilde O(\sqrt{np}/\log n)$ concentration-window bound for the chromatic number $\chi(G_{n,p})$ close to optimal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-033",
"literature-status:partially-solved",
"owr-year:2022"
] | The stated upper concentration bounds were extended to sparse regimes, and later work proves matching lower-order fluctuations in important dense regimes, but a general best-possible characterization remains open. | [
{
"url": "https://doi.org/10.37236/11638",
"label": "Surya and Warnke, Electronic Journal of Combinatorics"
},
{
"url": "https://arxiv.org/abs/2405.13914",
"label": "Yan, very dense random graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For $n^{-1/2+\delta}\ll p\leq1-\delta$, is the $\widetilde O(\sqrt{np}/\log n)$ concentration-window bound for the chromatic number $\chi(G_{n,p})$ close to optimal? | Is the upper bound of Theorem 17 on the concentration of the chro- matic number χpGn,p q of the random graph Gn,p close to best possible or not? Conjecture 16. For all k ě 6, k even, such that the dimension of the solution space of a1 x1 ` . . . ` ak xk “ 0, b1 x1 ` . . . ` bk xk “ 0 is k ´ 2, and q sufficiently large,... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,121 | OWR-10252930-034 | Long Twin Subsequences in Ternary Words | For ternary words, is the maximum twin-subsequence length asymptotically $n/2-o(n)$, both for a uniformly random word and in the worst case? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-034",
"literature-status:open",
"owr-year:2022"
] | For ternary words, known deterministic and random lower bounds are strictly below n over 2, while the asserted n over 2 minus little-o of n behavior has not been proved. | [
{
"url": "https://doi.org/10.1016/j.jcta.2013.01.001",
"label": "Axenovich, Person, and Puzynina, twins in words"
},
{
"url": "https://arxiv.org/abs/2112.14197",
"label": "Dudek, Grytczuk, and Rucinski, long twins in random words"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | For ternary words, is the maximum twin-subsequence length asymptotically $n/2-o(n)$, both for a uniformly random word and in the worst case? | Is it asymptotically almost surely true that tpW3 pnqq “ n\{2 ´ opnq? Is tpn, 3q “ n\{2 ´ opnq?} Andrzej Ruciński Fix an alphabet A with |A| “ k ě 2 and consider words w P An . Definition 19. Define a pair of subwords w1 , w2 of w to be twins if they are identical and disjoint. Example 2. The overline and underlined w... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,122 | OWR-10252930-035 | Size Ramsey Numbers of Ramanujan Graphs | Let $G$ be an $n$-vertex, $\Delta$-regular Ramanujan graph with $\Delta\geq3$, let $N=10^{10^{10\Delta n}}$, and let $p$ be the probability for which a random graph $G(N,p)$ has probability $1/2$ that every two-coloring contains a monochromatic copy of $G$. Is the size Ramsey number of $G$ equal to $\Theta(pN^2)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237](https://doi.org/10.4171/owr/2022/22)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252930-035",
"literature-status:open",
"owr-year:2022"
] | The Ramanujan-graph size-Ramsey assertion is stated as Conjecture 23, and existing expander and random-host results do not establish the claimed theta bound for every fixed-degree Ramanujan graph. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3964/OWR_2022_22.pdf?isAllowed=y&sequence=4",
"label": "official OWR report"
},
{
"url": "https://arxiv.org/abs/2110.01897",
"label": "Conlon, Nenadov, and Trujic, size-Ramsey of cubic graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/22 | null | null | null | Let $G$ be an $n$-vertex, $\Delta$-regular Ramanujan graph with $\Delta\geq3$, let $N=10^{10^{10\Delta n}}$, and let $p$ be the probability for which a random graph $G(N,p)$ has probability $1/2$ that every two-coloring contains a monochromatic copy of $G$. Is the size Ramsey number of $G$ equal to $\Theta(pN^2)$? | Informally, this question is asking whether for large sparse graphs which are expanders, the size Ramsey number is controlled by the construction coming from random graphs. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/22, pp. 1165--1237 |
30,005,123 | OWR-10252931-001 | Fermionized Yangians from Quivers with Potential | Can the cohomological Hall-algebra construction for preprojective algebras be partially fermionized to recover Yangians of classical Lie superalgebras such as $\mathfrak{gl}(m|n)$? Equivalently, can one choose a quiver $Q'$ and potential $W'$ so that $A_{Q',W'}$ partially fermionizes $A_{\widetilde Q,\widetilde W}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312](https://doi.org/10.4171/owr/2022/23)
## Literature ... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-10252931-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252931-001",
"literature-status:partially-solved",
"owr-year:2022"
] | Davison constructs a parity-switching fermionization for cohomological Hall algebras of preprojective algebras and relates it to Yangian phenomena, but the full requested realization of all classical Lie-superalgebra Yangians is not established. | [
{
"url": "https://doi.org/10.1017/S001708952200009X",
"label": "Davison, fermionization paper"
},
{
"url": "https://doi.org/10.4171/owr/2022/23",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/23 | null | null | null | Can the cohomological Hall-algebra construction for preprojective algebras be partially fermionized to recover Yangians of classical Lie superalgebras such as $\mathfrak{gl}(m|n)$? Equivalently, can one choose a quiver $Q'$ and potential $W'$ so that $A_{Q',W'}$ partially fermionizes $A_{\widetilde Q,\widetilde W}$? | Is there a “fermionized”, or partially odd version of the above con- struction? I.e. can we recover Yangians of classical super-algebras like gl(m|n)? Is there a choice of quiver Q′ and potential W ′ such that AQ′ ,W ′ “partially fermionizes” AQ̃,W̃ ? where aQ,\gamma (q) is the Kac polynomial, counting iso-classes of a... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312 |
30,005,124 | OWR-10252931-002 | Partial Fermionization of Cohomological Hall Algebras | Is there a choice of quiver Q′ and potential W ′ such that AQ′ ,W ′ “partially fermionizes” AQ̃,W̃ ? t7\tot\cdot\alpha // 0 // h A1 h. For \alpha \in h (not necessarily non-zero) we define Y \alpha via the rightmost, Cartesian, diagram. Then Y \alpha is a smooth threefold. The curve Ci corresponding to the vertex i \i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312](https://doi.org/10.4171/owr/2022/23)
## Literature ... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this is a duplicate extraction of the quiver-with-potential formulation already retained in OWR-10252931-0) | [
"OWR-10252931-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252931-002",
"literature-status:partially-solved",
"owr-year:2022"
] | A concrete fermionization procedure is known for important preprojective-algebra CoHAs, including central-extension and parity results, but no general quiver-and-potential construction answering the stated question is known. | [
{
"url": "https://doi.org/10.1017/S001708952200009X",
"label": "Davison, fermionization paper"
},
{
"url": "https://doi.org/10.4171/owr/2022/23",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/23 | null | null | null | null | Is there a choice of quiver Q′ and potential W ′ such that AQ′ ,W ′ “partially fermionizes” AQ̃,W̃ ? t7\tot\cdot\alpha // 0 // h A1 h. For \alpha \in h (not necessarily non-zero) we define Y \alpha via the rightmost, Cartesian, diagram. Then Y \alpha is a smooth threefold. The curve Ci corresponding to the vertex i \i... | unrecoverable | The official report confirms that this is a duplicate extraction of the quiver-with-potential formulation already retained in OWR-10252931-001. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312 |
30,005,125 | OWR-10252931-003 | Ideals and Central Reductions of the Virasoro Enveloping Algebra | Determine the containment relations among the Poisson primitive ideals of $S(\operatorname{Vir})$. If $\lambda\neq0$, is $U(\operatorname{Vir})/(z-\lambda)$ simple? Does $U(\operatorname{Vir})$ satisfy the ascending chain condition on two-sided ideals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312](https://doi.org/10.4171/owr/2022/23)
## Literature ... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252931-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The Poisson spectrum and Poisson simplicity of the Virasoro central reductions are substantially understood, including simplicity for nonzero central parameter, but the stated associative simplicity and ACC questions for enveloping-algebra quotients are not fully resolved. | [
{
"url": "https://arxiv.org/abs/2106.02565",
"label": "Poisson spectrum paper"
},
{
"url": "https://archive.intlpress.com/site/pub/files/_fulltext/journals/arkiv/2020/0058/0002/ARKIV-2020-0058-0002-a004.pdf",
"label": "Enveloping-algebra ideal paper"
},
{
"url": "https://doi.org/10.4171/... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/23 | null | null | null | Determine the containment relations among the Poisson primitive ideals of $S(\operatorname{Vir})$. If $\lambda\neq0$, is $U(\operatorname{Vir})/(z-\lambda)$ simple? Does $U(\operatorname{Vir})$ satisfy the ascending chain condition on two-sided ideals? | In particular, a sub-question of Question (1) is: Question. (1a) For which χ \in Vir ∗ does PCore(mχ ) \% (z − χ(z))? We also give a parameterisa- tion of Poisson prime ideals in S(W ) = S(Vir )/(z). (Recall that by Theorem 4, S(Vir )/(z − \lambda) is Poisson simple for \lambda 6= 0.) Open questions include: Question. ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312 |
30,005,126 | OWR-10252931-004 | Coincidence of Degeneration Orders for Representation-Directed Algebras | For representation-directed algebras, do the geometric and homological degeneration orders coincide? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312](https://doi.org/10.4171/owr/2022/23)
## Literature ... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252931-004",
"literature-status:open",
"owr-year:2022"
] | The cited report explicitly states the coincidence of the two degeneration orders for representation-directed algebras as a conjecture; no proof establishing it in the stated generality was found. | [
{
"url": "https://doi.org/10.4171/owr/2022/23",
"label": "Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/0001-8708(96)00035-1",
"label": "Bongartz, degeneration paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/23 | null | null | null | For representation-directed algebras, do the geometric and homological degeneration orders coincide? | We conjecture that for representation-directed algebras they do. ?? • ❄ ⑧⑧ ❄ . \textasciitilde{}\textasciitilde{} • • . ⑧?? ❄❄ ⑧⑧?? ?? L f ?? • ∇f ∇L ?? ❄❄ ⑧⑧ • ∇M ?⑧? ❄❄ ⑧?? ❄❄ ⑧?? ❄❄ ⑧?? • ❄❄ M ⑧ ⑧ ⑧ ⑧ • • • • • | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/23, pp. 1239--1312 |
30,005,127 | OWR-10252932-001 | Open Problems in K-Theory of Ring Pushouts | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354 Georg Tamme (joint with Markus Land) K-theory of pushouts of associative rings . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357 The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official source passage is a table-of-contents fragment ending in the word conjecture and contains no recoverable claim. No separate cle) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-001",
"literature-status:open",
"owr-year:2022"
] | The extracted record contains only a table-of-contents fragment ending in the word conjecture, so no definite mathematical claim can be identified; under the required uncertainty rule it is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | null | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354 Georg Tamme (joint with Markus Land) K-theory of pushouts of associative rings . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357 The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official source passage is a table-of-contents fragment ending in the word conjecture and contains no recoverable claim. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,128 | OWR-10252932-002 | Chromatic Lichtenbaum–Quillen and Redshift Conjectures | How does algebraic $K$-theory shift chromatic height; in particular, is the algebraic $K$-theory of an $L^f_{n-1}$-local ring $T(m+1)$-acyclic for every $m\geq n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-002",
"literature-status:partially-solved",
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] | Chromatic Lichtenbaum--Quillen and redshift statements are proved qualitatively in broad generality and quantitatively in important low-height cases, but the full quantitative conjecture and all proposed refinements are not established. | [
{
"url": "https://doi.org/10.4007/annals.2022.196.3.6",
"label": "Hahn--Wilson, redshift paper"
},
{
"url": "https://arxiv.org/abs/2505.00344",
"label": "Yang, Effective Redshift"
},
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | How does algebraic $K$-theory shift chromatic height; in particular, is the algebraic $K$-theory of an $L^f_{n-1}$-local ring $T(m+1)$-acyclic for every $m\geq n$? | conjecture. Here the word asymptotically comes in two flavours, the qualitative result that the fibre of the map K(R)(p) \to Lf1 K(R)(p) is bounded above, and the quantitative refinement specifying a bound and perhaps also describing LT (1) K(R) in some way. The second line is a direct higher chro- matic analog, hence cal... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,129 | OWR-10252932-003 | Homological Stability of Reductive Borel–Serre Categories | What homological-stability properties hold for reductive Borel–Serre categories, and do these categories possess higher homotopy commutativity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-003",
"literature-status:partially-solved",
"owr-year:2022"
] | Homological stability for reductive Borel--Serre spaces and related unstable algebraic K-theory has been proved in substantial ranges, but the broad stability theory asked for in the record is not complete. | [
{
"url": "https://arxiv.org/abs/2405.07566",
"label": "Randal-Williams, RBS stability"
},
{
"url": "https://arxiv.org/abs/2405.02065",
"label": "Jansen, unstable K-theory"
},
{
"url": "https://doi.org/10.1007/s00029-023-00900-8",
"label": "Clausen--Jansen, RBS model"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | What homological-stability properties hold for reductive Borel–Serre categories, and do these categories possess higher homotopy commutativity? | What kind of homological stability properties do the reductive Borel–Serre categories satisfy? ` 3. Does it satisfy higher homotopy commutativity? A more vague question is that of exploiting the geometric origins. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,130 | OWR-10252932-004 | Comparison Maps in p-Adic Cohomology | conjecture: (1) Hℓn (Y ) = Hℓn (Y (ǫ)) \to H n (\pi −1 (Y (ǫ))) \to Hℓn (Z), Theorem 3. Let Z be a smooth proper variety over a finite extension of Fp ((p♭ )) with residue field k, having a semistable formal model Z with log special fiber Z0 . Then we have a canonical quasi-isomorphism | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official source passage is a damaged splice between a conjectural comparison-map fragment and a proved theorem, so it does not identify ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-004",
"literature-status:open",
"owr-year:2022"
] | The extracted record contains only the label conjecture without an identifiable mathematical statement; the unresolved record is therefore normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | null | conjecture: (1) Hℓn (Y ) = Hℓn (Y (ǫ)) \to H n (\pi −1 (Y (ǫ))) \to Hℓn (Z), Theorem 3. Let Z be a smooth proper variety over a finite extension of Fp ((p♭ )) with residue field k, having a semistable formal model Z with log special fiber Z0 . Then we have a canonical quasi-isomorphism | unrecoverable | The official source passage is a damaged splice between a conjectural comparison-map fragment and a proved theorem, so it does not identify one recoverable problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,131 | OWR-10252932-005 | Determinant Formula for Leading Zeta Values | For a proper regular arithmetic scheme $X/\mathbb{Z}$ and $n\in\mathbb{Z}$, does the determinant isomorphism satisfy the conjectural leading-value formula $\det(\lambda_{X;n})=\pm\zeta^*(X;n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-005",
"literature-status:partially-solved",
"owr-year:2022"
] | The conjectural leading-term formula has important special cases and compatibility results, and recent work computes the de Rham correction factor, but the full formula for arbitrary proper regular arithmetic schemes remains unproved. | [
{
"url": "https://arxiv.org/abs/2603.21471",
"label": "Recent de Rham--syntomic paper"
},
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | For a proper regular arithmetic scheme $X/\mathbb{Z}$ and $n\in\mathbb{Z}$, does the determinant isomorphism satisfy the conjectural leading-value formula $\det(\lambda_{X;n})=\pm\zeta^*(X;n)$? | and we conjecture that C(X; n) : det(\lambdaX;n) ) = \pm ζ ∗ (X; n) where ζ ∗ (X; n) denotes the leading coefficient in the Taylor development of ζ(X; s) near s = n. Let X/Z be a proper regular arithmetic scheme and let n \in Z. Under some assumptions, we have a perfect complex of abelian groups RΓW,c (X; Z(n)). Using de... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,132 | OWR-10252932-007 | Künneth Equivalence for Weil Motivic Tate Categories | For algebraic varieties $X_1,X_2$ over $\mathbb F_p$, does exterior product induce an equivalence $$\operatorname{DTM}(X_1^{\mathrm{Weil}})\otimes_{\operatorname{DTM}(\mathbb F_p)}\operatorname{DTM}(X_2^{\mathrm{Weil}})\simeq\operatorname{DTM}(X_1^{\mathrm{Weil}}\times_{\mathbb F_p}X_2^{\mathrm{Weil}})$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-007",
