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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,004,116 | OWR-16929-002 | Pseudo-Arithmeticity of Higher-Dimensional Real-Hyperbolic Lattices | For every lattice $\Gamma\subset\operatorname{PO}(n,1)$ with $n\geq4$, is $\Gamma$ pseudo-arithmetic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070](https://doi.org/10.4171/owr/2019/17)
## Literature review (chec... | 3 | open | null | 2,019 | 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-16929-002",
"literature-status:open",
"owr-year:2019"
] | Known reflection and glued-lattice constructions are pseudo-arithmetic, but the cited literature poses pseudo-arithmeticity for arbitrary complex-hyperbolic lattices as an unresolved question. | [
{
"url": "https://arxiv.org/abs/1810.12837",
"label": "Pseudo-arithmetic complex hyperbolic lattices"
},
{
"url": "https://doi.org/10.4171/owr/2019/17",
"label": "Oberwolfach reflection-group report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/17 | null | null | null | For every lattice $\Gamma\subset\operatorname{PO}(n,1)$ with $n\geq4$, is $\Gamma$ pseudo-arithmetic? | For every lattice \Gamma\subset\mathrm{PO}(n,1) with n\ge 4, is \Gamma necessarily pseudo-arithmetic? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070 |
30,004,117 | OWR-16929-003 | Trace Fields of Hyperbolic Link Complements | Which number fields arise as invariant trace fields of hyperbolic link complements? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070](https://doi.org/10.4171/owr/2019/17)
## Literature review (chec... | 3 | open | null | 2,019 | 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-16929-003",
"literature-status:open",
"owr-year:2019"
] | Infinitely many CM fields are realized by explicit families of link complements, but the general classification of number fields that occur as invariant trace fields remains open. | [
{
"url": "https://arxiv.org/abs/1811.00679",
"label": "Invariant trace fields of link complements"
},
{
"url": "https://doi.org/10.4171/owr/2019/17",
"label": "Oberwolfach reflection-group report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/17 | null | null | null | Which number fields arise as invariant trace fields of hyperbolic link complements? | Which number fields arise as invariant trace fields of hyperbolic link complements? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070 |
30,004,118 | OWR-16929-006 | Arithmeticity Problems for Hyperbolic Lattices and Submanifolds | Does there exist a hyperbolic $n$-manifold, with $n\geq4$, containing no arithmetic totally geodesic $m$-submanifold for any $1<m<n$? Is the trace field of every lattice in $\operatorname{PO}(n,1)$, for $n\geq4$, totally real? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070](https://doi.org/10.4171/owr/2019/17)
## Literature review (chec... | 3 | open | null | 2,019 | 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-16929-006",
"literature-status:open",
"owr-year:2019"
] | The record contains three explicit questions about nonarithmetic complex or real hyperbolic lattices; the workshop report still labels all three open, and later constructions do not settle them. | [
{
"url": "https://ems.press/content/serial-article-files/46796",
"label": "Oberwolfach Report 19/2019, selected open problems"
},
{
"url": "https://doi.org/10.2140/agt.2020.20.925",
"label": "Deraux, A new nonarithmetic lattice in PU(3,1)"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/17 | null | null | null | Does there exist a hyperbolic $n$-manifold, with $n\geq4$, containing no arithmetic totally geodesic $m$-submanifold for any $1<m<n$? Is the trace field of every lattice in $\operatorname{PO}(n,1)$, for $n\geq4$, totally real? | Are there infinitely many commensurability classes of non-arithmetic lattices in \mathrm{PU}(2,1); does a hyperbolic n-manifold with n\ge4 exist that contains no arithmetic totally geodesic m-submanifold for any 1<m<n; and is the trace field of every lattice in \mathrm{PO}(n,1), n\ge4, necessarily totally real? | corrected_verified | The clause about nonarithmetic lattices in complex hyperbolic dimension two is subsumed by OWR-16929-001 and was removed; the two distinct arithmeticity questions remain. | null | null | null | null | null | Mini-Workshop: Reflection Groups in Negative Curvature (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/17, pp. 1043--1070 |
30,004,119 | OWR-16930-001 | Percolation Structure in Nearly Optimal Disk Packings | For a packing of unit disks in $\mathbb R^2$ whose density is sufficiently close to that of the triangular-lattice packing, join two centers when their distance is at most $2+\varepsilon$. Under what quantitative density assumptions must the resulting graph contain an infinite connected component? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Crystallisation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/18, pp. 1071--1111](https://doi.org/10.4171/owr/2019/18)
## Literature review (checked 2026-... | 3 | open | null | 2,019 | 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-16930-001",
"literature-status:open",
"owr-year:2019"
] | The hard-disk packing question is the Bowen--Lyons--Radin--Winkler percolation conjecture; available density and Gibbs-state results support it but do not prove the stated assertion for every near-optimal packing model. | [
{
"url": "https://doi.org/10.4171/owr/2019/18",
"label": "Oberwolfach Report 18/2019, Percolation of two-dimensional hard disks"
},
{
"url": "https://doi.org/10.1137/050647785",
"label": "Bowen--Lyons--Radin--Winkler, A solidification phenomenon in random packings"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/18 | null | null | null | For a packing of unit disks in $\mathbb R^2$ whose density is sufficiently close to that of the triangular-lattice packing, join two centers when their distance is at most $2+\varepsilon$. Under what quantitative density assumptions must the resulting graph contain an infinite connected component? | For unit-disk packings in the Euclidean plane, how much can the density differ from the triangular-lattice maximum while retaining analogous structure; in particular, if centers at distance at most 2+\varepsilon are joined, must the resulting graph have an infinite connected component? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mini-Workshop: Mathematics of Crystallisation (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/18, pp. 1071--1111 |
30,004,120 | OWR-16931-001 | Oberwolfach Seating Problem | For sufficiently large n people seated around round tables for (n-1)/2 meals, with n total seats and variable table sizes, does there exist a seating chart in which every pair of people sits next to each other exactly once? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | solved | null | 2,019 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | false | {
"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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "resolution",
"evidence": "published"
} | Unrecoverable OWR statement (The official report explicitly answers the sufficiently-large-order Oberwolfach seating problem affirmatively, so this extraction is a prove) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Glock–Joos–Kim–Kühn–Osthus solve the Oberwolfach problem for sufficiently large admissible orders. That is exactly the asymptotic scope in this record, and the original abstract explicitly reports the affirmative answer.