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"owr-year:2022"
] | The analogous Kunneth equivalence for constructible l-adic sheaves is known, but the stated equivalence for Weil-motivic Tate categories is presented as ongoing and has not been established in the required generality. | [
{
"url": "https://arxiv.org/abs/2012.02853",
"label": "Hemo--Richarz--Scholbach, sheaf Kunneth"
},
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | For algebraic varieties $X_1,X_2$ over $\mathbb F_p$, does exterior product induce an equivalence $$\operatorname{DTM}(X_1^{\mathrm{Weil}})\otimes_{\operatorname{DTM}(\mathbb F_p)}\operatorname{DTM}(X_2^{\mathrm{Weil}})\simeq\operatorname{DTM}(X_1^{\mathrm{Weil}}\times_{\mathbb F_p}X_2^{\mathrm{Weil}})$$? | Is there an equiv- alence \sim = DTM(X1Weil) ⊗DTM(Fp ) DTM(X2Weil) \to DTM(X1Weil \timesFp X2Weil)? Theorem 2 ([HRS20]). For algebraic varieties X1 , X2 /Fp the exterior product yields an equivalence \sim = Dbc (X1Weil) ⊗Db (Fp ) Dbc (X2Weil ) \to Dbc (X1Weil \timesFp X2Weil). c | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,133 | OWR-10252932-008 | Hopkins–Morel Input to Motivic Stable Homotopy | Making the degrees on the right hand side explicit, one finds in particular that \pi∗,0 (1(p) )(Fp ) ≃ Z(p) , and so MapSH(Fp )(p) (1, 1) ≃ Z(p) . Thus the main theorem follow from the Hopkins–Morel conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376](https://doi.org/10.4171/owr/2022/24)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official source passage explains that a proved main theorem follows from the Hopkins–Morel conjecture; it is not a separate unresolved p) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252932-008",
"literature-status:open",
"owr-year:2022"
] | The extracted record is a theorem fragment referring to the Hopkins--Morel conjecture and does not state an independently triageable claim; the unclear claim is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/24",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/24 | null | null | null | null | Making the degrees on the right hand side explicit, one finds in particular that \pi∗,0 (1(p) )(Fp ) ≃ Z(p) , and so MapSH(Fp )(p) (1, 1) ≃ Z(p) . Thus the main theorem follow from the Hopkins–Morel conjecture. The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The official source passage explains that a proved main theorem follows from the Hopkins–Morel conjecture; it is not a separate unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/24, pp. 1313--1376 |
30,005,134 | OWR-10252933-001 | Condition-Number-Robust Low-Rank Matrix Completion | Derive recovery guarantees for factorization-based low-rank matrix-completion algorithms whose dependence on matrix condition numbers matches their empirical performance. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Re-thinking High-dimensional Mathematical Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/25, pp. 1377--1430](https://doi.org/10.4171/owr/2022/25)
## Literature review (checke... | 3 | partially_solved | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252933-001",
"literature-status:partially-solved",
"owr-year:2022"
] | Low-rank matrix-completion theory gives recovery and stability guarantees under explicit sampling and incoherence assumptions, including approximate low rank, but arbitrary missing-entry patterns do not determine a unique completion. | [
{
"url": "https://doi.org/10.1137/21M1433812",
"label": "Zilber--Nadler, matrix completion"
},
{
"url": "https://proceedings.mlr.press/v162/zilber22a.html",
"label": "Inductive matrix completion"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/25 | null | null | null | Derive recovery guarantees for factorization-based low-rank matrix-completion algorithms whose dependence on matrix condition numbers matches their empirical performance. | Can we predict the missing entries, say assuming the matrix is (approximately) low rank ? Completing large matrices with only few observed entries: A one-line algorithm with provable guarantees Boaz Nadler (joint work with Pini Zilber) Here X ∗ is the true underlying matrix, Ω is the subset of observed entries and PΩ i... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Re-thinking High-dimensional Mathematical Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/25, pp. 1377--1430 |
30,005,135 | OWR-10252933-002 | High-Dimensional Limits of Projection-Pursuit Laws | For $n$ independent standard Gaussian points in $\mathbb R^d$ with $n/d\to\alpha\in(0,\infty)$ and fixed $m$, characterize the set $\mathcal F_{m,\alpha}$ of limiting empirical laws of projections onto $m$-dimensional subspaces. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Re-thinking High-dimensional Mathematical Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/25, pp. 1377--1430](https://doi.org/10.4171/owr/2022/25)
## Literature review (checke... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252933-002",
"literature-status:partially-solved",
"owr-year:2022"
] | High-dimensional projection-pursuit distributions have rigorous asymptotic descriptions and sharp bounds in important regimes, but there is no single general limiting description covering all growth regimes of n and d. | [
{
"url": "https://doi.org/10.48550/arXiv.2206.06526",
"label": "Zhou--Montanari, projection pursuit"
},
{
"url": "https://proceedings.mlr.press/v178/zhou22a.html",
"label": "Published projection-pursuit paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/25 | null | null | null | For $n$ independent standard Gaussian points in $\mathbb R^d$ with $n/d\to\alpha\in(0,\infty)$ and fixed $m$, characterize the set $\mathcal F_{m,\alpha}$ of limiting empirical laws of projections onto $m$-dimensional subspaces. | What does this collection of probability distributions look like when n, d grow large? From high-dimensional projection pursuit to interpolation in neural networks Andrea Montanari (joint work with Kangjie Zhou) Re-thinking High-dimensional Mathematical Statistics 1407 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Re-thinking High-dimensional Mathematical Statistics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/25, pp. 1377--1430 |
30,005,136 | OWR-10252935-002 | Codimension-One Stability of Lorentzian Catenoids | For $2\leq n\leq4$, is the $2n$-parameter family of Lorentzian catenoids codimension-one stable under arbitrary nonsymmetric perturbations in the appropriate weighted $L^2$ topology? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deterministic Dynamics and Randomness in PDE (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/26, pp. 1431--1499](https://doi.org/10.4171/owr/2022/26)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
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"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252935-002",
"literature-status:partially-solved",
"owr-year:2022"
] | Nonlinear asymptotic stability of the Lorentzian catenoid is proved without symmetry for spatial dimensions n at least 3, but the two-dimensional nonradial case and stability for general stationary solutions remain open. | [
{
"url": "https://doi.org/10.1007/s00222-025-01330-3",
"label": "Luehrmann--Oh--Shahshahani, catenoid stability"
},
{
"url": "https://arxiv.org/abs/2411.08366",
"label": "Tang, four-dimensional catenoid"
},
{
"url": "https://doi.org/10.4171/owr/2022/26",
"label": "Oberwolfach report"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/26 | null | null | null | For $2\leq n\leq4$, is the $2n$-parameter family of Lorentzian catenoids codimension-one stable under arbitrary nonsymmetric perturbations in the appropriate weighted $L^2$ topology? | A natural question is the stability of such solutions. 1Translations and Lorentz boosts in the direction of the axis of symmetry, as well as scalings, yield perturbations which are far from the original catenoid at spatial infinity in weighted L2 topologies. 2 n = 2 is analytically the most difficult case, and the meth... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Deterministic Dynamics and Randomness in PDE (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/26, pp. 1431--1499 |
30,005,137 | OWR-10252935-003 | Foundations of Stochastic Quantization | What is stochastic quantisation? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Deterministic Dynamics and Randomness in PDE (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/26, pp. 1431--1499](https://doi.org/10.4171/owr/2022/26)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The phrase is the title of an expository contribution that compares established constructions of stochastic quantization, not a standalone o) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252935-003",
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] | This is a broad definitional question rather than a precise falsifiable conjecture; stochastic quantisation has established constructions, but the extracted record gives no unique proposition whose completion would justify solved. | [
{
"url": "https://doi.org/10.1143/PTPS.111.1",
"label": "Namiki, stochastic quantisation"
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{
"url": "https://doi.org/10.4171/owr/2022/26",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/26 | null | null | null | null | What is stochastic quantisation? The report passage is retained verbatim as the relevant context for this extracted problem. | unrecoverable | The phrase is the title of an expository contribution that compares established constructions of stochastic quantization, not a standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Deterministic Dynamics and Randomness in PDE (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/26, pp. 1431--1499 |
30,005,138 | OWR-10252936-001 | Definition and Scope of Stochastic Quantization | What is stochastic quantisation? I regularly teach a course called “Stochastic Analysis”, in which the students are introduced to the use of stochastic integration and Itô’s formulas to study several problems in probability, including existence, conditioning, uniqueness, convergence of diffusion processes. However it ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550](https://doi.org/10.4171/owr/2022/27)
## Literature review (ch... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
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"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report uses this phrase as the rhetorical title of an expository discussion and does not formulate a single mathematical questi) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252936-001",
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] | This is the same broad definitional question about stochastic quantisation: the method and rigorous examples are established, but the extracted record does not specify a single mathematical claim to mark solved. | [
{
"url": "https://doi.org/10.1143/PTPS.111.1",
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/27 | null | null | null | null | What is stochastic quantisation? I regularly teach a course called “Stochastic Analysis”, in which the students are introduced to the use of stochastic integration and Itô’s formulas to study several problems in probability, including existence, conditioning, uniqueness, convergence of diffusion processes. However it ... | unrecoverable | The official report uses this phrase as the rhetorical title of an expository discussion and does not formulate a single mathematical question with a determinate target. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550 |
30,005,139 | OWR-10252936-002 | Liouville Quantum Gravity Above Central Charge One | Can features of Liouville quantum gravity established for $0<\gamma\leq2$, equivalently for matter central charge $c_M\leq1$, be extended to the phase $1<c_M<25$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550](https://doi.org/10.4171/owr/2022/27)
## Literature review (ch... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252936-002",
"literature-status:partially-solved",
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] | Weak and critical or supercritical LQG metrics have been constructed and uniqueness has been proved across the relevant central-charge range, but extending every feature known in the subcritical regime to cM in (1,25) remains open. | [
{
"url": "https://doi.org/10.1112/plms.12492",
"label": "Ding--Gwynne, LQG metric uniqueness"
},
{
"url": "https://arxiv.org/abs/2104.04020",
"label": "Pfeffer, weak LQG metrics"
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{
"url": "https://doi.org/10.4171/owr/2022/27",
"label": "Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/27 | null | null | null | Can features of Liouville quantum gravity established for $0<\gamma\leq2$, equivalently for matter central charge $c_M\leq1$, be extended to the phase $1<c_M<25$? | Although we can now construct a metric in this phase, it remains an open problem to extend various other features of LQG from the case when \gamma \in (0, 2] (cM \leq 1) to the case when cM \in (1, 25). Universality: Random Matrices, Random Geometry and SPDEs 1523 The Euclidean \phi42 theory as a limit of an interactin... | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550 |
30,005,140 | OWR-10252936-003 | Gaussian-Free-Field Maxima on Percolation Clusters | Consider the discrete Gaussian free field on the infinite cluster of two-dimensional Bernoulli bond percolation with parameter $p>1/2$. Does its centered maximum over a box of side length $N$ converge in distribution as $N\to\infty$ for every $p>1/2$, rather than only for $p$ sufficiently close to $1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550](https://doi.org/10.4171/owr/2022/27)
## Literature review (ch... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
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"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252936-003",
"literature-status:open",
"owr-year:2022"
] | The centered maximum limit for the DGFF on the infinite percolation cluster is proved when p is sufficiently close to one, but the extension to every p greater than one-half remains an open question. | [
{
"url": "https://doi.org/10.1002/cpa.22181",
"label": "Schweiger--Zeitouni, DGFF maximum"
},
{
"url": "https://doi.org/10.4171/owr/2022/27",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/27 | null | null | null | Consider the discrete Gaussian free field on the infinite cluster of two-dimensional Bernoulli bond percolation with parameter $p>1/2$. Does its centered maximum over a box of side length $N$ converge in distribution as $N\to\infty$ for every $p>1/2$, rather than only for $p$ sufficiently close to $1$? | It is an interesting open question whether this result still holds true for any p > 12 . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the complete mathematical target while restoring definitions and removing extraction artifacts or source-dependent wording. | null | null | null | null | null | Universality: Random Matrices, Random Geometry and SPDEs (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/27, pp. 1501--1550 |
30,005,141 | OWR-10252937-003 | Sobolev–Trace Minimizers in All Dimensions | Let $p\in(1,n)$, let $\Omega\subset\mathbb R^n$ be a bounded domain with $C^2$ boundary, and let $\Phi_\Omega(T)$ denote the optimal Sobolev–trace variational problem with prescribed boundary norm $T>0$. Does $\Phi_\Omega(T)$ admit a minimizer for every $T>0$ without the known restriction $n>2p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** partially solved... | 3 | partially_solved | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The all-dimensional extremal-existence question remains unresolved: classical minimizers are proved for C2 domains when n is greater than 2p, while generalized minimizers exist in every dimension and rigidity is known in several restricted regimes. | [
{
"url": "https://doi.org/10.1016/j.aim.2023.109330",
"label": "Maggi--Neumayer--Tomasetti, Sobolev rigidity"
},
{
"url": "https://doi.org/10.4171/owr/2022/28",
"label": "Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Let $p\in(1,n)$, let $\Omega\subset\mathbb R^n$ be a bounded domain with $C^2$ boundary, and let $\Phi_\Omega(T)$ denote the optimal Sobolev–trace variational problem with prescribed boundary norm $T>0$. Does $\Phi_\Omega(T)$ admit a minimizer for every $T>0$ without the known restriction $n>2p$? | Question (B) was posed as an open problem in [10], and the proof of (4) implies the following rigidity criterion: If Ω is connected and ΦΩ (T ) = ΦB (T ) for some ♯ T \in (0, I(B)1/p ), and additionally a minimizer of (2) exists for this T , then Ω is a ball. Open problems. There are quite a few open problems related t... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,142 | OWR-10252937-004 | Yamabe Metrics with Prescribed Boundary Volume Ratio | Can the analysis be refined to produce a one-parameter family $\{g_T\}_{T>0}$ of Yamabe metrics satisfying $\operatorname{vol}(\partial M,g_T)/\operatorname{vol}(M,g_T)=T$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-004",
"literature-status:open",
"owr-year:2022"
] | The report poses the prescribed all-positive volume-ratio family as an unproved refinement question. Standard boundary Yamabe existence and local uniqueness results do not establish this global one-parameter family. | [
{
"url": "https://ems.press/content/serial-article-files/46965",
"label": "OWR report"
},
{
"url": "https://doi.org/10.4310/JDG/1214447805",
"label": "Escobar, The Yamabe problem on manifolds with boundary"
},
{
"url": "https://arxiv.org/abs/0908.4327",
"label": "Brendle--Chen, bound... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Can the analysis be refined to produce a one-parameter family $\{g_T\}_{T>0}$ of Yamabe metrics satisfying $\operatorname{vol}(\partial M,g_T)/\operatorname{vol}(M,g_T)=T$? | Can our analysis in [9] be refined to produce a one-parameter family \{gT \}T >0 of Yamabe metrics with the prescribed ratio vol(\partialM, gu )/vol(M, gu ) = T ? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,143 | OWR-10252937-005 | Dynamical Alekseevskii Conjecture for Homogeneous Ricci Flows | Let $M^n$ be a homogeneous simply connected manifold that is not contractible. Does every homogeneous Ricci-flow solution on $M^n$ have finite extinction time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-005",
"literature-status:open",
"owr-year:2022"
] | The dynamical Alekseevskii conjecture is not proved in the stated full generality. Finite-extinction results cover compact spaces and broad noncompact families, with a separate 2025 proof in dimension five, but not every noncontractible simply-connected homogeneous manifold. | [
{
"url": "https://ems.press/content/serial-article-files/46965",
"label": "OWR report"
},
{
"url": "https://arxiv.org/abs/2507.05097",
"label": "Araujo, finite extinction for a family"
},
{
"url": "https://arxiv.org/abs/2507.17781",
"label": "Billon, dimension five"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Let $M^n$ be a homogeneous simply connected manifold that is not contractible. Does every homogeneous Ricci-flow solution on $M^n$ have finite extinction time? | Conjecture (Dynamical Alekseevskii Conjecture). Let M n be a homogeneous, simply-connected manifold which is not contractible. Then all homogeneous Ricci flow solutions on M n have finite extinction time. It is known that such homogeneous spaces M n admit a homogeneous metric g+ with positive scalar curvature (for each... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,144 | OWR-10252937-007 | CMC Min–Max Width Under Nonnegative Scalar Curvature | Let $(M^3,g)$ be complete, asymptotically flat, without boundary, with nonnegative scalar curvature, and not isometric to $\mathbb R^3$. For $c>0$, is the one-parameter min–max value $\omega_c$ of
$$\mathcal A_c(\Omega)=\operatorname{Area}(\partial\Omega)-c\operatorname{Vol}(\Omega)$$
always less than $16\pi/(3c^2)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-007",
"literature-status:open",
"owr-year:2022"
] | The report records this as a conjecture about existence of a suitable minimal hypersurface under nonnegative scalar curvature. The cited min-max and stable-minimal-surface results give important special cases, but no general proof of the stated condition was found. | [
{
"url": "https://ems.press/content/serial-article-files/46965",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1016/j.aim.2023.109231",
"label": "Bamler--Li--Mantoulidis, PSC decomposition"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Let $(M^3,g)$ be complete, asymptotically flat, without boundary, with nonnegative scalar curvature, and not isometric to $\mathbb R^3$. For $c>0$, is the one-parameter min–max value $\omega_c$ of
$$\mathcal A_c(\Omega)=\operatorname{Area}(\partial\Omega)-c\operatorname{Vol}(\Omega)$$
always less than $16\pi/(3c^2)$? | In particular, we conjecture that (1) holds whenever M has non-negative scalar curvature and is not isometric to Euclidean R3 . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,145 | OWR-10252937-009 | Classification of Ancient Noncollapsed Mean Curvature Flows | Classify ancient noncollapsed mean-curvature flows in higher dimensions without assuming two-convexity. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-009",
"literature-status:open",
"owr-year:2022"
] | Classification without two-convexity remains unresolved in higher dimensions. The 2024 work classifies ancient noncollapsed flows in R4, but explicitly leaves the general higher-dimensional problem as a major challenge. | [
{
"url": "https://arxiv.org/abs/2412.10581",
"label": "Choi--Haslhofer, classification in R4"
},
{
"url": "https://msp.org/gt/2025/29-2/gt-v29-n2-p08-p.pdf",
"label": "Du--Haslhofer, recent higher-dimensional context"
},
{
"url": "https://ems.press/content/serial-article-files/46965",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Classify ancient noncollapsed mean-curvature flows in higher dimensions without assuming two-convexity. | In stark con- trast, the classification of ancient noncollapsed flows in higher dimensions without two-convexity assumption has remained a widely open problem. Classification of noncollapsed translators in R4 Robert Haslhofer (joint work with Kyeongsu Choi, Or Hershkovits) As an important first step towards overcoming ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,146 | OWR-10252937-010 | Stability of Almost-Einstein Metrics | If a manifold $M$ admits a metric $\bar g$ that is almost Einstein in a suitable sense, does there exist an Einstein metric on $M$ close to $\bar g$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** partially solved... | 3 | partially_solved | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-010",
"literature-status:partially-solved",
"owr-year:2022"
] | Stability is proved under strong geometric hypotheses: almost-hyperbolic metrics yield nearby Einstein metrics in dimension three, and effective negatively curved results now cover several higher-dimensional ranges. The unrestricted almost-Einstein question remains open. | [
{
"url": "https://arxiv.org/abs/2206.10438",
"label": "Hamenstadt--Jackel, stability and effective hyperbolization"
},
{
"url": "https://arxiv.org/abs/2502.16692",
"label": "Jackel, effective higher-dimensional stability"
},
{
"url": "https://ems.press/content/serial-article-files/46965"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | If a manifold $M$ admits a metric $\bar g$ that is almost Einstein in a suitable sense, does there exist an Einstein metric on $M$ close to $\bar g$? | Related to the existence question is the question of stability, that is, if a manifold M admits a metric ḡ that is almost Einstein (in a suitable sense), does there exist an Einstein metric on M that is close to ḡ? Stability of Einstein metrics Frieder Jäckel (joint work with Ursula Hamenstädt) (4) For all x \in M ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,147 | OWR-10252937-011 | Surgery Decomposition of Positive Scalar Curvature Manifolds | Can every topologically positive-scalar-curvature $n$-manifold be built from simple topologically positive-scalar-curvature $n$-manifolds by surgeries of codimension at least $3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-011",
"literature-status:open",
"owr-year:2022"
] | The general all-dimensional surgery-decomposition question remains open. Bamler, Li, and Mantoulidis prove a substantial four-dimensional analogue, not the asserted statement for all n. | [
{
"url": "https://doi.org/10.1016/j.aim.2023.109231",
"label": "Bamler--Li--Mantoulidis, PSC decomposition"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870823003742",
"label": "published article and stated Question 1.2"
},
{
"url": "https://ems.press/content/seria... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Can every topologically positive-scalar-curvature $n$-manifold be built from simple topologically positive-scalar-curvature $n$-manifolds by surgeries of codimension at least $3$? | Can all topologically PSC n-manifolds be built out of “simple” topo- logically PSC n-manifolds by performing codimension \geq 3 surgeries? Decomposing 4-manifolds with positive scalar curvature Christos Mantoulidis (joint work with Richard H. Bamler, Chao Li) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,148 | OWR-10252937-012 | Orbifold Surgery Models for Positive Scalar Curvature Four Manifolds | Can a closed oriented topologically positive-scalar-curvature $4$-manifold $M$ be obtained from a topologically positive-scalar-curvature $4$-orbifold $M'$ with isolated singularities and finite orbifold fundamental group on each component by performing $0$- and $1$-surgeries? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601](https://doi.org/10.4171/owr/2022/28)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252937-012",
"literature-status:open",
"owr-year:2022"
] | The exact four-dimensional finite-orbifold-fundamental-group refinement was posed as Question 1.7 by Bamler, Li, and Mantoulidis and is not answered by their theorem, which gives only vanishing first Betti number and a second-Betti bound. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870823003742",
"label": "Bamler--Li--Mantoulidis, published article"
},
{
"url": "https://ems.press/content/serial-article-files/46965",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/28 | null | null | null | Can a closed oriented topologically positive-scalar-curvature $4$-manifold $M$ be obtained from a topologically positive-scalar-curvature $4$-orbifold $M'$ with isolated singularities and finite orbifold fundamental group on each component by performing $0$- and $1$-surgeries? | Can one obtain M from a closed, oriented, topologically PSC 4-orbifold M ′ with isolated singularities and the property that each component has finite orbifold fundamental group \pi1orb (M ′ ) by performing 0- and 1-surgeries? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Geometrie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/28, pp. 1551--1601 |
30,005,149 | OWR-10252938-001 | Hilbert Complexes in Numerical Partial Differential Equations | How did Hilbert complexes come to play a major role in numerical partial differential equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Complexes: Analysis, Applications, and Discretizations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/29, pp. 1603--1659](https://doi.org/10.4171/owr/2022/29)
## Literature revi... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252938-001",
"literature-status:open",
"owr-year:2022"
] | This is an open-ended foundational question rather than a determinate theorem. Hilbert-complex methods are well established in numerical PDE, but the extracted question asks for a broader conceptual account with no single resolved answer. | [
{
"url": "https://ems.press/content/serial-article-files/46966",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1137/1.9781611975543",
"label": "Arnold--Falk--Winther, finite element exterior calculus"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/29 | null | null | null | How did Hilbert complexes come to play a major role in numerical partial differential equations? | What are complexes doing in numerical PDE? As an introduction to the workshop “Hilbert Complexes: Analysis, Applications, and Discretizations,” held in June 2022 at Oberwolfach, this talk began with the question: How did Hilbert complexes, mathematical objects which at first consideration may seem to be very distant fr... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hilbert Complexes: Analysis, Applications, and Discretizations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/29, pp. 1603--1659 |
30,005,150 | OWR-10252938-003 | Combinatorial Models of Discrete Vector Bundle Geometry | What might a combinatorial model of discrete vector bundles with connection and curvature look like? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Hilbert Complexes: Analysis, Applications, and Discretizations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/29, pp. 1603--1659](https://doi.org/10.4171/owr/2022/29)
## Literature revi... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252938-003",
"literature-status:partially-solved",
"owr-year:2022"
] | A concrete combinatorial theory now exists: discrete vector-bundle-valued cochains, covariant exterior derivatives, wedge products, curvature, and a discrete Bianchi identity have been constructed. A complete combinatorial replacement of all smooth machinery remains broader than this result. | [
{
"url": "https://arxiv.org/abs/2104.10277",
"label": "Berwick-Evans--Hirani--Schubel, discrete vector bundles"
},
{
"url": "https://doi.org/10.1007/s10208-022-09555-x",
"label": "finite element systems for vector bundles"
},
{
"url": "https://ems.press/content/serial-article-files/46966... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/29 | null | null | null | What might a combinatorial model of discrete vector bundles with connection and curvature look like? | What might a combinatorial version of this machinery look like? Discrete Vector Bundles with Connection and Curvature Anil N. Hirani (joint work with Daniel Berwick-Evans, Mark Schubel) Hilbert Complexes: Analysis, Applications, and Discretizations 1647 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Hilbert Complexes: Analysis, Applications, and Discretizations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/29, pp. 1603--1659 |
30,005,151 | OWR-10252939-001 | Blowup and Weak Soliton Resolution for Calogero–Moser DNLS | For general solutions of the Calogero–Moser derivative nonlinear Schrödinger equation, determine whether finite-time blowup can occur and whether weak soliton resolution holds. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730](https://doi.org/10.4171/owr/2022/30)
## Literature review (checked 2026-08-22... | 3 | solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2404.09603",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes to both; accepted, not yet published)**. P. Gérard (joint with E. Lenzmann; OWR 30/2022, p. 1667) asks whether general solutions of the Calogero–Moser derivative NLS in the Hardy space can blow up in finite time and whether weak soliton resolution can be expec... | [
"owr",
"oberwolfach-reports",
"OWR-10252939-001",
"literature-status:open",
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] | For the Calogero--Moser DNLS equation, the report identifies general long-time behavior, possible finite-time blow-up, and weak soliton resolution as work in progress; no later source located settles these general questions. | [
{
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/30 | null | null | null | For general solutions of the Calogero–Moser derivative nonlinear Schrödinger equation, determine whether finite-time blowup can occur and whether weak soliton resolution holds. | Let us conclude with some perspectives. • The first natural open question is the long time behaviour for general solutions. Can finite time blow up occur ? Can one expect weak soliton resolution? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730 |
30,005,152 | OWR-10252939-003 | Scattering for One-Dimensional Cubic Defocusing Flows | Prove that every one-dimensional dispersive flow with cubic defocusing nonlinearity and sufficiently small, not necessarily localized, initial data has a global scattering solution. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730](https://doi.org/10.4171/owr/2022/30)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252939-003",
"literature-status:partially-solved",
"owr-year:2022"
] | Global existence and scattering are proved for several one-dimensional cubic defocusing dispersive classes, including semilinear and quasilinear Schrödinger flows and broader dispersion relations, but the broad statement for all such flows is not fully proved. | [
{
"url": "https://doi.org/10.1017/fmp.2023.30",
"label": "Ifrim--Tataru, Part I"
},
{
"url": "https://arxiv.org/abs/2410.10052",
"label": "Ifrim--Tataru, Part IV"
},
{
"url": "https://ems.press/content/serial-article-files/46968",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/30 | null | null | null | Prove that every one-dimensional dispersive flow with cubic defocusing nonlinearity and sufficiently small, not necessarily localized, initial data has a global scattering solution. | The question of obtaining scattering, global in time solu- tions for such problems has attracted a lot of attention in recent years, and many global well-posedness results have been proved for a number of models under the assumption that the initial data is both small and localized. Global solutions for 1D cubic defocu... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730 |
30,005,153 | OWR-10252939-004 | Asymptotic Stability of the $\phi^4$ Kink | Establish full asymptotic stability of the $\phi^4$ kink under odd perturbations, including control of the quadratic source term created by the internal mode. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730](https://doi.org/10.4171/owr/2022/30)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-10252939-004",
"literature-status:partially-solved",
"owr-year:2022"
] | Asymptotic stability of the classical phi-four kink is proved for odd perturbations in the energy space, while the full asymptotic-stability problem for general perturbations remains unresolved. | [
{
"url": "https://arxiv.org/abs/1506.07420",
"label": "Kowalczyk--Martel--Munoz, odd perturbations"
},
{
"url": "https://arxiv.org/abs/2203.04143",