**What remains.** Small orders outside the stated sufficiently-large range are not claimed by this... | [
{
"url": "https://doi.org/10.4171/jems/1060",
"label": "Glock–Joos–Kim–Kühn–Osthus, Resolution of the Oberwolfach problem (2021)"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--... | 2026-09-28T00:00:00 | Glock–Joos–Kim–Kühn–Osthus, Resolution of the Oberwolfach problem (2021): https://doi.org/10.4171/jems/1060
Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189: https://doi.org/10.4171/owr/2019/19 | https://doi.org/10.4171/owr/2019/19 | null | null | null | null | For sufficiently large n people seated around round tables for (n-1)/2 meals, with n total seats and variable table sizes, does there exist a seating chart in which every pair of people sits next to each other exactly once? | unrecoverable | The official report explicitly answers the sufficiently-large-order Oberwolfach seating problem affirmatively, so this extraction is a proved result rather than an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,121 | OWR-16931-005 | Rational Exponents for Extremal Graph Functions | For every rational number $r\in(1,2)$, does there exist a graph $H$ such that $$\operatorname{ex}(n,H)=\Theta(n^r)$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-005",
"literature-status:open",
"owr-year:2019"
] | The single-graph rational exponents conjecture remains open: later work realizes broad infinite families of rational exponents, but does not prove realizability by one forbidden graph for every rational in the interval. | [
{
"url": "https://doi.org/10.1016/j.jctb.2020.12.003",
"label": "Kang--Kim--Liu, On the rational Turan exponents conjecture"
},
{
"url": "https://arxiv.org/abs/2607.19607",
"label": "Jiang--Longbrake--Yepremyan, Rational exponents near 3/2"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For every rational number $r\in(1,2)$, does there exist a graph $H$ such that $$\operatorname{ex}(n,H)=\Theta(n^r)$$? | Rational exponents conjecture: for every rational r\in(1,2), there exists a graph H such that ex(n,H)=\Theta(n^r). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,122 | OWR-16931-006 | Conlon–Lee Conjecture for Graph Subdivisions | Let $k\geq2$ be even, let $H$ be a graph, and write $H^{k-1}$ for the subdivision obtained by replacing every edge of $H$ with a path having exactly $k-1$ new internal vertices. Does there exist $\delta>0$ such that $$\operatorname{ex}(n,H^{k-1})=O(n^{1+1/k-\delta})$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,019 | 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-16931-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The displayed L-subdivision problem is completely resolved by the stated Corollary 13, but the following Conlon--Lee subdivision conjecture is only proved for bipartite graphs and remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, Theorem 12 and Corollary 13"
},
{
"url": "https://doi.org/10.1093/imrn/rnz088",
"label": "Conlon--Lee, On the extremal number of subdivisions"
},
{
"url": "https://doi.org/10.1007/s00493-020-4202-1",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Let $k\geq2$ be even, let $H$ be a graph, and write $H^{k-1}$ for the subdivision obtained by replacing every edge of $H$ with a path having exactly $k-1$ new internal vertices. Does there exist $\delta>0$ such that $$\operatorname{ex}(n,H^{k-1})=O(n^{1+1/k-\delta})$$? | Conlon--Lee conjecture: for every even integer k\ge2 and every graph H, there exists \delta>0 such that ex(n,H^{k-1})=O(n^{1+1/k-\delta}). | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,123 | OWR-16931-007 | Asymptotics of Online Random Ramsey Numbers | Does the diagonal online random Ramsey number satisfy $$\widetilde r_{\mathrm{rand}}(n,n)=2^{(1+o(1))(2/3)n}$$? For every fixed $m\geq3$, does the off-diagonal number satisfy $$\widetilde r_{\mathrm{rand}}(m,n)=n^{(1+o(1))(2/3)m}$$ as $n\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-007",
"literature-status:open",
"owr-year:2019"
] | The diagonal and off-diagonal online random Ramsey asymptotics are stated as conjectures in the primary paper; its results give lower bounds, not the matching asymptotics. | [
{
"url": "https://arxiv.org/abs/1806.09726",
"label": "Conlon--Fox--Grinshpun--He, Online Ramsey numbers and the subgraph query problem"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Does the diagonal online random Ramsey number satisfy $$\widetilde r_{\mathrm{rand}}(n,n)=2^{(1+o(1))(2/3)n}$$? For every fixed $m\geq3$, does the off-diagonal number satisfy $$\widetilde r_{\mathrm{rand}}(m,n)=n^{(1+o(1))(2/3)m}$$ as $n\to\infty$? | Conjecture: the diagonal online random Ramsey number satisfies \widetilde r_{\rm rand}(n,n)=2^{(1+o(1))(2/3)n}, and for fixed m\ge3 as n\to\infty, \widetilde r_{\rm rand}(m,n)=n^{(1+o(1))(2/3)m}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,124 | OWR-16931-008 | Regular Graph Families with Connected Higher-Order Links | For arbitrary positive integers $a,b,c,d,e$, do there exist infinite families of $(a,b,c,d,e)$-regular graphs in which the links of every vertex, edge, triangle, $K_4$, and $K_5$ are connected? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,019 | 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 | {
"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)**; the dataset currently labels it open. E. Friedgut, OWR 19/2019, p. 1132: are there infinite families of (a,b,c,d,e)-regular graphs whose links of every vertex, edge, triangle, K₄ and K₅ are connected, for some integers (a,b,c,d,e)? E. Friedgut, Y. Iluz, Is... | [
"owr",
"oberwolfach-reports",
"OWR-16931-008",
"literature-status:open",
"owr-year:2019"
] | The record states an explicit open existence question about infinite families of regular graphs with connected links of all listed orders; no primary result located by the check resolves it. | [
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, connected-link regular graphs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For arbitrary positive integers $a,b,c,d,e$, do there exist infinite families of $(a,b,c,d,e)$-regular graphs in which the links of every vertex, edge, triangle, $K_4$, and $K_5$ are connected? | Do there exist infinite families of (a,b,c,d,e)-regular graphs whose links of every order are connected, meaning the neighborhoods of every vertex, edge, triangle, K_4, and K_5 are connected? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,125 | OWR-16931-009 | Explicit RIP Matrices Beyond Square-Root Sparsity | For fixed $\varepsilon>0$, construct explicit real-valued restricted-isometry matrices in the polynomial regime $n=p^{O(1)}$ with sparsity $s\geq n^{1/2+\varepsilon}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-009",
"literature-status:open",
"owr-year:2019"
] | Explicit RIP constructions exist in several polynomial regimes, but the polylogarithmic-dimension regime and the stated real-valued parameter range remain unresolved; the Ramsey-hardness result explains the obstruction rather than solving it. | [
{
"url": "https://doi.org/10.1002/cpa.21873",
"label": "Gamarnik, Explicit construction of RIP matrices is Ramsey-hard"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, RIP matrices"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For fixed $\varepsilon>0$, construct explicit real-valued restricted-isometry matrices in the polynomial regime $n=p^{O(1)}$ with sparsity $s\geq n^{1/2+\varepsilon}$. | Construct explicit real-valued (s,\delta)-RIP matrices in the open square-root-bottleneck regimes, including polylogarithmic or polynomial n and s; in particular, can one achieve s\ge c\sqrt n in the polylogarithmic regime n=\log^{O(1)}p? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,126 | OWR-16931-010 | Square-Root Sparsity for Explicit RIP Matrices | Does there exist an explicit construction of real-valued restricted-isometry matrices with sparsity $s\geq c\sqrt n$ in the polylogarithmic regime $n=(\log p)^{O(1)}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-010",
"literature-status:open",
"owr-year:2019"
] | The cited construction gives an almost-square-root sparsity bound in the polylogarithmic regime, but the record explicitly says that closing the gap to the square-root barrier remains open. | [
{
"url": "https://doi.org/10.1002/cpa.21873",
"label": "Gamarnik, Explicit construction of RIP matrices is Ramsey-hard"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, RIP matrices"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Does there exist an explicit construction of real-valued restricted-isometry matrices with sparsity $s\geq c\sqrt n$ in the polylogarithmic regime $n=(\log p)^{O(1)}$? | Does there exist an explicit construction of real-valued RIP matrices that achieves the square-root sparsity barrier s\ge c\sqrt n in the polylogarithmic regime n=\log^{O(1)}p? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,127 | OWR-16931-012 | Sample Complexity of Vertex-Distribution-Free Graph Testing | Does every extendable hereditary graph property admit a vertex-distribution-free tester whose sample complexity is asymptotically comparable to that of a tester in the standard dense-graph model? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-012",
"literature-status:open",
"owr-year:2019"
] | The VDF paper poses this exact sample-complexity comparison as Problem 5.6 and says it cannot answer it; it proves equality only for several subclasses. | [
{
"url": "https://eccc.weizmann.ac.il/report/2019/083/revision/1/download/",