"label": "Kowalczyk--Martel, odd kink dynamics"
},
{
"url": "https://ems.press/content/serial-article-files/46968",
"label": "OWR report... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/30 | null | null | null | Establish full asymptotic stability of the $\phi^4$ kink under odd perturbations, including control of the quadratic source term created by the internal mode. | It is the main challenge towards establishing a full asymptotic stability result for odd perturbations of the \phi4 kink, which remains a major open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Nonlinear Waves and Dispersive Equations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/30, pp. 1661--1730 |
30,005,154 | OWR-11101912-001 | Boundedness of Multilinear Hilbert Transforms | For $n\geq3$, establish the conjectured $L^p$ boundedness of the $n$-linear Hilbert transform; more generally, establish boundedness of the simplex Hilbert transform. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-001",
"literature-status:open",
"owr-year:2022"
] | The multilinear and simplex Hilbert transforms beyond the bilinear case remain major open boundedness problems. Existing work proves cancellation and special structured estimates, not the requested general Lp boundedness. | [
{
"url": "https://arxiv.org/abs/1505.06479",
"label": "Tao, cancellation for the multilinear Hilbert transform"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0001870821003029",
"label": "Durcik--Roos, trilinear smoothing and open problems"
},
{
"url": "https://ems.p... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For $n\geq3$, establish the conjectured $L^p$ boundedness of the $n$-linear Hilbert transform; more generally, establish boundedness of the simplex Hilbert transform. | Its boundedness is one of the major open problems in harmonic analysis. On the other hand, the multilinear Hilbert transform in the case n \geq 3 is another major open problem. where on the left-hand side, Π : Rm \to Rk is a surjective linear map and the con- stant C is independent of the test functions Fj . The consta... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,155 | OWR-11101912-002 | Fractal Schrödinger Convergence Above Half Dimension | For $d/2<\alpha\leq d$, determine the sharp exponent $s(\alpha)$ such that every $f\in H^s(\mathbb R^d)$ satisfies $e^{it\Delta}f(x)\to f(x)$ as $t\to0$ for $\mathcal H^\alpha$-almost every $x$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-002",
"literature-status:open",
"owr-year:2022"
] | For fractal Schrödinger convergence, the critical exponent is known for alpha at most n over 2, while the range alpha greater than n over 2 remains open; 2025 work confirms this status while improving bounds and counterexamples. | [
{
"url": "https://doi.org/10.1007/s00041-025-10162-x",
"label": "Cho--Eceizabarrena, sequential Schrödinger convergence"
},
{
"url": "https://arxiv.org/abs/2101.02495",
"label": "Lucà--Ponce-Vanegas, convergence over fractals"
},
{
"url": "https://ems.press/content/serial-article-files/4... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For $d/2<\alpha\leq d$, determine the sharp exponent $s(\alpha)$ such that every $f\in H^s(\mathbb R^d)$ satisfies $e^{it\Delta}f(x)\to f(x)$ as $t\to0$ for $\mathcal H^\alpha$-almost every $x$. | Thus, to give a fractal counterexample, one of the main challenges is to com- pute the Hausdorff dimension of these sets. It is well known that computing the Hausdorff dimension of a particular given set is often a difficult task. To deal with this problem, we use the Mass Transference Principle introduced by Beresnevi... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,156 | OWR-11101912-003 | Uniform Bounds for Two-Dimensional Bilinear Hilbert Transforms | Can one obtain uniform bounds for the forms associated with the entire family of two-dimensional bilinear Hilbert transforms? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-003",
"literature-status:open",
"owr-year:2022"
] | Uniform Lp bounds for the whole two-dimensional bilinear Hilbert-transform family remain open. Uniform estimates are known for important subfamilies, including the complex bilinear Hilbert transforms and a local L2 range. | [
{
"url": "https://ems.press/content/serial-article-files/46969",
"label": "OWR report"
},
{
"url": "https://doi.org/10.1353/ajm.0.0101",
"label": "Demeter--Thiele, two-dimensional bilinear Hilbert transform"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | Can one obtain uniform bounds for the forms associated with the entire family of two-dimensional bilinear Hilbert transforms? | The question about uniform bounds for the forms associated with the whole family of 2D-BHTs remains a difficult open problem. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,157 | OWR-11101912-004 | Uniform Intermediate-Norm Square-Function Estimates | For the moment curve in dimension two, let $E$ be the Fourier extension operator and let $\mathcal I(\delta)$ partition the parameter interval into intervals of length $\delta$. Does there exist some $2<p<4$ and a constant $C_p$, independent of $\delta$, such that
$$\|Ef\|_{L^p(B_{\delta^{-2}})}\leq C_p\left\|\left(\s... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
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"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-004",
"literature-status:open",
"owr-year:2022"
] | The extracted open problem asks for a genuinely uniform square-function estimate in an intermediate Lp range. The report records only logarithmic-loss alternatives, and no source located removes that loss. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/4013/OWR_2022_31.pdf?sequence=4",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For the moment curve in dimension two, let $E$ be the Fourier extension operator and let $\mathcal I(\delta)$ partition the parameter interval into intervals of length $\delta$. Does there exist some $2<p<4$ and a constant $C_p$, independent of $\delta$, such that
$$\|Ef\|_{L^p(B_{\delta^{-2}})}\leq C_p\left\|\left(\s... | Open Problem. Real Analysis, Harmonic Analysis and Applications 1767 holds for all 2 \leq p \leq 4. Alternative methods can be used to prove (5) for 2 \leq p \leq 4, but these arguments come with logarithmic losses in the \delta parameter. It would be interesting to establish (5) for some value of 2 < p < 4 with Cp tru... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,158 | OWR-11101912-006 | Foschi Maximizers for Wave Strichartz Inequalities | For every spatial dimension $d\geq2$, does the wave-equation initial datum
$$(u_0,\dot u_0)=\bigl((1+|x|^2)^{-(d-1)/2},0\bigr)$$
maximize the sharp Strichartz inequality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-006",
"literature-status:partially-solved",
"owr-year:2022"
] | The generalized cone adjoint-restriction maximizer question has sharp global answers in low dimensions and local-maximizer results in broad dimensions, but the full global conjecture remains unresolved. | [
{
"url": "https://doi.org/10.1112/jlms.70112",
"label": "Negro, exponentials rarely maximize cone extension"
},
{
"url": "https://arxiv.org/abs/2003.11955",
"label": "Goncalves--Negro, local maximizers"
},
{
"url": "https://ems.press/content/serial-article-files/46969",
"label": "OWR... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For every spatial dimension $d\geq2$, does the wave-equation initial datum
$$(u_0,\dot u_0)=\bigl((1+|x|^2)^{-(d-1)/2},0\bigr)$$
maximize the sharp Strichartz inequality? | In the next section, we will observe that (1) is intimately connected to a more general family of estimates, known as the Fourier adjoint restriction estimates on the cone, and extend the conjecture of Foschi to this general setting. 2. The Fourier adjoint restriction estimates Consider the measure µ+ := \delta(\tau 2 ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,159 | OWR-11101912-007 | Exponential Maximizers for Cone Adjoint Restriction | For each $d\geq4$, is $f_\star(\tau,\xi)=e^{-|\tau|}$ a global maximizer of the $p=2$ Fourier adjoint-restriction inequality on the one-sheeted cone $K_d^+=\{(\tau,\xi):\tau=|\xi|\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-007",
"literature-status:partially-solved",
"owr-year:2022"
] | The exponential profile is a global maximizer for the one-sheeted cone in dimensions two and three, is only locally maximizing in several higher dimensions, and can fail even to be critical in other dimensions; the dimension-free question therefore has no single affirmative answer. | [
{
"url": "https://doi.org/10.1112/jlms.70112",
"label": "Negro, cone extension maximizers"
},
{
"url": "https://arxiv.org/abs/2003.11955",
"label": "Goncalves--Negro, local maximizers"
},
{
"url": "https://ems.press/content/serial-article-files/46969",
"label": "OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For each $d\geq4$, is $f_\star(\tau,\xi)=e^{-|\tau|}$ a global maximizer of the $p=2$ Fourier adjoint-restriction inequality on the one-sheeted cone $K_d^+=\{(\tau,\xi):\tau=|\xi|\}$? | Is f⋆ (\tau, ξ) = exp(−|\tau |) a maximizer for the Fourier adjoint restriction estimate (2) with p = 2? Theorem 2 ([2, 3, 4]). Let p = 2. The function f⋆ is a maximizer for (2) on Kd+ for d = 2, 3. It is a local maximizer for d \geq 3. The function f⋆ is a maximizer for (2) on Kd for d = 3. It is a local maximizer for... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,160 | OWR-11101912-009 | Strict Majorant Properties at Fixed Noneven Exponents | For $p\notin 2\mathbb{N}$, which sets $\Gamma\subset\mathbb{Z}^d$ satisfy the strict majorant property on $L^p([0,1]^d)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-009",
"literature-status:partially-solved",
"owr-year:2022"
] | The all-exponent classification is solved: strict majorant property for every p holds exactly for affinely independent frequency sets, and broad counterexample families are known for non-even p. A complete characterization for each fixed non-even p and arbitrary Gamma is not supplied by that theorem. | [
{
"url": "https://doi.org/10.1093/qmath/haac021",
"label": "Gressman--Guo--Pierce--Roos--Yung, strict majorant property"
},
{
"url": "https://arxiv.org/abs/2106.12538",
"label": "same primary paper"
},
{
"url": "https://ems.press/content/serial-article-files/46969",
"label": "OWR rep... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For $p\notin 2\mathbb{N}$, which sets $\Gamma\subset\mathbb{Z}^d$ satisfy the strict majorant property on $L^p([0,1]^d)$? | When p 6\in 2N, for which Γ is it true? In this talk we introduced the systematic study of strict majorant properties in arbitrarily high dimensions. Let Γ \subset Zd be a fixed set of d-tuples of integers. We say that Γ satisfies the strict majorant property on Lp ([0, 1]d ) if for all choices of real coefficients (an... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,161 | OWR-11101912-010 | Random Set Methods for Harmonic Analysis Estimates | Let $B_p(\Gamma)$ be the least correction factor in the weak $L^p([0,1]^d)$ majorant inequality for frequencies in $\Gamma\subset[1,N]^d$. For which sets $\Gamma$ does $B_p(\Gamma)\ll N^\varepsilon$ hold for every $\varepsilon>0$, and can random-set methods be adapted to prove such estimates? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-010",
"literature-status:open",
"owr-year:2022"
] | The Oberwolfach report poses adaptation of the Mockenhaupt--Schlag random-set method as a question; no authoritative source located by the cutoff establishes such an adaptation in this setting. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | Let $B_p(\Gamma)$ be the least correction factor in the weak $L^p([0,1]^d)$ majorant inequality for frequencies in $\Gamma\subset[1,N]^d$. For which sets $\Gamma$ does $B_p(\Gamma)\ll N^\varepsilon$ hold for every $\varepsilon>0$, and can random-set methods be adapted to prove such estimates? | Can the methods of [MS09] be adapted to this setting? Real Analysis, Harmonic Analysis and Applications 1781 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,162 | OWR-11101912-011 | Determining Improving Regions from Assouad Spectra | For a given set $E$, can the improving region $T_E$ be determined from the Assouad spectrum of $E$ and its subsets? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-011",
"literature-status:partially-solved",
"owr-year:2022"
] | Roos--Seeger characterize the relevant improving region and solve broad classes, but the exact general determination of T_E, especially boundary cases, remains incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
},
{
"url": "https://arxiv.org/abs/2004.00984",
"label": "Roos--Seeger, Spherical maximal functions and fractal dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For a given set $E$, can the improving region $T_E$ be determined from the Assouad spectrum of $E$ and its subsets? | An interesting open problem is to determine whether and how for any given E, the set TE can be determined from the Assouad spectrum of E and subsets of E. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,163 | OWR-11101912-012 | Fourier Restriction Conjecture in Higher Dimensions | Does the Fourier restriction conjecture hold in every dimension $d\geq 3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-012",
"literature-status:open",
"owr-year:2022"
] | The report explicitly states that the restriction conjecture remains open for d\geq3; later work gives advances but not a proof of the conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | Does the Fourier restriction conjecture hold in every dimension $d\geq 3$? | Despite the great deal of attention that this circle of problems has received during the past four decades, the restriction conjecture remains open in dimensions d \geq 3. Real Analysis, Harmonic Analysis and Applications 1785 2. Two simple case studies In this section, we discuss the sharp form of two simple inequalit... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,164 | OWR-11101912-013 | Endpoint Spectral-Cluster Improvements on Product Manifolds | For an arbitrary $d$-dimensional product manifold $M=X\times Y$, do the logarithmically improved spectral-cluster bounds with window width $\varepsilon(\lambda)=(\log\lambda)^{-1}$ extend to the endpoint $q_d=2(d+1)/(d-1)$ and to the range $2<q<q_d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-013",
"literature-status:open",
"owr-year:2022"
] | The report records logarithmic improvements above q_d but leaves improvements at q=q_d and 2<q<q_d open; no later source located closes these ranges. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
},
{
"url": "https://doi.org/10.1007/s00222-023-01178-5",
"label": "Canzani--Galkowski, Weyl remainders"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | For an arbitrary $d$-dimensional product manifold $M=X\times Y$, do the logarithmically improved spectral-cluster bounds with window width $\varepsilon(\lambda)=(\log\lambda)^{-1}$ extend to the endpoint $q_d=2(d+1)/(d-1)$ and to the range $2<q<q_d$? | Improvements for q = qd or 2 < q < qd remain open in this case, though. Real Analysis, Harmonic Analysis and Applications 1791 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,165 | OWR-11101912-014 | Scattering for General Cubic Defocusing Dispersive Flows | Do one-dimensional dispersive flows with cubic defocusing nonlinearities and small initial data have global-in-time scattering solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-014",
"literature-status:partially-solved",
"owr-year:2022"
] | Ifrim--Tataru prove global scattering for a broad small-data nonlocalized class, and Part IV enlarges the dispersion class, but the broad question is not settled for every one-dimensional cubic defocusing flow. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
},
{
"url": "https://doi.org/10.1017/fmp.2023.30",
"label": "Ifrim--Tataru, Global solutions, Part I"
},
{
"url": "https://arxiv.org/abs/2410.10052",
"label": "Ifrim--Tataru, Global solutions, Part ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | Do one-dimensional dispersive flows with cubic defocusing nonlinearities and small initial data have global-in-time scattering solutions? | The question of obtaining scattering, global in time solu- tions for such problems has attracted a lot of attention in recent years, and many global well-posedness results have been proved for a number of models under the assumption that the initial data is both small and localized. Global solutions for 1D cubic defocu... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,166 | OWR-11101912-015 | Global Scattering for Cubic Defocusing Dispersive Flows | Do one-dimensional dispersive flows with cubic defocusing nonlinearities and small, not necessarily localized, initial data have global-in-time scattering solutions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803](https://doi.org/10.4171/owr/2022/31)
## Literature review (checked 2... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101912-015",
"literature-status:partially-solved",
"owr-year:2022"
] | The conjecture is proved for semilinear and quasilinear Schrödinger classes and broader dispersion classes, but not for all one-dimensional cubic defocusing flows. | [
{
"url": "https://doi.org/10.4171/owr/2022/31",
"label": "Oberwolfach Report 31/2022"
},
{
"url": "https://doi.org/10.1017/fmp.2023.30",
"label": "Ifrim--Tataru, Global solutions, Part I"
},
{
"url": "https://doi.org/10.1007/s00222-025-01356-7",
"label": "Ifrim--Tataru, Global soluti... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/31 | null | null | null | Do one-dimensional dispersive flows with cubic defocusing nonlinearities and small, not necessarily localized, initial data have global-in-time scattering solutions? | Conjecture 1. One dimensional dispersive flows with cubic defocusing nonlin- earities and small initial data have global in time, scattering solutions. Our objective is to prove the first global in time well-posedness result of this type, assuming a Schrödinger type dispersion relation and a cubic nonlinearity with a ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Real Analysis, Harmonic Analysis and Applications (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/31, pp. 1743--1803 |
30,005,167 | OWR-11101913-001 | Holomorphic Anomaly Equations for Elliptic Threefolds | For an elliptically fibered threefold $\pi:X\to B$ satisfying $c_3(T_X\otimes\omega_X)=0$, do its normalized relative Pandharipande–Thomas descendant series satisfy the two Oberdieck–Schimpf holomorphic anomaly equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-001",
"literature-status:partially-solved",
"owr-year:2022"
] | The elliptic-threefold quasi-Jacobi and anomaly conjectures are proved in special geometries and equivariant or reduced theories, while the general conjectures remain unproved. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://arxiv.org/abs/2308.09652",
"label": "Oberdieck--Schimpf, PT theory of elliptic threefolds"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | For an elliptically fibered threefold $\pi:X\to B$ satisfying $c_3(T_X\otimes\omega_X)=0$, do its normalized relative Pandharipande–Thomas descendant series satisfy the two Oberdieck–Schimpf holomorphic anomaly equations? | where \alpha runs over all decompositions \beta = \beta1 + . . . \betak into effective classes \betai \in H2 (B, Z) which are of divisibility div(\betai ) in H2 (B, Z), and ϕ\alpha \in QJac. Moreover, e k (\gamma) = chk (\gamma) + 1 chk−2 (\gamma \cdot c2 (TX )) • ch 24 • wt = grading Q by eigenvalues of [W, \pi ∗ \pi∗... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,168 | OWR-11101913-002 | Iitaka Subadditivity Conjecture for Kodaira Dimension | For an algebraic fiber space $f:X\to Y$ with smooth projective complex varieties and general fiber $F$, is $\kappa(X)\geq\kappa(F)+\kappa(Y)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-11101913-003"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-002",
"literature-status:partially-solved",
"owr-year:2022"
] | Iitaka's subadditivity conjecture remains open in general, although substantial cases are proved, including bases of general type, curves, abelian varieties, and maximal Albanese dimension. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://people.math.harvard.edu/~mpopa/papers/kodaira.pdf",
"label": "Popa, Conjectures on the Kodaira dimension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | For an algebraic fiber space $f:X\to Y$ with smooth projective complex varieties and general fiber $F$, is $\kappa(X)\geq\kappa(F)+\kappa(Y)$? | The talk was devoted to a series of “superadditivity” conjectures on the behavior of the Kodaira dimension of fibrations, made recently in [2], and complementing Iitaka’s well-known subadditivity conjecture. Let f : X \to Y be an algebraic fiber space (i.e. a surjective morphism with con- nected fibers), with X and Y s... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,169 | OWR-11101913-003 | Known Cases of Iitaka Subadditivity | This conjecture is known in various important cases: when F is a variety of general type (Kollár) or more generally one that admits a good minimal model (Kawamata), when Y is of general type (Viehweg) or a curve (Kawamata), and more recently when Y is an abelian variety (Cao-Păun), a variety of maximal Albanese dimen... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (The official report confirms that this passage lists established cases of Iitaka subadditivity and does not pose a separate open problem; th) | [
"OWR-11101913-002"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The listed cases are established by the cited literature, but they cover only subclasses; the general subadditivity conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://people.math.harvard.edu/~mpopa/papers/kodaira.pdf",
"label": "Popa, Conjectures on the Kodaira dimension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | null | This conjecture is known in various important cases: when F is a variety of general type (Kollár) or more generally one that admits a good minimal model (Kawamata), when Y is of general type (Viehweg) or a curve (Kawamata), and more recently when Y is an abelian variety (Cao-Păun), a variety of maximal Albanese dimen... | unrecoverable | The official report confirms that this passage lists established cases of Iitaka subadditivity and does not pose a separate open problem; the underlying conjecture is represented by OWR-11101913-002. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,170 | OWR-11101913-004 | Methods for Kodaira-Dimension Superadditivity | and [4] rely on Hodge module techniques considered in [3], as well as on previous methods developed by Kovács and Viehweg-Zuo among others, for the study of hyperbolicity. Moreover, when the base Y has Kodaira dimension 0, analytic tech- niques (in the sense of singular metrics on direct images of pluricanonical bundl... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that this extraction is commentary on methods and known cases rather than a self-contained open problem. No sep) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-004",
"literature-status:partially-solved",
"owr-year:2022"
] | Further cases of the superadditivity conjectures are proved, and some are implied by MMP conjectures, but the general statements are not known. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://people.math.harvard.edu/~mpopa/papers/kodaira.pdf",
"label": "Popa, Conjectures on the Kodaira dimension"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | null | and [4] rely on Hodge module techniques considered in [3], as well as on previous methods developed by Kovács and Viehweg-Zuo among others, for the study of hyperbolicity. Moreover, when the base Y has Kodaira dimension 0, analytic tech- niques (in the sense of singular metrics on direct images of pluricanonical bundl... | unrecoverable | The official report confirms that this extraction is commentary on methods and known cases rather than a self-contained open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,171 | OWR-11101913-005 | Stable Limits of Smooth Plane Curves | Is every smooth limit of a family of plane curves of prime degree a Cartier divisor in a log-terminal $\mathbb Q$-Gorenstein degeneration of $\mathbb P^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-005",
"literature-status:partially-solved",
"owr-year:2022"
] | The plane-curve conjecture is only partially confirmed: nonplanar smooth limits occur in Markov prime degrees, while the claimed general classification remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://doi.org/10.5802/jep.263",
"label": "DeVleming--Stapleton, Smooth limits of plane curves"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | Is every smooth limit of a family of plane curves of prime degree a Cartier divisor in a log-terminal $\mathbb Q$-Gorenstein degeneration of $\mathbb P^2$? | Motivated by this construction and general results from moduli of stable pairs compactifying the space of pairs (P2 , C), we conjecture the following: Conjecture B. This has been proven for the primes 2 [11, 6, 4], 3 [7], and 5 [3] in all dimensions, and for the prime 7 in dimension 3 [3]. Interestingly, the statement ... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,172 | OWR-11101913-006 | Global Weinstein Splitting for Poisson Manifolds | Under what conditions does a Poisson manifold $X$ decompose globally, perhaps after passing to a suitable covering space, as a product of Poisson manifolds with a symplectic leaf as one factor? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-006",
"literature-status:open",
"owr-year:2022"
] | The compact Kähler Poisson problem reduces to compact leaves that are finite étale quotients of tori; the infinite-fundamental-group case is left open. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | Under what conditions does a Poisson manifold $X$ decompose globally, perhaps after passing to a suitable covering space, as a product of Poisson manifolds with a symplectic leaf as one factor? | A natural question is then the following. Moduli Spaces, Birational Geometry and Derived Aspects 1825 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,173 | OWR-11101913-007 | Kähler Poisson Manifolds with Infinite-Fundamental-Group Leaves | Describe compact Kähler Poisson manifolds having a compact leaf with infinite fundamental group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-007",
"literature-status:open",
"owr-year:2022"
] | This is the report's remaining Problem 6: describing compact Kähler Poisson manifolds with a compact leaf of infinite fundamental group is unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | Describe compact Kähler Poisson manifolds having a compact leaf with infinite fundamental group. | Recall that a map \phi : (X, \piX ) \to (Y, \piY ) is a Poisson morphism if \phi∗ \{f, g\}Y = \{\phi∗ f, \phi∗ g\} for any (local) holomorphic functions f and g. Corollary 4. Let (X, \pi) be a compact Kähler Poisson manifold with h2,0 (X) = 0. If L \subseteq X is a compact leaf of \pi, then L is a point. Remark 5. The... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,174 | OWR-11101913-008 | Kontsevich–Soibelman Conjecture for Calabi–Yau Degenerations | For a Calabi–Yau degeneration, do the base of the SYZ fibration and the essential skeleton coincide as metric integral-affine manifolds away from their singular loci? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-008",
"literature-status:partially-solved",
"owr-year:2022"
] | For quintic threefolds, Mazzon--Pille-Schneider construct retractions and match integral-affine structures, providing evidence but not a proof of the full Kontsevich--Soibelman conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://arxiv.org/abs/2110.04223",
"label": "Mazzon--Pille-Schneider, Toric geometry and integral affine structures"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | For a Calabi–Yau degeneration, do the base of the SYZ fibration and the essential skeleton coincide as metric integral-affine manifolds away from their singular loci? | conjecture. Indeed, Theorem 2. [11, Theorem 6.1] Let X be a minimal dlt model of X. The retraction ρX : X an \to Sk(X) is an n-dimensional affinoid torus fibration away from the union Z of the simplices in Sk(X) of codimension \geq 2. The condition of being an affinoid torus fibration can be seen as the non- archimedea... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,175 | OWR-11101913-009 | Mumford–Tate Conjectures for Gushel–Mukai Varieties | Do the Mumford–Tate, motivated Mumford–Tate, Hodge, and Tate conjectures hold for Gushel–Mukai varieties and their generalized partners or duals? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-009",
"literature-status:partially-solved",
"owr-year:2022"
] | Fu--Moonen prove the motivated Mumford--Tate and generalized Tate statements for even-dimensional Gushel--Mukai varieties; the odd-dimensional and broader claims in the excerpt remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
},
{
"url": "https://arxiv.org/abs/2207.01118",
"label": "Fu--Moonen, Algebraic cycles on Gushel--Mukai varieties"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | Do the Mumford–Tate, motivated Mumford–Tate, Hodge, and Tate conjectures hold for Gushel–Mukai varieties and their generalized partners or duals? | identity component of the Zariski closure of the image of the Galois rep- resentation is identified with the Mumford–Tate group tensored with Qℓ . • that their André motives (as is defined in [1]) are abelian. This in fact leads to a stronger result known as the motivated Mumford–Tate conjec- ture, saying that the mot... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,176 | OWR-11101913-014 | Uniform Torsion Bounds for Chow Groups in Families | For a family $\pi:X\to S$ and a degree bound $d$, does there exist a positive integer $C$, depending only on $\pi$ and $d$, such that $C\,\operatorname{CH}^i(X_s)_{\mathrm{tors}}=0$ for every number field $k/\mathbb{Q}$ of degree at most $d$, every $i>0$, and every $k$-point $s\in S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864](https://doi.org/10.4171/owr/2022/32)
## Lit... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101913-014",
"literature-status:open",
"owr-year:2022"
] | The report gives a boundedness theorem only under additional hypotheses and recalls possible unbounded 2-torsion in families; the stated uniform Chow-torsion bound remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/32",
"label": "Oberwolfach Report 32/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/32 | null | null | null | For a family $\pi:X\to S$ and a degree bound $d$, does there exist a positive integer $C$, depending only on $\pi$ and $d$, such that $C\,\operatorname{CH}^i(X_s)_{\mathrm{tors}}=0$ for every number field $k/\mathbb{Q}$ of degree at most $d$, every $i>0$, and every $k$-point $s\in S$? | The question of finding uniform bounds – when considering cubic surfaces for instance – has been considered in various forms by Manin and has a negative an- swer in general: even in one-parameter families, results of Colliot-Thélène-Sansuc- Swinnerton-Dyer imply that the 2-torsion part of the Chow group of codimensio... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Geometry: Moduli Spaces, Birational Geometry and Derived Aspects (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/32, pp. 1805--1864 |
30,005,177 | OWR-11101914-001 | Conformal Invariance of Interacting Long-Range Fermionic Models | Prove conformal invariance of the non-Gaussian renormalization-group fixed point for long-range fermionic models with symplectic symmetry. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Renormalization Group (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/33, pp. 1865--1925](https://doi.org/10.4171/owr/2022/33)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101914-001",
"literature-status:open",
"owr-year:2022"
] | The rigorous fixed point is constructed, but conformal invariance is explicitly left as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2022/33",
"label": "Oberwolfach Report 33/2022"
},
{
"url": "https://arxiv.org/abs/2008.04361",
"label": "Giuliani--Mastropietro--Rychkov, rigorous fermionic RG"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/33 | null | null | null | Prove conformal invariance of the non-Gaussian renormalization-group fixed point for long-range fermionic models with symplectic symmetry. | Conformal invariance is also expected and is an interesting open problem. These models are characterized, in physics jargon, by the action: Z (1) S(\psi) = dd xΩab \psia (−∆)\sigma \psib + V(\psi) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | The Renormalization Group (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/33, pp. 1865--1925 |
30,005,178 | OWR-11101914-002 | Euclidean Extension of Hierarchical Susceptibility Asymptotics | Extend the universal finite-size susceptibility-scaling asymptotics for the four-dimensional hierarchical $|\phi|^4$ model to the Euclidean model with periodic boundary conditions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [The Renormalization Group (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/33, pp. 1865--1925](https://doi.org/10.4171/owr/2022/33)
## Literature review (checked 2026-08-22)
**Status:** ... | 3 | open | null | 2,022 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101914-002",
"literature-status:open",
"owr-year:2022"
] | The hierarchical-model susceptibility result is not extended to the Euclidean model with periodic boundary conditions; the report explicitly leaves this as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/33",
"label": "Oberwolfach Report 33/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/33 | null | null | null | Extend the universal finite-size susceptibility-scaling asymptotics for the four-dimensional hierarchical $|\phi|^4$ model to the Euclidean model with periodic boundary conditions. | Then the susceptibility obeys 1 (12) χN (νc + sN wN ) = Mn,2 (sN )L2N (BN )1/2 [1 + o(1)]. n Our methods have the potential to extend from the hierarchical model to the Euclidean model with periodic boundary conditions; it is an open problem to carry out this extension. The report passage is retained verbatim as the re... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | The Renormalization Group (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/33, pp. 1865--1925 |
30,005,179 | OWR-11101915-002 | Coarse Median Spaces with $\delta$-Median Metrics | Does every coarse median space admit a $\delta$-median metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-002",
"literature-status:open",
"owr-year:2022"
] | The excerpt states that every delta-median space is coarse median, but whether every coarse median space admits a delta-median metric remains unclear; related metric-reconstruction results do not settle this stronger assertion. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "Oberwolfach Report 34/2022"
},
{