"label": "Goldreich--Orenstein, Testing properties in the vertex-distribution-free model"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Does every extendable hereditary graph property admit a vertex-distribution-free tester whose sample complexity is asymptotically comparable to that of a tester in the standard dense-graph model? | Does every extendable hereditary graph property P have a VDF tester with the same, or asymptotically comparable, sample complexity as in the standard dense graph model? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,128 | OWR-16931-013 | Restricted Models of Vertex-Distribution-Free Testing | How does vertex-distribution-free graph-property testing change if testers are required to work only on sufficiently large graphs, or if the vertex distribution is restricted by lower or upper bounds on its atom weights? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-013",
"literature-status:open",
"owr-year:2019"
] | This is an incomplete contextual fragment about restricted VDF models; the cited paper resolves some restricted cases but explicitly leaves further characterization questions unresolved. | [
{
"url": "https://eccc.weizmann.ac.il/report/2019/083/revision/1/download/",
"label": "Goldreich--Orenstein, Testing properties in the vertex-distribution-free model"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | How does vertex-distribution-free graph-property testing change if testers are required to work only on sufficiently large graphs, or if the vertex distribution is restricted by lower or upper bounds on its atom weights? | What is the effect on VDF graph-property testing of requiring the tester to work only on sufficiently large graphs, or of forbidding the vertex distribution from assigning extremely small or large weights? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,129 | OWR-16931-017 | Decomposing Complete Graphs into Bounded-Degree Regular Factors | For every \Delta\in\mathbb N, does there exist n_0 such that for all n\ge n_0, whenever F_1,\ldots,F_t are n-vertex r_i-regular graphs with r_i\le\Delta and \sum_i r_i=n-1, the complete graph K_n decomposes into F_1,\ldots,F_t? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report confirms the bounded-degree regular-factor conjecture, but the identical conjecture is already represented by the earlie) | [
"OWR-16763-018"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-017",
"literature-status:open",
"owr-year:2019"
] | The bounded-degree regular-factor decomposition is explicitly presented as a conjecture beyond the large-cycle-factor theorem; no complete proof of the general statement was found. | [
{
"url": "https://doi.org/10.4171/JEMS/1060",
"label": "Glock--Joos--Kim--Kuhn--Osthus, Resolution of the Oberwolfach problem"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, Conjecture 3"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | null | For every \Delta\in\mathbb N, does there exist n_0 such that for all n\ge n_0, whenever F_1,\ldots,F_t are n-vertex r_i-regular graphs with r_i\le\Delta and \sum_i r_i=n-1, the complete graph K_n decomposes into F_1,\ldots,F_t? | unrecoverable | The official report confirms the bounded-degree regular-factor conjecture, but the identical conjecture is already represented by the earlier canonical record OWR-16763-018. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,130 | OWR-16931-018 | Complexity of Approximate Counting in Spin Systems | Determine the worst-case complexity of approximate counting and sampling for the ferromagnetic Potts model and for the hard-core model on bipartite graphs. Do these problems admit polynomial-time algorithms, or are they NP-hard? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16931-018",
"literature-status:open",
"owr-year:2019"
] | The approximate counting and sampling complexity of the ferromagnetic Potts and bipartite hard-core models remains captured by the unresolved intermediate problem #BIS; known reductions and algorithms do not settle its complexity. | [
{
"url": "https://arxiv.org/abs/1702.05543",
"label": "Futorny--Goldberg--Jerrum, A fixed-parameter perspective on #BIS"
},
{
"url": "https://doi.org/10.1016/j.jcss.2014.06.006",
"label": "Chen--Dyer--Goldberg--Jerrum--Lu--McQuillan--Richerby, Conservative counting CSPs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Determine the worst-case complexity of approximate counting and sampling for the ferromagnetic Potts model and for the hard-core model on bipartite graphs. Do these problems admit polynomial-time algorithms, or are they NP-hard? | Determine the worst-case computational complexity of approximate counting and sampling for models such as the ferromagnetic Potts model and the hard-core model on bipartite graphs; in particular, is there a polynomial-time algorithm or an NP-hardness result? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,131 | OWR-16931-019 | Large-Deviation Asymptotics for Triangle Counts | Let $X$ be the number of triangles in $G_{n,p}$. Determine the logarithmic lower-tail asymptotics $$-\log\Pr\!\left(X\leq(1-\delta)\mathbb EX\right)$$ throughout the unresolved sparse regimes, particularly when $p=O(n^{-1/2})$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-019",
"literature-status:open",
"owr-year:2019"
] | Dense and off-critical regimes are understood and the critical window has substantial new partial results, but the general triangle lower-tail logarithmic asymptotics remain unresolved. | [
{
"url": "https://arxiv.org/abs/2411.18563",
"label": "Jenssen--Perkins--Potukuchi--Simkin, Lower tails for triangles inside the critical window"
},
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, triangle lower tails"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Let $X$ be the number of triangles in $G_{n,p}$. Determine the logarithmic lower-tail asymptotics $$-\log\Pr\!\left(X\leq(1-\delta)\mathbb EX\right)$$ throughout the unresolved sparse regimes, particularly when $p=O(n^{-1/2})$. | Determine the asymptotics of -\log\Pr(X\ge(1+\delta)\mathbb E X) and -\log\Pr(X\le(1-\delta)\mathbb E X) when X is the number of triangles in G_{n,p}, including the sparse regime p\to0. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,132 | OWR-16931-021 | Antiferromagnetic Homomorphism Bounds Without Triangle-Freeness | Let $H$ be a weighted graph whose edge-weight matrix has at most one positive eigenvalue. Can the triangle-free assumption on a $d$-regular graph $G$ be removed from the reverse-Sidorenko homomorphism inequality for $\operatorname{hom}(G,H)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-021",
"literature-status:open",
"owr-year:2019"
] | The anti-ferromagnetic extension is still a conjecture in the original reverse-Sidorenko paper; 2025 Lorentzian-polynomial work proves important subclasses but not all antiferromagnetic targets and source graphs. | [
{
"url": "https://doi.org/10.4171/owr/2019/19",
"label": "Oberwolfach Report 19/2019, weighted homomorphisms"
},
{
"url": "https://arxiv.org/abs/2506.13659",
"label": "Lee--Oh--Seo, Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Let $H$ be a weighted graph whose edge-weight matrix has at most one positive eigenvalue. Can the triangle-free assumption on a $d$-regular graph $G$ be removed from the reverse-Sidorenko homomorphism inequality for $\operatorname{hom}(G,H)$? | If H is anti-ferromagnetic, meaning all eigenvalues of its edge-weight matrix except the top one are nonpositive, is the triangle-free hypothesis on G removable from the homomorphism inequality for d-regular graphs? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,133 | OWR-16931-022 | Polynomial Induced Removal Bounds for Graph Pairs | For graphs $H_1,H_2$, let $\delta_{H_1,H_2}(\varepsilon)$ be the largest $\delta$ such that every graph that is $\delta$-close to being induced-$H_i$-free for each $i\in\{1,2\}$ is $\varepsilon$-close to being induced-$\{H_1,H_2\}$-free. Is $\delta_{H_1,H_2}(\varepsilon)$ polynomial in $\varepsilon$ for every pair? For... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,019 | 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-16931-022",
"literature-status:partially-solved",
"owr-year:2019"
] | Polynomial induced-removal bounds are known in special cases, including a positive exponent-two instance, and later work gives further polynomial results for ordered graphs. The general all-pairs polynomial bound and the claimed exponent question remain unresolved. | [
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/47388107-8726-4158-8c92-21a2323c2cf7/content",
"label": "Oberwolfach problem report"
},
{
"url": "https://arxiv.org/abs/2110.03577",
"label": "Polynomial ordered-graph removal"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For graphs $H_1,H_2$, let $\delta_{H_1,H_2}(\varepsilon)$ be the largest $\delta$ such that every graph that is $\delta$-close to being induced-$H_i$-free for each $i\in\{1,2\}$ is $\varepsilon$-close to being induced-$\{H_1,H_2\}$-free. Is $\delta_{H_1,H_2}(\varepsilon)$ polynomial in $\varepsilon$ for every pair? For... | For graphs H_1,H_2 and the parameter \delta_{H_1,H_2}(\varepsilon) defined by induced-freeness testing, is \delta_{H_1,H_2}(\varepsilon)=\operatorname{poly}(\varepsilon) for every pair; and for every a>0 do there exist H_1,H_2 with \delta_{H_1,H_2}(\varepsilon)\le O(\varepsilon^a)? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,134 | OWR-16931-023 | Second-Order Cut Bounds for Uniform Hypergraphs | Fix integers $k\geq r\geq2$, with either $r\geq3$ or $k\geq4$. Does every $k$-uniform hypergraph with $m$ edges have an $r$-cut of size at least $$\alpha_{r,k}m+\Omega(m^{2/3}),\qquad \alpha_{r,k}=\frac{S(k,r)r!}{r^k}$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | partially_solved | null | 2,019 | 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-16931-023",