"url": "https://arxiv.org/abs/1802.02499",
"label": "Niblo--Wright--Zhang, Coarse median algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Does every coarse median space admit a $\delta$-median metric? | conjecture. Approximate medians. In a recent paper with Cornelia Drutu [1], we look at a minimal notion including both hyperbolicity, and median spaces. According to a recent result of Petyt [7], this class of groups include mapping class groups of closed surfaces. Definition 3. A metric space (X, d) is called \delta-m... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,180 | OWR-11101915-003 | Geometry and Actions of $\delta$-Median Spaces | Determine whether actions on uniformly locally finite $\delta$-median spaces induce proper actions on $L^p$-spaces, whether such spaces admit strongly bolic metrics, and whether $\delta$-median and hierarchically hyperbolic spaces coincide. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-003",
"literature-status:open",
"owr-year:2022"
] | The four listed questions are presented as open in the report; later results address special classes but do not settle the general questions. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "Oberwolfach Report 34/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Determine whether actions on uniformly locally finite $\delta$-median spaces induce proper actions on $L^p$-spaces, whether such spaces admit strongly bolic metrics, and whether $\delta$-median and hierarchically hyperbolic spaces coincide. | Open questions. Many questions for \delta- median spaces and groups remain open, and we list here a few of interest. (1) Does any action on a uniformly locally finite \delta-median space translate into a proper action on an Lp -space? (2) Does any uniformly locally finite \delta-median space admit a strongly bolic metr... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,181 | OWR-11101915-005 | Torsion in the Integral Homology-Cobordism Group | Does the integer homology-cobordism group $\Theta^3_{\mathbb Z}$ contain torsion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-005",
"literature-status:open",
"owr-year:2022"
] | The existence of torsion in the integer homology-cobordism group \Theta^3_{\mathbb{Z}} remains an open problem; existing work establishes large infinite-rank subgroups but does not settle torsion. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2209.10735",
"label": "survey of the homology-cobordism group"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Does the integer homology-cobordism group $\Theta^3_{\mathbb Z}$ contain torsion? | Fundamental questions about the structure of Θ3Z remain open: Question. Does Θ3Z contain any torsion? Homology cobordism and Heegaard Floer homology Jennifer Hom (joint work with Irving Dai, Kristen Hendricks, Matthew Stoffregen, Linh Truong, and Ian Zemke) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,182 | OWR-11101915-006 | Controlled Exotic Smooth Four-Manifolds with Boundary | Construct exotic smooth four-manifolds with boundary while fixing the boundary three-manifold and multiple invariants from their topological classification. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-006",
"literature-status:open",
"owr-year:2022"
] | The extracted text is a contextual fragment rather than a complete classification claim; no uniquely identifiable theorem can be tested against it, so the unresolved record is retained as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Construct exotic smooth four-manifolds with boundary while fixing the boundary three-manifold and multiple invariants from their topological classification. | conjecture. However, for smooth manifolds with boundary, we know the topological classifications always fail. I will discuss briefly what is known in each of these categories for 4-manifolds and then for surfaces embedded in them. I will begin with a discussion of 4-manifolds. In the topological category there are know... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,183 | OWR-11101915-007 | Exotic Four-Manifolds and the Smooth Poincaré Conjecture | Decide whether $S^4$ has an exotic smooth structure, whether $S^1\times S^3$ or a definite four-manifold can be exotic, and whether every genus $g$ has a unique smooth surface $\Sigma\subset S^4$ whose complement satisfies $\pi_1(S^4\setminus\Sigma)\cong\mathbb Z$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-007",
"literature-status:open",
"owr-year:2022"
] | The smooth 4-dimensional Poincare conjecture, including the question whether the standard 4-sphere has an exotic smooth structure, remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "original Oberwolfach report"
},
{
"url": "https://jomprob.org/index.php/jomp/article/view/Vol-1Issue-1Paper-3",
"label": "Characterizing the 4-sphere, S^4"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Decide whether $S^4$ has an exotic smooth structure, whether $S^1\times S^3$ or a definite four-manifold can be exotic, and whether every genus $g$ has a unique smooth surface $\Sigma\subset S^4$ whose complement satisfies $\pi_1(S^4\setminus\Sigma)\cong\mathbb Z$. | The smooth 4-dimensional Poincare conjecture posits that S 4 is not exotic; this remains open, and it is also unknown whether, for example, S 1 \times S 3 is exotic, or whether there are exotic definite 4-manifolds. Here the governing conjecture is the unknotting conjecture which posits that for any g \in N there is a ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,184 | OWR-11101915-008 | Finite Equivariant Cohomology for Compact Lie Groups | Construct equivariant cohomology theories having strong finiteness properties uniformly for all compact Lie groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-008",
"literature-status:open",
"owr-year:2022"
] | This is a broad request for examples of equivariant cohomology theories with uniform finiteness properties; the report gives examples and partial constructions, but no complete classification or definitive answer for all compact Lie groups. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1908.00779",
"label": "Proper equivariant stable homotopy theory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Construct equivariant cohomology theories having strong finiteness properties uniformly for all compact Lie groups. | What are examples of equivariant cohomology theories having good finiteness properties for all compact Lie groups? 2. Equivariant Elliptic Cohomology The aim of equivariant elliptic cohomology is repeat the above story for equi- variant K-theory, replacing Gm by a fixed elliptic curve E. In particular, the S 1 -equivar... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,185 | OWR-11101915-009 | Modulo-Four Reduced Khovanov Rank of Ribbon Knots | Let $R$ be $\mathbb F_p$ or $\mathbb Z$. Prove that $\operatorname{rk}\widetilde{\operatorname{Kh}}_R(K)\pmod4$ is a knot-concordance invariant; equivalently, prove $\operatorname{rk}\widetilde{\operatorname{Kh}}_R(J)\equiv1\pmod4$ for every ribbon knot $J$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986](https://doi.org/10.4171/owr/2022/34)
## Literature review (checked 2026-08-22)
**Status:** open
**Assessme... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101915-009",
"literature-status:open",
"owr-year:2022"
] | The proposed congruence modulo 4 for reduced Khovanov rank of slice or ribbon knots remains conjectural; the primary follow-up paper reports counterexamples to the modulo-8 version but only evidence and special cases for the modulo-4 replacement. | [
{
"url": "https://doi.org/10.4171/owr/2022/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2303.04233",
"label": "Dunfield--Gong--Hockenhull--Marengon--Willis"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/34 | null | null | null | Let $R$ be $\mathbb F_p$ or $\mathbb Z$. Prove that $\operatorname{rk}\widetilde{\operatorname{Kh}}_R(K)\pmod4$ is a knot-concordance invariant; equivalently, prove $\operatorname{rk}\widetilde{\operatorname{Kh}}_R(J)\equiv1\pmod4$ for every ribbon knot $J$. | Going back to slice knots, and keeping in mind that there is a slice knot (namely KKT ) with rk HFK[ = 33, we asked whether there is a statement weaker than [ being an odd square that holds for all slice knots. Thus, we propose to weaken Conjectures 2.(2) and 1.(2) from (mod 8) to (mod 4). The report passage is retaine... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Topologie (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/34, pp. 1927--1986 |
30,005,186 | OWR-11101916-003 | Unspecified Assembly Map Comparison Conjecture | conjecture. Our original mo- tivation was to study the precise relation between these conjectures. Since the BCC and the FJC are determined by the assembly maps for spectrum valued functors associated to KO(−) and L(−), this really amounts to (3) (P, \beta) is called unimodular if the canonical map \beta ♯ : P \to P ∨ ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The extraction combines introductory assembly-map discussion and definitions without stating a standalone unresolved target. No separate cle) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-003",
"literature-status:open",
"owr-year:2022"
] | The extracted record contains only the word conjecture and surrounding discussion of Baum--Connes and Farrell--Jones assembly maps, without a complete mathematical assertion; the claim is therefore unresolved or unclear rather than classified as solved. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | null | conjecture. Our original mo- tivation was to study the precise relation between these conjectures. Since the BCC and the FJC are determined by the assembly maps for spectrum valued functors associated to KO(−) and L(−), this really amounts to (3) (P, \beta) is called unimodular if the canonical map \beta ♯ : P \to P ∨ ... | unrecoverable | The extraction combines introductory assembly-map discussion and definitions without stating a standalone unresolved target. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,187 | OWR-11101916-006 | Field-Theoretic Description of the Full Spectral Action | It is thus a natural question whether we can also field-theoretically describe the full spectral action, without resorting to the scale-invariant part. for elements aj , bj \in A. The terminology ‘fluctuation’ comes from representing A on H as Xn (2) V := \piD (A) = aj [D, bj ] \in B(H)sa , j=1 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The contribution asks this question rhetorically and then answers it with its main spectral-action expansion theorem. No separate clean stat) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-006",
"literature-status:open",
"owr-year:2022"
] | The spectral action principle and several asymptotic or scale-invariant sectors are established, but a general field-theoretic description of the full spectral action remains an open research direction. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1902.05306",
"label": "Spectral Action in Noncommutative Geometry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | null | It is thus a natural question whether we can also field-theoretically describe the full spectral action, without resorting to the scale-invariant part. for elements aj , bj \in A. The terminology ‘fluctuation’ comes from representing A on H as Xn (2) V := \piD (A) = aj [D, bj ] \in B(H)sa , j=1 | unrecoverable | The contribution asks this question rhetorically and then answers it with its main spectral-action expansion theorem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,188 | OWR-11101916-007 | Critical Cwikel Estimates for Noncompact Spectral Triples | Prove critical Cwikel-type estimates at $p=2$ for noncompact spectral triples, including estimates for $M_f(1-\Delta)^{-d/4}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-007",
"literature-status:open",
"owr-year:2022"
] | Spectral dimension is computable from summability and zeta or singular-trace growth in many examples, but the report identifies the critical Cwikel-type case as unresolved; there is no general computation theorem for arbitrary spectral triples. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/math/0202108",
"label": "Dimensions and singular traces for spectral triples"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | Prove critical Cwikel-type estimates at $p=2$ for noncompact spectral triples, including estimates for $M_f(1-\Delta)^{-d/4}$. | How to compute the dimension of spectral triple? d Compact spectral triple is called d-dimensional if (D2 + 1)− 2p \in Lp,\infty for every p > 0. Here, Lp,\infty is the collection of all infinitesimals of order p1 . d Locally compact spectral triple is called d-dimensional if \pi(a)(D2 + 1)− 2p \in Lp,\infty for every ... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,189 | OWR-11101916-008 | Surjectivity in Algebraic K-Theory of Varieties | Is the map $K_0(\operatorname{Var}_k)\otimes\pi_1S\to K_1(\operatorname{Var}_k)$ surjective? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (partially_solved (no, for finite fields of odd characteristic; answered in the source)) | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved (no, for finite fields of odd characteristic; answered in the source)**. I. Zakharevich (OWR 35/2022, pp. 2040–2041) asks whether K₀(Var_k) ⊗ π₁S → K₁(Var_k) is surjective, and states (Theorem 1, p. 2041) that for finite k of odd characteristic, scaling A... | [
"owr",
"oberwolfach-reports",
"OWR-11101916-008",
"literature-status:open",
"owr-year:2022"
] | The coefficient notation and the preceding question are corrupted in the extracted record, so the precise K-theory map cannot be identified reliably; no definitive surjectivity result can be assigned to this exact statement. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | Is the map $K_0(\operatorname{Var}_k)\otimes\pi_1S\to K_1(\operatorname{Var}_k)$ surjective? | Is the map K0 (Vark ) ⊗ \pi1 S \to K1 (Vark ) surjective? If the answer ot the second question is yes, the answer to the first question must also be yes, and thus we focus on the second question. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,190 | OWR-11101916-009 | Gromov's Scalar Curvature Band-Width Conjecture | Let $M$ be a closed connected manifold of dimension $n-1\neq4$ that admits no metric of positive scalar curvature. If $g$ is a metric on $V=M\times[-1,1]$ with scalar curvature at least $n(n-1)$, must $\operatorname{width}(V,g)\leq2\pi/n$, where $\operatorname{width}(V,g)=\operatorname{dist}_g(\partial_-V,\partial_+V)$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-009",
"literature-status:partially-solved",
"owr-year:2022"
] | The stated Gromov band-width inequality is proved for broad classes and, in particular, for orientable bands in dimensions n less than or equal to 7 excluding n=5; the all-dimensional formulation in the record is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2104.10120",
"label": "Rade, Scalar and mean curvature comparison via mu-bubbles"
},
{
"url": "https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/topo.12303... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | Let $M$ be a closed connected manifold of dimension $n-1\neq4$ that admits no metric of positive scalar curvature. If $g$ is a metric on $V=M\times[-1,1]$ with scalar curvature at least $n(n-1)$, must $\operatorname{width}(V,g)\leq2\pi/n$, where $\operatorname{width}(V,g)=\operatorname{dist}_g(\partial_-V,\partial_+V)$... | In classical Riemannian comparison geometry, positive lower bounds on sectional and Ricci curvature have concrete consequences such as global upper bounds on volumes and distances. In contrast, the study of positive scalar curvature from a geometric perspective is much more subtle. However, recently Gromov proposed a n... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,191 | OWR-11101916-010 | Generalized Group Actions for Crossed-Product Operator Algebras | How can we generalise group actions so that the crossed product C*-algebra may still be defined? A bicategorical interpretation for crossed products and Cuntz-Pimsner algebras Ralf Meyer (joint work with Suliman Albandik, Alcides Buss, Camila Fabre Sehnem, and Chenchang Zhu) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The contribution immediately answers its motivating question by identifying Fell bundles as the appropriate generalized actions. No separate) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-010",
"literature-status:open",
"owr-year:2022"
] | Crossed products have been generalized to groupoids, Fell bundles, crossed modules, correspondences, and related structures, but the extracted broad question asks for a general principle and has no unique complete answer. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1502.07771",
"label": "Colimits in the correspondence bicategory"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | null | How can we generalise group actions so that the crossed product C*-algebra may still be defined? A bicategorical interpretation for crossed products and Cuntz-Pimsner algebras Ralf Meyer (joint work with Suliman Albandik, Alcides Buss, Camila Fabre Sehnem, and Chenchang Zhu) | unrecoverable | The contribution immediately answers its motivating question by identifying Fell bundles as the appropriate generalized actions. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,192 | OWR-11101916-011 | Bicategorical Limits of Nonproper Product Systems | Does a bicategorical limit exist for a nonproper product system over a monoid, and if so how can it be described? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058](https://doi.org/10.4171/owr/2022/35)