"literature-status:partially-solved",
"owr-year:2019"
] | The exact conjectured order m^{2/3} bound is not known in general. Special cases have stronger bounds, and recent work proves an approximate m^{2/3-epsilon} result in broad ranges, so the conjecture has substantial but incomplete progress. | [
{
"url": "https://arxiv.org/abs/1803.08462",
"label": "Conlon--Fox--Kwan--Sudakov"
},
{
"url": "https://arxiv.org/abs/2511.08501",
"label": "Janzer--Portier"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Fix integers $k\geq r\geq2$, with either $r\geq3$ or $k\geq4$. Does every $k$-uniform hypergraph with $m$ edges have an $r$-cut of size at least $$\alpha_{r,k}m+\Omega(m^{2/3}),\qquad \alpha_{r,k}=\frac{S(k,r)r!}{r^k}$$? | For fixed k\ge r\ge2 with r\ge3 or k\ge4, does every k-uniform hypergraph with m edges have an r-cut of size at least \alpha_{r,k}m+\Omega(m^{2/3}), where \alpha_{r,k}=S(k,r)r!/r^k? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,135 | OWR-16931-024 | Long Increasing Paths in Edge-Ordered Graphs | Does there exist $\varepsilon>0$ such that every edge-ordered graph $G$ contains an increasing path of length $$\Omega\!\left((e(G)/|V(G)|)^{1/2+\varepsilon}\right)$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-024",
"literature-status:open",
"owr-year:2019"
] | Nearly linear monotone paths are proved for complete graphs and for reasonably dense edge-ordered graphs, but the fixed-average-degree sparse regime in the stated problem remains unresolved. | [
{
"url": "https://arxiv.org/abs/1809.01468",
"label": "Bucic--Kwan--Pokrovskiy--Sudakov--Tran--Wagner"
},
{
"url": "https://people.math.ethz.ch/~sudakovb/monotone-path-complete-graph.pdf",
"label": "Published paper"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Does there exist $\varepsilon>0$ such that every edge-ordered graph $G$ contains an increasing path of length $$\Omega\!\left((e(G)/|V(G)|)^{1/2+\varepsilon}\right)$$? | Does there exist \varepsilon>0 such that every edge-ordered graph G has an increasing path of length \Omega((e(G)/|G|)^{1/2+\varepsilon})? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,136 | OWR-16931-025 | Equality of List and Ordinary Ramsey Numbers | For the list Ramsey number $R_L$, is $$R_L(K_k,2)=R(K_k,2)$$ for every $k$, and is $$R_L(K_3,r)=R(K_3,r)$$ for every $r$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-025",
"literature-status:open",
"owr-year:2019"
] | The list-Ramsey literature gives bounds and examples, but equality with the ordinary Ramsey number is still not decided even for the relevant clique cases. The two equality questions therefore remain open. | [
{
"url": "https://arxiv.org/abs/1902.07018",
"label": "List Ramsey numbers"
},
{
"url": "https://doi.org/10.1002/jgt.22610",
"label": "Journal of Graph Theory version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For the list Ramsey number $R_L$, is $$R_L(K_k,2)=R(K_k,2)$$ for every $k$, and is $$R_L(K_3,r)=R(K_3,r)$$ for every $r$? | For list Ramsey numbers, are R_L(K_k,2)=R(K_k,2) for every k, and is R_L(K_3,r)=R(K_3,r) for every r? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,137 | OWR-16931-026 | Giant Components in Nonlinear Degree-Dependent Random Graphs | Determine the emergence and size of the giant component in the degree-dependent random-graph processes $G^f_{n,m}$ and $G^{f,*}_{n,m}$ when the attachment function $f$ is genuinely nonlinear. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-026",
"literature-status:open",
"owr-year:2019"
] | Giant-component behavior is understood for several linear or specially structured degree-dependent attachment rules, but the stated genuinely nonlinear preferential-attachment problem is not settled in general. | [
{
"url": "https://arxiv.org/abs/1904.11861",
"label": "Janson--Warnke"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/47388107-8726-4158-8c92-21a2323c2cf7/download",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | Determine the emergence and size of the giant component in the degree-dependent random-graph processes $G^f_{n,m}$ and $G^{f,*}_{n,m}$ when the attachment function $f$ is genuinely nonlinear. | Study the giant-component transition in the degree-dependent random graph processes G_{n,m}^f and G_{n,m}^{f,*} when the attachment function f is genuinely nonlinear. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,138 | OWR-16931-027 | Ramsey Bounds for Edge-Ordered Graphs | For every edge-ordered graph $H$ on $n$ vertices, is $$r_{\mathrm{edge}}(H)=2^{O(n)}$$? If $H$ is also $d$-degenerate, is $$r_{\mathrm{edge}}(H)=O(C(d)n)$$ for some function $C$ depending only on $d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189](https://doi.org/10.4171/owr/2019/19)
## Literature review (checked 2026-08-22... | 3 | open | null | 2,019 | 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-16931-027",
"literature-status:open",
"owr-year:2019"
] | Known general bounds for edge-ordered Ramsey numbers and polynomial bounds for bounded-degeneracy graphs do not establish the conjectured exponential vertex bound or the stated linear-in-n bounded-degeneracy bound. No proof or counterexample to these assertions is known. | [
{
"url": "https://arxiv.org/abs/1906.08234",
"label": "Fox--Li"
},
{
"url": "https://arxiv.org/abs/1906.08698",
"label": "Balko--Vizer"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/19 | null | null | null | For every edge-ordered graph $H$ on $n$ vertices, is $$r_{\mathrm{edge}}(H)=2^{O(n)}$$? If $H$ is also $d$-degenerate, is $$r_{\mathrm{edge}}(H)=O(C(d)n)$$ for some function $C$ depending only on $d$? | For every edge-ordered graph H on n vertices, is r_{\rm edge}(H)=2^{O(n)}; and for every d-degenerate edge-ordered H on n vertices, is r_{\rm edge}(H)=O(C(d)n)? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Combinatorics, Probability and Computing (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/19, pp. 1113--1189 |
30,004,139 | OWR-16933-001 | Lefschetz Properties of PL Sphere Face Rings | Let $\Sigma$ be a piecewise-linear $(d-1)$-sphere with graded face ring $R[\Sigma]$. Are there open dense sets of Artinian reductions $A(\Sigma)$ and degree-one elements $\ell$ such that, for every $k\leq d/2$, multiplication by $\ell^{d-2k}$ gives an isomorphism $A^k(\Sigma)\to A^{d-k}(\Sigma)$ and the form $Q_{\ell,k... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-16933-001",
"literature-status:open",
"owr-year:2019"
] | The extracted record is a malformed fragment beginning with a conjecture marker and does not identify one precise remaining claim. The cited generic Lefschetz theorem settles the displayed generic result, but the broader fragment cannot be classified as solved; under the stated rule it is open. | [
{
"url": "https://webusers.imj-prg.fr/~karim.adiprasito/bpa.pdf",
"label": "Adiprasito"
},
{
"url": "https://oa.tib.eu/renate/bitstreams/c7cf2c12-9287-45b9-8906-bd4f4d10a9da/download",
"label": "Oberwolfach problem report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | Let $\Sigma$ be a piecewise-linear $(d-1)$-sphere with graded face ring $R[\Sigma]$. Are there open dense sets of Artinian reductions $A(\Sigma)$ and degree-one elements $\ell$ such that, for every $k\leq d/2$, multiplication by $\ell^{d-2k}$ gives an isomorphism $A^k(\Sigma)\to A^{d-k}(\Sigma)$ and the form $Q_{\ell,k... | For a PL (d-1)-sphere \Sigma with graded face ring R[\Sigma], there are open dense sets of Artinian reductions and degree-one elements \ell such that, for k\le d/2, multiplication by \ell^{d-2k}:A^k(\Sigma)\to A^{d-k}(\Sigma) is an isomorphism, and Q_{\ell,k}(a,b)=\deg(ab\ell^{d-2k}) is nondegenerate on every squarefre... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,140 | OWR-16933-002 | Positivity Criteria for Tropical Tori | For a tropical torus $X=\mathbb{R}^n/\Lambda$, determine whether the positivity criterion for representing an integral (1,1)-class by an effective tropical cycle can be inverted, whether tropical analogues of the Nakai–Moishezon and Kleiman criteria exist, and which hypersurface combinatorial types allow large or small... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-16933-002",
"literature-status:open",
"owr-year:2019"
] | The report poses positivity, tropical Nakai--Moishezon or Kleiman, and Picard-rank criteria as open directions. The literature checked does not provide a general theorem resolving these questions. | [
{
"url": "https://ems.press/content/serial-article-files/46800",
"label": "Tropical geometry problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | For a tropical torus $X=\mathbb{R}^n/\Lambda$, determine whether the positivity criterion for representing an integral (1,1)-class by an effective tropical cycle can be inverted, whether tropical analogues of the Nakai–Moishezon and Kleiman criteria exist, and which hypersurface combinatorial types allow large or small... | For a tropical torus X=\mathbb{R}^n/\Lambda, determine whether the positivity criterion for representing an integral (1,1)-class by an effective tropical cycle can be inverted, whether tropical analogues of the Nakai--Moishezon and Kleiman criteria exist, and which hypersurface combinatorial types allow large or small ... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,141 | OWR-16933-003 | Compactifying Lagrangian Lifts of Tropical Hypersurfaces | When a tropical hypersurface in a toric moment polytope meets the boundary, determine whether its Lagrangian lift compactifies to a smooth Lagrangian submanifold without boundary. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-16933-003",
"literature-status:open",
"owr-year:2019"
] | Tropical Lagrangian constructions give smooth families in low-dimensional torus settings, but a general smooth boundaryless compactification inside the toric polytope is not established. | [
{
"url": "https://ems.press/content/serial-article-files/46800",
"label": "Tropical geometry problem report"
},
{
"url": "https://doi.org/10.1007/s00029-020-00614-1",
"label": "Tropical Lagrangians in toric del-Pezzo surfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | When a tropical hypersurface in a toric moment polytope meets the boundary, determine whether its Lagrangian lift compactifies to a smooth Lagrangian submanifold without boundary. | When a tropical hypersurface in a toric moment polytope meets the boundary, determine whether its Lagrangian lift compactifies to a smooth Lagrangian submanifold without boundary. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,142 | OWR-16933-004 | Lagrangian Sphere Generators for Quintic-Type Fourfolds | Let $X$ be a symplectic four-dimensional manifold diffeomorphic to a quintic in $\mathbb P^4$ and equipped with a Lagrangian fibration. Can tropical hypersurfaces in the base be lifted to enough Lagrangian spheres to generate $H_3(X,\mathbb Z)$, which has rank $204$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,019 | 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-16933-004",
"literature-status:partially-solved",
"owr-year:2019"
] | Tropical constructions in the mirror quintic produce closed embedded Lagrangian rational homology spheres and more than 300 mutually disjoint examples. They do not establish the stated generation of H3 by the requested family of 204 Lagrangian spheres. | [
{
"url": "https://arxiv.org/abs/1904.11780",
"label": "Mak--Ruddat"
},
{
"url": "https://doi.org/10.1017/fms.2020.54",
"label": "Forum of Mathematics Sigma version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | Let $X$ be a symplectic four-dimensional manifold diffeomorphic to a quintic in $\mathbb P^4$ and equipped with a Lagrangian fibration. Can tropical hypersurfaces in the base be lifted to enough Lagrangian spheres to generate $H_3(X,\mathbb Z)$, which has rank $204$? | For a symplectic four-dimensional manifold X diffeomorphic to a quintic in \mathbb{P}^4 with a Lagrangian fibration, can tropical hypersurfaces in the base be lifted to enough Lagrangian spheres to generate H_3(X,\mathbb{Z}), which has rank 204? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,143 | OWR-16933-005 | Fundamental Groups of Tropical Curves | For a connected abstract tropical curve represented by a weighted finite metric graph, define a fundamental-group theory, including graph-of-groups constructions that classify covers, harmonic morphisms, and realizations of admissible covers. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | open | null | 2,019 | 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-16933-005",
"literature-status:open",
"owr-year:2019"
] | The underlying graph has an ordinary free fundamental group, but tropical curves admit graph-of-groups, stack, and orbifold interpretations with different fundamental groups. A unique general notion answering the question has not been established. | [
{
"url": "https://ems.press/content/serial-article-files/46800",
"label": "Tropical geometry problem report"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-021-00651-4",
"label": "Non-Archimedean graph-of-groups fundamental groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | For a connected abstract tropical curve represented by a weighted finite metric graph, define a fundamental-group theory, including graph-of-groups constructions that classify covers, harmonic morphisms, and realizations of admissible covers. | For a connected abstract tropical curve given by a weighted finite metric graph, what is its appropriate fundamental group, including the graph-of-groups constructions that classify covers, harmonic morphisms, or realizations of admissible covers? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,144 | OWR-16933-006 | Motion and Trace of Real Divisors | Let $X$ be a nonsingular projective real algebraic curve and let $A$ be a simple real divisor. How can $A$ move within its linear-equivalence class while remaining simple and real? What is $\pi_1(\operatorname{Emb}(A,X))$, and what can be the image of its trace homomorphism to $H_1(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,019 | 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-16933-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The real-divisor trace theorem determines important cases of motion within a linear equivalence class, including when the trace is trivial or infinite cyclic. The full fundamental group of the embedding space is not determined in general. | [
{
"url": "https://ems.press/content/serial-article-files/46800",
"label": "Tropical geometry problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | Let $X$ be a nonsingular projective real algebraic curve and let $A$ be a simple real divisor. How can $A$ move within its linear-equivalence class while remaining simple and real? What is $\pi_1(\operatorname{Emb}(A,X))$, and what can be the image of its trace homomorphism to $H_1(X)$? | Given a nonsingular projective real algebraic curve X and a simple real divisor A, how can A move within its linear equivalence class while remaining simple and real, what is \pi_1(\operatorname{Emb}(A,X)), and what can be the image of its trace homomorphism to H_1(X)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,145 | OWR-16933-007 | Embedding Spaces of Divisors on Real Cubics | Let $X$ be a plane projective $M$-curve of degree $3$, and let $A$ be a transverse real divisor of degree $9$. Is $\pi_1(\operatorname{Emb}(A,X))$ trivial, and how does the answer depend on the distribution of $A$ among the connected components of $X(\mathbb R)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308](https://doi.org/10.4171/owr/2019/21)
## Literature review (checked 2026-08-22)
**St... | 3 | partially_solved | null | 2,019 | 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-16933-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The trace-homomorphism theorem and explicit low-degree cases resolve substantial instances of the embedding-space question. A general proof that the fundamental group is trivial, or a complete description when it is not, remains unavailable. | [
{
"url": "https://ems.press/content/serial-article-files/46800",
"label": "Tropical geometry problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/21 | null | null | null | Let $X$ be a plane projective $M$-curve of degree $3$, and let $A$ be a transverse real divisor of degree $9$. Is $\pi_1(\operatorname{Emb}(A,X))$ trivial, and how does the answer depend on the distribution of $A$ among the connected components of $X(\mathbb R)$? | For a plane projective M-curve X of degree 3 and a transverse real divisor A of degree 9, determine whether \pi_1(\operatorname{Emb}(A,X)) is trivial; the answer may depend on the placement of A among the components of RX. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Tropical Geometry: new directions (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/21, pp. 1245--1308 |
30,004,146 | OWR-16935-005 | Moduli Spaces of Higgs Harder–Narasimhan Strata | Can coarse moduli spaces be constructed for Higgs Harder–Narasimhan strata and ordinary Harder–Narasimhan strata? Do the refined strata carry comparably rich geometry, including compatible group actions and Hitchin fibrations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometry and Physics of Higgs Bundles (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/23, pp. 1357--1417](https://doi.org/10.4171/owr/2019/23)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,019 | 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-16935-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Non-reductive GIT constructs refined Harder--Narasimhan and Hesselink--Harder--Narasimhan stratifications with quasi-projective coarse moduli spaces and projective completions. This does not fully settle the question for the unrefined strata in the stated generality. | [
{
"url": "https://arxiv.org/abs/1911.13194",
"label": "Hamilton"
},
{
"url": "https://ora.ox.ac.uk/objects/uuid:6267baf5-3fde-405a-abc7-7618b0439e98",
"label": "Oxford thesis record"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/23 | null | null | null | Can coarse moduli spaces be constructed for Higgs Harder–Narasimhan strata and ordinary Harder–Narasimhan strata? Do the refined strata carry comparably rich geometry, including compatible group actions and Hitchin fibrations? | Can coarse moduli spaces be constructed for the Higgs Harder--Narasimhan and Harder--Narasimhan strata, and do the refined strata have comparably rich geometric structures, including compatible actions and Hitchin fibrations? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Geometry and Physics of Higgs Bundles (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/23, pp. 1357--1417 |