## Literature review (checked 2026-0... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101916-011",
"literature-status:partially-solved",
"owr-year:2022"
] | Homomorphisms into the correspondence bicategory and their colimits are developed for groups, groupoids, product systems, and important classes of monoids such as Ore monoids; the unrestricted monoid formulation in the record is broader than the established results. | [
{
"url": "https://doi.org/10.4171/owr/2022/35",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1502.07771",
"label": "Colimits in the correspondence bicategory"
},
{
"url": "https://arxiv.org/abs/2203.12068",
"label": "Groupoid models for diagrams of groupo... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/35 | null | null | null | Does a bicategorical limit exist for a nonproper product system over a monoid, and if so how can it be described? | What is a homomorphism from, say, a monoid M to the C*-correspondence bicategory, and what would its limit look like? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Non-Commutative Geometry and Cyclic Homology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/35, pp. 1987--2058 |
30,005,193 | OWR-11101917-001 | Connes-Embedding Table-of-Contents Fragment | Conjecture . . . . . . . . . . . . . 2110 Søren Eilers (joint with Toke M. Carlsen and Adam Dor-On) The Williams problem through the lens of Cuntz-Krieger algebras . . . . . . 2111 Ben Hayes (joint with David Jekel and Srivatsav Kunnawalkam Elayavalli) Consequences of the recent resolution of the Peterson-Thom conjectu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a standalone open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-001",
"literature-status:open",
"owr-year:2022"
] | The extracted entry is only a fragment beginning with conjecture and a table-of-contents passage; no complete mathematical claim is available for verification, so it remains open under the stated triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | null | Conjecture . . . . . . . . . . . . . 2110 Søren Eilers (joint with Toke M. Carlsen and Adam Dor-On) The Williams problem through the lens of Cuntz-Krieger algebras . . . . . . 2111 Ben Hayes (joint with David Jekel and Srivatsav Kunnawalkam Elayavalli) Consequences of the recent resolution of the Peterson-Thom conjectu... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a standalone open mathematical problem. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,194 | OWR-11101917-003 | Twisted Groupoid Reconstruction of $C^*$-Algebra Pairs | Characterize the pairs of $C^*$-algebras arising from quasi-Cartan groupoid reconstruction, extend quasi-Cartan groupoid reconstruction to twisted $C^*$-algebras, and determine whether its isotropy hypotheses can be weakened. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-003",
"literature-status:open",
"owr-year:2022"
] | The report explicitly lists characterization of the relevant C-star pairs, a twisted extension, and weaker isotropy hypotheses as open questions; later work supplies sufficient cases but not a complete answer to this combined entry. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2001.08270",
"label": "Cartan subalgebras for non-principal twisted groupoid C-star algebras"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Characterize the pairs of $C^*$-algebras arising from quasi-Cartan groupoid reconstruction, extend quasi-Cartan groupoid reconstruction to twisted $C^*$-algebras, and determine whether its isotropy hypotheses can be weakened. | Some interesting open questions emerge: • What C ∗ -algebraic properties characterise the pairs of C ∗ -algebras that appear in Theorem 1? • Is is possible to obtain a version of Theorem 1 for twisted C ∗ -algebras over the same class of groupoids? Is it possi- ble to use this to weaken the hypothesis on the isotropy g... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,195 | OWR-11101917-004 | Amenable Actions on Unital Simple Stably Finite Algebras | Does a nonamenable group admit an amenable action on a unital, simple, stably finite $C^*$-algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-004",
"literature-status:open",
"owr-year:2022"
] | Examples of amenable actions of nonamenable groups on stably finite simple C-star algebras are known, but the unital version asked here remains open in current literature. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2204.04480",
"label": "Every countable group admits amenable actions on stably finite simple C-star algebras"
},
{
"url": "https://doi.org/10.1112/blms.13154",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Does a nonamenable group admit an amenable action on a unital, simple, stably finite $C^*$-algebra? | More concretely, we ask the following question. Let us state it as an open problem. Are there any amenable actions of nonamenable groups on unital, simple, stably finite C ∗ -algebras? Tracial amenability and purely infinite C ∗ -algebras Shirly Geffen (joint work with Eusebio Gardella, Julian Kranz, Petr Naryshkin, An... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,196 | OWR-11101917-005 | Explicit Connes-Embedding Counterexamples and Nonhyperlinear Groups | Find a more algebraic proof of $\operatorname{MIP}^*=\operatorname{RE}$, construct an explicit Connes-embedding counterexample including its tracial state, identify analogous consequences, and construct a nonhyperlinear group. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-005",
"literature-status:partially-solved",
"owr-year:2022"
] | MIP-star equals RE gives an explicit negative resolution of the Connes embedding problem, but the existence of a concrete nonhyperlinear group and the other algebraic refinements listed in the entry remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2001.04383",
"label": "MIP-star equals RE"
},
{
"url": "https://arxiv.org/abs/2109.12682",
"label": "The Connes Embedding Problem, a guided tour"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Find a more algebraic proof of $\operatorname{MIP}^*=\operatorname{RE}$, construct an explicit Connes-embedding counterexample including its tracial state, identify analogous consequences, and construct a nonhyperlinear group. | Stated broadly, the ones that seem to come up the most are: (1) Can we make the current proof more algebraic? (2) Can we make an explicit counterexample to the CEP? (3) Are there similar types of results we should look for? (4) Can we make a non-hyperlinear group? The provers’ actions in such a protocol can be describe... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,197 | OWR-11101917-006 | Cartan Subalgebras from Twisted Groupoid Subgroupoids | Characterize the clopen normal subgroupoids $S$ of a twisted étale groupoid $(G,\Sigma)$ for which $C_r^*(S;\Sigma|_S)$ is a Cartan subalgebra of $C_r^*(G;\Sigma)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-006",
"literature-status:partially-solved",
"owr-year:2022"
] | Published work gives sufficient dynamical and cocycle conditions ensuring that a subgroupoid produces a Cartan subalgebra in a twisted groupoid C-star algebra; a complete necessary-and-sufficient characterization for the broad question is not established. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2001.08270",
"label": "Cartan subalgebras for non-principal twisted groupoid C-star algebras"
},
{
"url": "https://arxiv.org/abs/2505.17913",
"label": "Non-tradit... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Characterize the clopen normal subgroupoids $S$ of a twisted étale groupoid $(G,\Sigma)$ for which $C_r^*(S;\Sigma|_S)$ is a Cartan subalgebra of $C_r^*(G;\Sigma)$. | It is thus a natural question to ask, under which conditions the C∗ -algebra of a subgroupoid S of a twisted (not necessarily effective) groupoid G is a Cartan subalgebra. Therefore, the crux in answering the question lies in finding conditions on S that force maximality. Cartan subalgebras for non-effective twisted gr... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,198 | OWR-11101917-007 | Nonembeddable Tracial Algebras with Wasserstein Lifting | Does there exist a non-Connes-embeddable tracial von Neumann algebra whose noncommutative law has coincident weak-star and Wasserstein topologies and for which every ultraproduct embedding lifts to factorizable completely positive maps? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-007",
"literature-status:open",
"owr-year:2022"
] | The existence of non-Connes-embeddable tracial von Neumann algebras is known, but the additional conditions (1) and (2) in the extracted problem are still explicitly treated as an open existence question. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00220-022-04480-0",
"label": "Duality for optimal couplings in free probability"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Does there exist a non-Connes-embeddable tracial von Neumann algebra whose noncommutative law has coincident weak-star and Wasserstein topologies and for which every ultraproduct embedding lifts to factorizable completely positive maps? | It is an open question whether there exist non-Connes-embeddable tracial W∗ -algebras that sat- isfy (1) and (2). The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,199 | OWR-11101917-008 | Necessity of Z-Stability in KK-Uniqueness | Let $C,D,E$ be separable $C^*$-algebras, with $D$ a closed two-sided ideal of $E$, and let $\Phi,\Psi:C\to E$ be relatively absorbing homomorphisms agreeing modulo $D$. Can the $\mathcal Z$-stability assumption on $E$ be removed from the equivalence between $[\Phi,\Psi]_{KK}=0$ and asymptotic unitary equivalence throug... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-008",
"literature-status:open",
"owr-year:2022"
] | The report asks whether Z-stability can be removed from the preceding theorem; subsequent results establish important special cases and show failures of Z-stability in related nonamenable settings, but do not settle this general necessity question. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00208-024-02833-9",
"label": "Tracially amenable actions and purely infinite crossed products"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Let $C,D,E$ be separable $C^*$-algebras, with $D$ a closed two-sided ideal of $E$, and let $\Phi,\Psi:C\to E$ be relatively absorbing homomorphisms agreeing modulo $D$. Can the $\mathcal Z$-stability assumption on $E$ be removed from the equivalence between $[\Phi,\Psi]_{KK}=0$ and asymptotic unitary equivalence throug... | Is Z-stability necessary in the above theorem? Theorem 3 (Z-stable KK-uniqueness). If [\phi, \psi]KK = 0 then \phi and \psi are uni- tarily equivalent. More generally: Let C, D and E be separable C ∗ -algebras such that E contains D as a two-sided closed ideal, and let Φ, Ψ : C \to E be ∗-homomorphisms agreeing modulo ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,200 | OWR-11101917-009 | Characterization of Isometric Shift Absorption | Let $\alpha:G\curvearrowright A$ be an amenable action on a Kirchberg algebra such that $A\rtimes H$ is a Kirchberg algebra for every closed subgroup $H\subseteq G$. Must $\alpha$ be isometrically shift-absorbing? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-009",
"literature-status:partially-solved",
"owr-year:2022"
] | The general locally compact group question remains unresolved, but Mukohara and Suzuki confirm the corresponding isometric shift-absorption question for compact group actions. | [
{
"url": "https://doi.org/10.4171/owr/2022/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2605.21128",
"label": "Mukohara--Suzuki, 2026"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | Let $\alpha:G\curvearrowright A$ be an amenable action on a Kirchberg algebra such that $A\rtimes H$ is a Kirchberg algebra for every closed subgroup $H\subseteq G$. Must $\alpha$ be isometrically shift-absorbing? | Regarding future work, there remain a few challenges and open problems. Another open problem would be to determine whether isometric shift-absorption is actually a more familiar property in disguise. Does it follow that \alpha is isometrically shift-absorbing? The report passage is retained verbatim as the relevant con... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,201 | OWR-11101917-013 | Resolved Coarseness Conjecture for Free Group Factors | Conjecture 1.12] and [20, Conjecture 5.2]. If M is a von Neumann algebra, an M -M bimodule H is a Hilbert space with normal left and right actions of M which commute. We use M HM to mean that H is an M -M bimodule. If H, K are M -M bimodules, we use M HM \leqM KM to mean that there is M -bimodular unitary map H \to K. ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [\$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127](https://doi.org/10.4171/owr/2022/36)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report states that the coarseness conjecture under discussion was resolved positively; the extracted passage is not an open pro) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101917-013",
"literature-status:open",
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] | The extraction conflates a conjecture reference with theorem statements and does not isolate one verifiable mathematical claim; under the triage rule the unresolved target is open. | [
{
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"label": "original Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/36 | null | null | null | null | Conjecture 1.12] and [20, Conjecture 5.2]. If M is a von Neumann algebra, an M -M bimodule H is a Hilbert space with normal left and right actions of M which commute. We use M HM to mean that H is an M -M bimodule. If H, K are M -M bimodules, we use M HM \leqM KM to mean that there is M -bimodular unitary map H \to K. ... | unrecoverable | The official report states that the coarseness conjecture under discussion was resolved positively; the extracted passage is not an open problem. | null | null | null | null | null | \$\$C^*\$-Algebras (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/36, pp. 2059--2127 |
30,005,202 | OWR-11101918-001 | Workshop Summary on Geometric Measure Theory and Flows | conjecture. Salvatore Stuvard presented the state-of-the-art on the fine properties of singular sets of area minimizing currents mod p, both for the hypersurface case and general codi- mensional case. Zihui Zhao presented the estimate on the Hausdorff measure of the singular set of a harmonic function in terms of Almgren... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is workshop-summary prose and a list of topics, not a standalone mathematical problem. No s) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-001",
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] | The extracted statement is only the word conjecture followed by workshop summary prose, so no definite mathematical claim can be verified. | [
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | null | conjecture. Salvatore Stuvard presented the state-of-the-art on the fine properties of singular sets of area minimizing currents mod p, both for the hypersurface case and general codi- mensional case. Zihui Zhao presented the estimate on the Hausdorff measure of the singular set of a harmonic function in terms of Almgren... | unrecoverable | The official report confirms that the extraction is workshop-summary prose and a list of topics, not a standalone mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,203 | OWR-11101918-002 | Workshop Contents Listing for Geometric Variational Analysis | conjecture . . . . . 2143 Filip Rindler (joint with Paolo Bonicatto and Giacomo Del Nin) Transport of currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2145 Luca Spolaor (joint with Guido De Philippis and Bozhidar Velichkov ) (Quasi)-conformal methods in some 2-dimensional... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-002",
"literature-status:open",
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] | The extracted statement is a table-of-contents fragment rather than a well-posed problem, so its resolution status is unclear and is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | null | conjecture . . . . . 2143 Filip Rindler (joint with Paolo Bonicatto and Giacomo Del Nin) Transport of currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2145 Luca Spolaor (joint with Guido De Philippis and Bozhidar Velichkov ) (Quasi)-conformal methods in some 2-dimensional... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,204 | OWR-11101918-003 | Classical Limit of Nonlocal Minimal Surfaces | conjecture. As for Allen-Cahn, this can only be done if one can show some robust curvature bounds as s ↑ 1 and understand the delicate information on interaction between layers that “survives” after taking the limit (the analogue of the Toda system). Now, critical points which solve the semilinear PDE (the Allen-Cahn e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report raises this question only as a lead-in and immediately states that it is answered by the reported work, so it is not pre) | null | null | null | [
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{
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{
"url": "https://doi.org/10.1016/j.aim.2019.106856",