30,004,147 | OWR-16936-001 | Uniqueness of Rough Continuity Equations | For the continuity equation $\partial_tu+\operatorname{div}(bu)=0$ in $d$ dimensions, with bounded divergence-free $b\in W^{1,p}$ and $u\in L^q$, are distributional solutions unique and Lagrangian throughout the regime $1<1/p+1/q<1+1/d$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/24, pp. 1419--1497](https://doi.org/10.4171/owr/2019/24)
## Literature rev... | 3 | partially_solved | null | 2,019 | 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-16936-001",
"literature-status:partially-solved",
"owr-year:2019"
] | The continuity-equation literature proves uniqueness and Lagrangianity under several hypotheses, including important lack-of-integrability regimes. The report's stated range has only partial results, so the full distributional claim remains unresolved. | [
{
"url": "https://arxiv.org/abs/1608.04324",
"label": "Caravenna--Crippa"
},
{
"url": "https://doi.org/10.1016/j.crma.2016.10.009",
"label": "Comptes Rendus version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/24 | null | null | null | For the continuity equation $\partial_tu+\operatorname{div}(bu)=0$ in $d$ dimensions, with bounded divergence-free $b\in W^{1,p}$ and $u\in L^q$, are distributional solutions unique and Lagrangian throughout the regime $1<1/p+1/q<1+1/d$? | For the continuity equation \partial_tu+\operatorname{div}(bu)=0 in d dimensions, with bounded divergence-free b\in W^{1,p} and u\in L^q, are distributional solutions unique and Lagrangian throughout the regime 1<1/p+1/q<1+1/d? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/24, pp. 1419--1497 |
30,004,148 | OWR-16936-002 | Anomalous Dissipation in Stochastic Navier–Stokes Equations | Do there exist stationary martingale solutions of the three-dimensional stochastic Navier–Stokes equations on $\mathbb{T}^3$ satisfying weak anomalous dissipation, $\lim_{\nu\to0}\nu\mathbb{E}\lVert u\rVert_{L^2_x}^2=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/24, pp. 1419--1497](https://doi.org/10.4171/owr/2019/24)
## Literature rev... | 3 | open | null | 2,019 | 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-16936-002",
"literature-status:open",
"owr-year:2019"
] | The four-fifths-law result is conditional on the weak anomalous dissipation property, while existence of suitable Navier--Stokes solutions or sequences satisfying that property is explicitly left open. | [
{
"url": "https://arxiv.org/abs/1803.09695",
"label": "Bedrossian--Coti Zelati--Punshon-Smith--Weber"
},
{
"url": "https://ems.press/content/serial-article-files/46803",
"label": "Oberwolfach problem report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/24 | null | null | null | Do there exist stationary martingale solutions of the three-dimensional stochastic Navier–Stokes equations on $\mathbb{T}^3$ satisfying weak anomalous dissipation, $\lim_{\nu\to0}\nu\mathbb{E}\lVert u\rVert_{L^2_x}^2=0$? | Do there exist stationary martingale solutions of the three-dimensional stochastic Navier--Stokes equations on \mathbb{T}^3 satisfying weak anomalous dissipation, \lim_{\nu\to0}\nu\mathbb{E}\lVert u\rVert_{L^2_x}^2=0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Nonlinear Hyperbolic Problems: Modeling, Analysis, and Numerics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/24, pp. 1419--1497 |
30,004,149 | OWR-16937-001 | Causal Discovery from Partially Observed Event Processes | When only some coordinates of a multivariate event process are observed, what aspects of the causal structure can be learned from the induced local-independence model? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571](https://doi.org/10.4171/owr/2019/25)
## Literature review (checked 2... | 3 | partially_solved | null | 2,019 | 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-16937-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Marginalized local-independence graphs, mu-separation, and Markov-equivalence results provide a framework for partial observation. General identification of causal structure from only some observed process coordinates remains incomplete. | [
{
"url": "https://projecteuclid.org/journals/annals-of-statistics/volume-48/issue-1/Markov-equivalence-of-marginalized-local-independence-graphs/10.1214/19-AOS1821.pdf",
"label": "Mogensen--Hansen"
},
{
"url": "https://nrhstat.org/publication/2018-uai/2018-uai.pdf",
"label": "Hansen--Mogensen--M... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/25 | null | null | null | When only some coordinates of a multivariate event process are observed, what aspects of the causal structure can be learned from the induced local-independence model? | When only some coordinates of a multivariate event process are observed, what aspects of the causal structure can be learned from the induced local-independence model? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571 |
30,004,150 | OWR-16937-002 | Distinguishing Confounding from Estimation Noise | When an estimated regression vector $\hat a$ differs from the causal vector $a$ because of either finite-sample noise or confounding, why should algorithms distinguish the two causes, and can regularization mitigate confounding as it mitigates overfitting? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571](https://doi.org/10.4171/owr/2019/25)
## Literature review (checked 2... | 3 | partially_solved | null | 2,019 | 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-16937-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Causal regularization shows in an explicit multivariate confounder model why confounding can resemble overfitting and proves a corresponding generalization bound. The broad question outside those assumptions is not fully resolved. | [
{
"url": "https://arxiv.org/abs/1906.12179",
"label": "Janzing"
},
{
"url": "https://papers.nips.cc/paper/9432-causal-regularization",
"label": "NeurIPS version"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/25 | null | null | null | When an estimated regression vector $\hat a$ differs from the causal vector $a$ because of either finite-sample noise or confounding, why should algorithms distinguish the two causes, and can regularization mitigate confounding as it mitigates overfitting? | When an estimated regression vector \hat a differs from the causal vector a because of either finite-sample noise or confounding, why should algorithms distinguish the two causes, and can regularization mitigate confounding as it mitigates overfitting? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571 |
30,004,151 | OWR-16937-003 | Identifiable Longitudinal Causal Mediation | Develop identifiable causal mediation effects for a longitudinal mediator process and a survival outcome by separating treatment paths with an augmented directed acyclic graph, avoiding the ill-defined nested counterfactual and post-treatment-confounding problems. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571](https://doi.org/10.4171/owr/2019/25)
## Literature review (checked 2... | 3 | partially_solved | null | 2,019 | 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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"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-16937-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Interventionist and separable-effects frameworks formalize alternative treatment paths and give identification results under explicit assumptions. They address important mediation settings but do not resolve the general path-specific causal question. | [
{
"url": "https://arxiv.org/abs/2008.06019",
"label": "Robins--Richardson"
},
{
"url": "https://arxiv.org/abs/1901.09472",
"label": "Separable effects"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/25 | null | null | null | Develop identifiable causal mediation effects for a longitudinal mediator process and a survival outcome by separating treatment paths with an augmented directed acyclic graph, avoiding the ill-defined nested counterfactual and post-treatment-confounding problems. | Develop identifiable causal mediation effects for a longitudinal mediator process and a survival outcome by separating treatment paths with an augmented directed acyclic graph, avoiding the ill-defined nested counterfactual and post-treatment-confounding problems. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571 |
30,004,152 | OWR-16937-004 | Generalization across Repeatedly Constructed Test Sets | What does good performance on a held-out test set imply about performance on a new test set created from the same data source and cleaning protocol, and how can such generalization be characterized? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571](https://doi.org/10.4171/owr/2019/25)
## Literature review (checked 2... | 3 | partially_solved | null | 2,019 | 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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"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-16937-004",
"literature-status:partially-solved",
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] | On ImageNet and CIFAR, new test sets reduce absolute accuracy while largely preserving model rankings and relative improvements; relative difficulty explains much of the apparent failure. This is strong empirical evidence, not a universal theorem about all test-set shifts. | [
{
"url": "https://arxiv.org/abs/1902.10811",
"label": "Recht--Roelofs--Schmidt--Shankar"
},
{
"url": "https://proceedings.mlr.press/v119/shankar20c/shankar20c.pdf",
"label": "Shankar et al."