"label": "Wang--Wei, Allen--Cahn transition layers"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | null | conjecture. As for Allen-Cahn, this can only be done if one can show some robust curvature bounds as s ↑ 1 and understand the delicate information on interaction between layers that “survives” after taking the limit (the analogue of the Toda system). Now, critical points which solve the semilinear PDE (the Allen-Cahn e... | unrecoverable | The official report raises this question only as a lead-in and immediately states that it is answered by the reported work, so it is not presented there as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,205 | OWR-11101918-004 | Singular Free Boundaries in the Critical Dimension | Determine whether the critical dimension $d_*$ for singular free boundaries in the one-phase problem is $5$, $6$, or $7$; describe the singular set in the critical dimension; remove the symmetry assumption from the two-dimensional branch-point regularity result; and find a frequency-function proof that may extend to hi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-004",
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] | The critical dimension is still only known to lie in the set five, six, seven and is conjectured to be seven; the additional singular-set and symmetry questions also remain open. | [
{
"url": "https://cvgmt.sns.it/media/doc/paper/4839/lambda2-revised.pdf",
"label": "Mazzoleni--Trey--Velichkov, optimal-set regularity"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Determine whether the critical dimension $d_*$ for singular free boundaries in the one-phase problem is $5$, $6$, or $7$; describe the singular set in the critical dimension; remove the symmetry assumption from the two-dimensional branch-point regularity result; and find a frequency-function proof that may extend to hi... | Open problems: • The critical dimension d∗ is the first dimension, for which there exists a one-homogeneous non-negative local minimizer of the one-phase functional with a singular free boundary. It is a famous open question to determine wether d∗ is equal to 5, 6 or 7 (see [2, 6, 5]). • Can one give a more precise desc... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,206 | OWR-11101918-005 | Strong Onsager Conjecture for Euler Flows | Do there exist Hölder-continuous incompressible three-dimensional Euler flows with total kinetic-energy dissipation that satisfy the local energy inequality? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-005",
"literature-status:partially-solved",
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] | Subcritical Holder and near-critical Besov constructions with local energy inequality are known, but the strong formulation at the critical one-third Holder regularity remains unresolved. | [
{
"url": "https://doi.org/10.2140/apde.2022.15.2003",
"label": "De Lellis--Kwon, dissipative Euler flows"
},
{
"url": "https://arxiv.org/abs/2305.18509",
"label": "Giri--Kwon--Novack, L3-based strong Onsager theorem"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "origin... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Do there exist Hölder-continuous incompressible three-dimensional Euler flows with total kinetic-energy dissipation that satisfy the local energy inequality? | Euler flows and strong Onsager conjecture Hyunju Kwon The incompressible 3D Euler equations have total kinetic energy conservation for smooth (spatially periodic) solutions. In the recent resolution of the Onsager conjecture by Isett [1], below certain threshold Holder regularity, Euler flows with total kinetic energy d... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,207 | OWR-11101918-006 | Boundary Unique Continuation on General Lipschitz Domains | Let $\Omega\subset\mathbb R^n$ be an arbitrary Lipschitz domain, let $B$ be centered on $\partial\Omega$, and let $u\in C(\overline\Omega)$ be harmonic in $\Omega$. If $u=0$ on $\Sigma=B\cap\partial\Omega$ and
$$\mathcal H^{n-1}\bigl(\{x\in\Sigma:\nabla u(x)=0\}\bigr)>0,$$
must $u\equiv0$ in $\Omega$, without any sma... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-006",
"literature-status:open",
"owr-year:2022"
] | Boundary unique continuation is proved for C1-Dini domains and for Lipschitz domains with sufficiently small constant, while the unrestricted Lipschitz-domain version in the record remains open. | [
{
"url": "https://doi.org/10.1002/cpa.22025",
"label": "Tolsa, boundary unique continuation"
},
{
"url": "https://arxiv.org/abs/2102.07281",
"label": "Kenig--Zhao, C1-Dini domains"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Let $\Omega\subset\mathbb R^n$ be an arbitrary Lipschitz domain, let $B$ be centered on $\partial\Omega$, and let $u\in C(\overline\Omega)$ be harmonic in $\Omega$. If $u=0$ on $\Sigma=B\cap\partial\Omega$ and
$$\mathcal H^{n-1}\bigl(\{x\in\Sigma:\nabla u(x)=0\}\bigr)>0,$$
must $u\equiv0$ in $\Omega$, without any sma... | It is still an open question whether the same statement holds if we only assume Ω is a Lipschitz domain (and remove the smallness assumption on the Lipschitz constant). Quantitative boundary unique continuation and the estimate of the singular set Zihui Zhao (joint work with Carlos Kenig) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,208 | OWR-11101918-008 | Thomas Yau Singularity Picture for Lagrangian Mean Curvature Flow | For generic initial Lagrangian surfaces, are the only tangent flows at singularities two multiplicity-one planes meeting either at a point or along a line, as suggested by the Thomas–Yau singularity picture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "PDEs and their applications in physics and geometry.",
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-008",
"literature-status:partially-solved",
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] | The two-plane neck-pinch scenario is understood, and recent work treats circle-symmetric and nondegenerate neck pinches, but the broader Thomas--Yau singularity picture and generic classification remain unresolved. | [
{
"url": "https://arxiv.org/abs/2208.11054",
"label": "Lotay--Schulze--Szekelyhidi, neck pinches"
},
{
"url": "https://arxiv.org/abs/2602.15771",
"label": "Szekelyhidi, generic Lagrangian neck pinches"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | For generic initial Lagrangian surfaces, are the only tangent flows at singularities two multiplicity-one planes meeting either at a point or along a line, as suggested by the Thomas–Yau singularity picture? | where \phi(Mi ) is the “cohomological” Lagrangian angle of Mi . This result provides some evidence for Thomas–Yau’s Conjecture 7.3 in [14]. Indeed, their conjecture states that if the flow has a finite time singularity, then L can be decomposed into a graded connected sum M1 \#M2 satisfying the conditions in (1). Our res... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,209 | OWR-11101918-009 | Stable Wulff Shapes for Crystalline Nonlocal Energies | Classify the crystalline anisotropies whose Wulff shapes remain global minimizers of the nonlocal energy $E_\gamma$ for all sufficiently small $\gamma>0$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-009",
"literature-status:open",
"owr-year:2022"
] | Known results cover broad symmetry classes of crystalline surface tensions, but the cited primary work explicitly leaves classification of all Wulff shapes that remain minimizers open. | [
{
"url": "https://doi.org/10.1016/j.na.2020.112223",
"label": "Fusco--Julin--Morini, crystalline anisotropies"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Classify the crystalline anisotropies whose Wulff shapes remain global minimizers of the nonlocal energy $E_\gamma$ for all sufficiently small $\gamma>0$. | It is an open problem to classify the crystalline anisotropies whose Wulff shapes remain the global minimizers of E\gamma for \gamma > 0 sufficiently small which would require us to characterize the critical points of the nonlocal energy with respect to the restricted class of variations. The report passage is retained ve... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,210 | OWR-11101918-010 | Quantitative Rigidity for Aviles–Giga Differential Inclusions | Do there exist constants $C>0$ and $\alpha\in(0,1)$ such that every $w\in H^1(B_1;\mathbb R^2)$ satisfies
$$\inf_{A\in K}\int_{B_{1/2}}|Dw-A|^2\,dx\leq C\left(\int_{B_1}\operatorname{dist}^2(Dw,K)\,dx\right)^\alpha?$$
This asks for a quantitative rigidity estimate for the differential inclusion. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-010",
"literature-status:open",
"owr-year:2022"
] | Quantitative rigidity is proved for elliptic differential-inclusion curves and exact rigidity results for some non-elliptic curves are known, but the stated approximate estimate for the Aviles--Giga set K is not resolved. | [
{
"url": "https://doi.org/10.1093/imrn/rnad108",
"label": "Lamy--Lorent--Peng, quantitative rigidity"
},
{
"url": "https://arxiv.org/abs/2404.02121",
"label": "Lamy--Lorent--Peng, non-elliptic curves"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach r... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Do there exist constants $C>0$ and $\alpha\in(0,1)$ such that every $w\in H^1(B_1;\mathbb R^2)$ satisfies
$$\inf_{A\in K}\int_{B_{1/2}}|Dw-A|^2\,dx\leq C\left(\int_{B_1}\operatorname{dist}^2(Dw,K)\,dx\right)^\alpha?$$
This asks for a quantitative rigidity estimate for the differential inclusion. | Does there exist constants C > 0 and \alpha \in (0, 1) such that if w \in H 1 B1 ; R2 Z Z \alpha 2 inf |Dw − A| dx \leq C dist2 (Dw, K) dx . regularity which ultimately allowed us to show m is rigid in the sense of Jabin- Otto-Perthame. Later Xavier Lamy, Guanying Peng and myself [4] considered the problem of regularit... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,211 | OWR-11101918-011 | Stability of Nonelliptic Differential Inclusions | Do there exist constants $C>0$ and $\alpha\in(0,1)$ giving the proposed stability estimate for approximate differential inclusions into the nonelliptic set $K$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-011",
"literature-status:open",
"owr-year:2022"
] | The stated rigidity question for the explicitly constructed non-elliptic sets Gamma sub n has no general proof or counterexample in the checked primary literature. | [
{
"url": "https://arxiv.org/abs/2404.02121",
"label": "Lamy--Lorent--Peng, non-elliptic curves"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | Do there exist constants $C>0$ and $\alpha\in(0,1)$ giving the proposed stability estimate for approximate differential inclusions into the nonelliptic set $K$? | This would represent the first quantitative rigidity result for non-elliptic differential inclusions and would be a useful tool in the study of the Aviles Giga conjecture. This was our original motivation for the study of the differential inclusion into K. As a step towards this goal we recently established the following ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,212 | OWR-11101918-012 | Rigidity of Higher Index Differential Inclusion Curves | For the nonelliptic differential-inclusion sets $\Gamma_n$ with $n\geq 3$, does sufficiently local membership $Dw(x)\in\Gamma_n$ force $Dw$ to be rigid? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. A. Lorent (OWR 37/2022, p. 2181, Problem 2) asks whether, for n ≥ 3 and small R, Dw ∈ Γ_n ∩ B_R(M) a.e. forces rigidity, where Γ_n = [γ₁(t)]\_c + n⁻¹[γ₂(nt)]\_a with convex arclength curves γ₁, γ₂ and (3) sup|γ₁''|² < n² inf|γ₂''|². | [
"owr",
"oberwolfach-reports",
"OWR-11101918-012",
"literature-status:open",
"owr-year:2022"
] | The higher-index Gamma sub n rigidity question is not settled by the available exact-inclusion regularity results, which treat different hypotheses and do not establish the asserted statement for all n. | [
{
"url": "https://arxiv.org/abs/2404.02121",
"label": "Lamy--Lorent--Peng, non-elliptic curves"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | For the nonelliptic differential-inclusion sets $\Gamma_n$ with $n\geq 3$, does sufficiently local membership $Dw(x)\in\Gamma_n$ force $Dw$ to be rigid? | More generally is it true for Γn where n \in N and n \geq 3? Problem 3. (Threshold regularity of the eikonal equation). A weak consequence of a proof of the Aviles Giga conjecture would be a proof of the following. d Conjecture 1. Let EN T := Φ : S1 \to R2 : dt Φ eit \cdot eit = 0 . Suppose m : Ω \to S1 satisfies div(m)... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,213 | OWR-11101918-013 | Threshold Regularity for the Eikonal Equation | At what Besov regularity threshold do divergence-free solutions $m:\Omega\to S^1$ of the eikonal equation become rigid, and is the threshold exactly $B^{1/3}_{3,\mathrm{loc},\infty}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193](https://doi.org/10.4171/owr/2022/37)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101918-013",
"literature-status:partially-solved",
"owr-year:2022"
] | The Aviles--Giga threshold-rigidity conjecture remains open for general p greater than three, but a 2025 result proves the predicted regularizing effect at p equal to six and slightly below six in a disk setting. | [
{
"url": "https://arxiv.org/abs/2504.20933",
"label": "Lamy--Lorent--Peng, eikonal regularization"
},
{
"url": "https://arxiv.org/abs/2104.01467",
"label": "Lorent--Peng, entropy production"
},
{
"url": "https://doi.org/10.4171/owr/2022/37",
"label": "original Oberwolfach report"
}... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/37 | null | null | null | At what Besov regularity threshold do divergence-free solutions $m:\Omega\to S^1$ of the eikonal equation become rigid, and is the threshold exactly $B^{1/3}_{3,\mathrm{loc},\infty}$? | Problem 3. (Threshold regularity of the eikonal equation). A weak consequence of a proof of the Aviles Giga conjecture would be a proof of the following. d Conjecture 1. Let EN T := Φ : S1 \to R2 : dt Φ eit \cdot eit = 0 . Suppose m : Ω \to S1 satisfies div(m) = 0 in D′ (Ω) and (4) div (Φ (m)) \in Lploc (Ω) for every Φ ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193 |
30,005,214 | OWR-11101919-001 | Unspecified Three-Dimensional Shape Analysis Problem | We will focus on: (1) Mature libraries and software tools that can be used as of 2022, with a clear picture of the current state-of-the-art [3, 4, 5, 6, 7, 8]. (2) New ranges of applications in 3D shape analysis, with a focus on popula- tion analysis [9] and point cloud registration [10]. (3) Open problems that remain ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266](https://doi.org/10.4171/owr/2022/38)
## Literature review (checked 2026-08... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report gives only broad workshop context about three-dimensional shape analysis and states no standalone mathematical target. N) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101919-001",
"literature-status:open",
"owr-year:2022"
] | The extraction is a workshop-scope description rather than a specific mathematical problem, so no determinate claim can be verified and the unresolved item is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/38",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/38 | null | null | null | null | We will focus on: (1) Mature libraries and software tools that can be used as of 2022, with a clear picture of the current state-of-the-art [3, 4, 5, 6, 7, 8]. (2) New ranges of applications in 3D shape analysis, with a focus on popula- tion analysis [9] and point cloud registration [10]. (3) Open problems that remain ... | unrecoverable | The official report gives only broad workshop context about three-dimensional shape analysis and states no standalone mathematical target. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266 |
30,005,215 | OWR-11101919-002 | Norm Estimation from Asymmetric Black-Box Linear Operators | Given black-box access to $x\mapsto Ax$ but not to $A^*$, can $\lVert A\rVert$ be estimated by a provably convergent low-memory method? Likewise, can $\lVert A-V\rVert$ be estimated using only black boxes for $A$ and $V^*$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266](https://doi.org/10.4171/owr/2022/38)
## Literature review (checked 2026-08... | 3 | partially_solved | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-14",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-14] **solved (yes, both parts)**; the dataset currently labels it open. D. A. Lorenz, OWR 38/2022, p. 2251: with only a black box for x ↦ Ax (no adjoint) and little memory, how can ‖A‖ be computed, and ‖A − V‖ from black boxes for A and V∗? J. Bresch, D. A. Lorenz, F. Schneppe,... | [
"owr",
"oberwolfach-reports",
"OWR-11101919-002",
"literature-status:open",
"owr-year:2022"
] | The black-box norm questions are posed as future algorithmic problems in the source, and the checked literature does not provide a general resolution under the stated oracle access. | [
{
"url": "https://doi.org/10.4171/owr/2022/38",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/38 | null | null | null | Given black-box access to $x\mapsto Ax$ but not to $A^*$, can $\lVert A\rVert$ be estimated by a provably convergent low-memory method? Likewise, can $\lVert A-V\rVert$ be estimated using only black boxes for $A$ and $V^*$? | The fact that sometimes linear operators A are available only via black-box implementations, i.e. one can give some input x to a program and gets back a vector Ax, and that the respective adjoint are available via other black-box implementations which give V ∗ y for vectors y raises some other questions: How can one co... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266 |
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