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/25 | null | null | null | What does good performance on a held-out test set imply about performance on a new test set created from the same data source and cleaning protocol, and how can such generalization be characterized? | What does good performance on a held-out test set imply about performance on a new test set created from the same data source and cleaning protocol, and how can such generalization be characterized? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Foundations and new horizons for causal inference (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/25, pp. 1499--1571 |
30,004,153 | OWR-16938-001 | Automatic Recognition of Numerically Unstable Quadratic Programs | Consider a quadratically constrained quadratic program with $$ (x_1-1)^2+x_2^2\geq3+s^2,\qquad a_i-a_{i-1}^2=0,\qquad a_0=s/2,$$ where a finite chain of the $a_i$ amplifies numerical error through repeated square roots. How can solvers automatically recognize such severely ill-conditioned instances? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637](https://doi.org/10.4171/owr/2019/26)
## Litera... | 3 | open | null | 2,019 | 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,
"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-16938-001",
"literature-status:open",
"owr-year:2019"
] | The extracted question is a broad, underspecified request about automatic recognition of mixed-integer nonlinear optimization problems; no determinate mathematical claim or general solution is stated. | [
{
"url": "https://doi.org/10.4171/owr/2019/26",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/26 | null | null | null | Consider a quadratically constrained quadratic program with $$ (x_1-1)^2+x_2^2\geq3+s^2,\qquad a_i-a_{i-1}^2=0,\qquad a_0=s/2,$$ where a finite chain of the $a_i$ amplifies numerical error through repeated square roots. How can solvers automatically recognize such severely ill-conditioned instances? | For the QCQP instance with (x_1-1)^2+x_2^2\ge3+s^2 and recursively constrained square-root variables, how can numerically unstable solver instances be recognized automatically? | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637 |
30,004,154 | OWR-16938-002 | Exact Higher-Order Matrix Decomposability | Given a matrix $Q$ and an integer $k>2$, find necessary and sufficient conditions for $Q$ to admit an exact $k\times k$ decomposition into positive-semidefinite principal-block contributions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637](https://doi.org/10.4171/owr/2019/26)
## Litera... | 3 | open | null | 2,019 | 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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"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-16938-002",
"literature-status:open",
"owr-year:2019"
] | The report gives a characterization for exact 2\times2 decompositions but explicitly leaves conditions for exact k\timesk decomposability with k greater than 2 open; no general criterion was found. | [
{
"url": "https://doi.org/10.4171/owr/2019/26",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/26 | null | null | null | Given a matrix $Q$ and an integer $k>2$, find necessary and sufficient conditions for $Q$ to admit an exact $k\times k$ decomposition into positive-semidefinite principal-block contributions. | For a given matrix Q, develop necessary and sufficient conditions for exact k\times k decomposability when k>2. | corrected_verified | The official Oberwolfach report was checked directly; the clean statement preserves the mathematical target while restoring definitions and removing source-dependent wording. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637 |
30,004,155 | OWR-16938-003 | Vizing's Conjecture and Algebraic Sum-of-Squares Certificates | Prove Vizing's conjecture for arbitrary graphs, and develop symmetry-reduced or Gröbner-basis-free sum-of-squares and semidefinite certificates for its algebraic formulation at larger parameter values. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637](https://doi.org/10.4171/owr/2019/26)
## Litera... | 3 | open | null | 2,019 | 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"
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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-16938-003",
"literature-status:open",
"owr-year:2019"
] | Vizing's conjecture remains unresolved for arbitrary graphs; recent work proves only improved constant-factor lower bounds and the SOS formulation does not constitute a proof of the conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2019/26",
"label": "OWR primary report"
},
{
"url": "https://arxiv.org/abs/2606.14414",
"label": "constant-factor progress on Vizing's conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/26 | null | null | null | Prove Vizing's conjecture for arbitrary graphs, and develop symmetry-reduced or Gröbner-basis-free sum-of-squares and semidefinite certificates for its algebraic formulation at larger parameter values. | Determine whether Vizing's conjecture holds, and develop symmetry-based or Groebner-basis-free sum-of-squares and semidefinite certificates for larger parameter values in its algebraic formulation. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637 |
30,004,156 | OWR-16938-004 | Maximum Equiangular Line Systems in Euclidean Space | Determine the maximum number of pairwise equiangular lines in $\mathbb R^n$, both without fixing the common angle and for each prescribed common angle. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637](https://doi.org/10.4171/owr/2019/26)
## Litera... | 3 | open | null | 2,019 | 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"
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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-16938-004",
"literature-status:open",
"owr-year:2019"
] | The maximum number of equiangular lines is known in many dimensions and has strong general bounds, but exact values remain unknown in general, including unresolved dimensions documented in current primary work. | [
{
"url": "https://doi.org/10.4171/owr/2019/26",
"label": "OWR primary report"
},
{
"url": "https://arxiv.org/abs/2002.08085",
"label": "equiangular lines in low dimensions"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/26 | null | null | null | Determine the maximum number of pairwise equiangular lines in $\mathbb R^n$, both without fixing the common angle and for each prescribed common angle. | Determine the maximum number of pairwise equiangular lines that can exist in n-dimensional Euclidean space, for general n and prescribed common angle. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637 |
30,004,157 | OWR-16938-005 | Semidefinite Hierarchies for Equiangular Line Bounds | For the $k$-point semidefinite-programming bounds $\Delta_k(G_{n,a})^*$ for equiangular lines, explain their stabilization at $$(1/a^2-2)(1/a^2-1)/2,$$ determine whether $\Delta_k(G_{n,a})^*=\Theta(n^2)$ for fixed $k$ and $a$, and compare the corresponding level-$\alpha$ bound with the Lasserre hierarchy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637](https://doi.org/10.4171/owr/2019/26)
## Litera... | 3 | open | null | 2,019 | 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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"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-16938-005",
"literature-status:open",
"owr-year:2019"
] | These three asymptotic and hierarchy-comparison questions are stated as open in the source, and no primary result located by the cutoff settles them in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/26",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/26 | null | null | null | For the $k$-point semidefinite-programming bounds $\Delta_k(G_{n,a})^*$ for equiangular lines, explain their stabilization at $$(1/a^2-2)(1/a^2-1)/2,$$ determine whether $\Delta_k(G_{n,a})^*=\Theta(n^2)$ for fixed $k$ and $a$, and compare the corresponding level-$\alpha$ bound with the Lasserre hierarchy. | For the k-point semidefinite-programming bounds \Delta_k(G_{n,a})^* for the equiangular-line graph, explain their stabilization at (1/a^2-2)(1/a^2-1)/2, determine whether \Delta_k(G_{n,a})^*=\Theta(n^2) for fixed k and a, and compare the corresponding alpha-level bound with the Lasserre hierarchy. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/26, pp. 1573--1637 |
30,004,158 | OWR-16939-002 | Theta Function Rings and Symplectic Cohomology | Let $(M,D)$ be a positive maximally degenerate pair, let $X=M\setminus D$, and let $A$ be the ring generated by its Gross–Siebert theta functions. Beyond the known additive identification, is $A$ isomorphic as a ring to the symplectic cohomology $SH^*(X)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Enumerative Geometry and Mirror Symmetry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/27, pp. 1639--1695](https://doi.org/10.4171/owr/2019/27)
## Literature review (checke... | 3 | partially_solved | null | 2,019 | 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,
"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-16939-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The additive identification with theta-function basis elements is established and the product is computed in important special cases, but the claimed ring isomorphism between theta functions and symplectic cohomology remains conjectural in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/27",
"label": "OWR primary report"
},
{
"url": "https://doi.org/10.2140/gt.2019.23.2701",
"label": "Pascaleff on symplectic cohomology of log Calabi--Yau surfaces"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/27 | null | null | null | Let $(M,D)$ be a positive maximally degenerate pair, let $X=M\setminus D$, and let $A$ be the ring generated by its Gross–Siebert theta functions. Beyond the known additive identification, is $A$ isomorphic as a ring to the symplectic cohomology $SH^*(X)$? | For a positive maximally degenerate pair (M,D), is the ring A of Gross--Siebert theta functions isomorphic as a ring to the symplectic cohomology of X=M\setminus D, beyond the cases where the additive identification is known? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Logarithmic Enumerative Geometry and Mirror Symmetry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/27, pp. 1639--1695 |
30,004,159 | OWR-16939-003 | Smooth Modular Compactifications of Abelian-Differential Strata | Construct a proper smooth compactification of the stratum $\mathbb P\Omega\mathcal M_g(\mu)$ of abelian differentials that has a natural modular interpretation. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Logarithmic Enumerative Geometry and Mirror Symmetry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/27, pp. 1639--1695](https://doi.org/10.4171/owr/2019/27)
## Literature review (checke... | 3 | partially_solved | null | 2,019 | 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-16939-003",
"literature-status:partially-solved",
"owr-year:2019"
] | Logarithmic and related compactifications of strata of abelian differentials have been constructed, but the exact requirement of a compactification that is simultaneously proper, smooth, and naturally modular is not established in the extracted generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/27",
"label": "OWR primary report"
},
{
"url": "https://arxiv.org/abs/1910.13492",
"label": "moduli space of multi-scale differentials"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/27 | null | null | null | Construct a proper smooth compactification of the stratum $\mathbb P\Omega\mathcal M_g(\mu)$ of abelian differentials that has a natural modular interpretation. | Construct a proper, smooth compactification of the stratum \mathbb{P}\Omega\mathcal{M}_g(\mu) of abelian differentials that has a natural modular interpretation. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Logarithmic Enumerative Geometry and Mirror Symmetry (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/27, pp. 1639--1695 |
30,004,160 | OWR-16940-001 | Relative Perturbation Bounds for Empirical Covariance Operators | For random matrices, obtain precise or tight estimates for the relevant operator and covariance-operator norms, including the effects of their quadratic structure and effective rank. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Methodology and Theory for Functional and Topological Data (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/28, pp. 1697--1735](https://doi.org/10.4171/owr/2019/28)
## Literat... | 3 | open | null | 2,019 | 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"
} | {
"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 presents an approach to relative perturbation bounds for empirical covariance operators, not a standalone unresolved pro) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16940-001",
"literature-status:open",
"owr-year:2019"
] | Precise norm estimates for random matrices are available under many ensembles and regimes, but the extracted broad request does not specify a norm, ensemble, or asymptotic regime and is not resolved as stated. | [
{
"url": "https://doi.org/10.4171/owr/2019/28",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/28 | null | null | null | null | For random matrices, obtain precise or tight estimates for the relevant operator and covariance-operator norms, including the effects of their quadratic structure and effective rank. | unrecoverable | The official report presents an approach to relative perturbation bounds for empirical covariance operators, not a standalone unresolved problem with a specified ensemble, norm, and asymptotic regime. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Statistical Methodology and Theory for Functional and Topological Data (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/28, pp. 1697--1735 |
30,004,161 | OWR-16940-002 | Nonparametric Bootstrap for High-Dimensional Spectral Statistics | For high-dimensional sample covariance matrices, determine whether a fully nonparametric bootstrap consistently approximates centered linear spectral statistics. The ordinary bootstrap can fail, while an $m$-out-of-$n$ and $q$-out-of-$p$ scheme preserving the dimension-to-sample ratio may succeed under representative-s... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Statistical Methodology and Theory for Functional and Topological Data (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/28, pp. 1697--1735](https://doi.org/10.4171/owr/2019/28)
## Literat... | 3 | partially_solved | null | 2,019 | 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-16940-002",
"literature-status:partially-solved",
"owr-year:2019"
] | In the high-dimensional covariance setting, classical and ordinary m-out-of-n nonparametric bootstraps fail, while a dimension-subsampling m-out-of-n method is proved consistent under additional structural assumptions; there is no universal resolution of the broad question. | [
{
"url": "https://doi.org/10.4171/owr/2019/28",
"label": "OWR primary report"
},
{
"url": "https://proceedings.mlr.press/v89/karoui19a.html",
"label": "nonparametric bootstrap in high dimension"
},
{
"url": "https://arxiv.org/abs/2406.16849",
"label": "later nonparametric covariance ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/28 | null | null | null | For high-dimensional sample covariance matrices, determine whether a fully nonparametric bootstrap consistently approximates centered linear spectral statistics. The ordinary bootstrap can fail, while an $m$-out-of-$n$ and $q$-out-of-$p$ scheme preserving the dimension-to-sample ratio may succeed under representative-s... | For high-dimensional sample covariance matrices, determine whether a fully nonparametric bootstrap consistently approximates centered linear spectral statistics; the ordinary bootstrap can fail, while an m-out-of-n and q-out-of-p scheme preserving the dimension-to-sample ratio may succeed under representative-subpopula... | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Statistical Methodology and Theory for Functional and Topological Data (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/28, pp. 1697--1735 |
30,004,162 | OWR-16941-001 | Special Zeta Values via Weil–Étale Cohomology | For a regular scheme $X$ that is projective and flat over the integers, can its special zeta values be expressed conjecturally in terms of Weil–étale motivic, singular, and de Rham cohomology, compatibly with Serre's functional equation? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-001",
"literature-status:open",
"owr-year:2019"
] | The extracted record is a truncated table-of-contents fragment ending with the word conjecture and contains no identifiable mathematical statement to triage. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | For a regular scheme $X$ that is projective and flat over the integers, can its special zeta values be expressed conjecturally in terms of Weil–étale motivic, singular, and de Rham cohomology, compatibly with Serre's functional equation? | For a regular scheme X projective and flat over the integers, conjecturally express special values of its zeta-function in terms of Weil-etale motivic, singular, and de Rham cohomology, compatibly with Serre's functional equation. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,163 | OWR-16941-002 | Perfectness of Grothendieck's Component-Group Pairing | Let $K$ be a complete discrete valuation field with perfect residue field of characteristic $p>0$, and let $A$ and $B$ be dual abelian varieties with Néron special fibers $A_x$ and $B_x$. Is the canonical pairing
$$
\pi_0(A_x)\times\pi_0(B_x)\longrightarrow\mathbb Q/\mathbb Z
$$
perfect? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-002",
"literature-status:open",
"owr-year:2019"
] | The record stops after introducing Grothendieck's local-duality setup and does not state the pairing or the precise assertion, so the extracted claim is incomplete even though the related conjecture has later proofs. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | Let $K$ be a complete discrete valuation field with perfect residue field of characteristic $p>0$, and let $A$ and $B$ be dual abelian varieties with Néron special fibers $A_x$ and $B_x$. Is the canonical pairing
$$
\pi_0(A_x)\times\pi_0(B_x)\longrightarrow\mathbb Q/\mathbb Z
$$
perfect? | Let K be a complete discrete valuation field with perfect residue field of characteristic p>0, and let A and B be dual abelian varieties with Neron special fibers A_x and B_x; is the canonical pairing pi_0(A_x)\times pi_0(B_x)\to\mathbb{Q}/\mathbb{Z} perfect? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,164 | OWR-16941-003 | K-Regularity Criterion for Ring Regularity | If $A$ is an algebra essentially of finite type over a field $k$, of Krull dimension $d$, and $A$ is $K_{d+1}$-regular, must $A$ be regular? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-003",
"literature-status:open",
"owr-year:2019"
] | The extracted passage introduces Vorst's conjecture but is truncated before stating it; because the exact claim is unclear, it is classified as open under the queue rule. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | If $A$ is an algebra essentially of finite type over a field $k$, of Krull dimension $d$, and $A$ is $K_{d+1}$-regular, must $A$ be regular? | If A is an algebra essentially of finite type over a field k, of Krull dimension d, and A is K_{d+1}-regular, must A be regular? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,165 | OWR-16941-006 | Equivariant Haar Measures for Algebra Actions | What is an appropriate notion of an equivariant Haar measure for locally compact abelian groups with a right action by a finite-dimensional semisimple algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-006",
"literature-status:open",
"owr-year:2019"
] | The extracted problem is only the question What does this even mean? and the surrounding commentary is explanatory prose rather than a determinate mathematical claim. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | What is an appropriate notion of an equivariant Haar measure for locally compact abelian groups with a right action by a finite-dimensional semisimple algebra? | What is an appropriate notion of an equivariant Haar measure for locally compact abelian groups with a right action by a finite-dimensional semisimple algebra? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,166 | OWR-16941-007 | Motivic Origins of Étale Height Pairings | For homologically trivial cycles on a smooth projective variety over a function field, does the generalized Beilinson étale height pairing arise from a motivic pairing with values in the rational Picard group of the base? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-007",
"literature-status:open",
"owr-year:2019"
] | The generalized Beilinson height pairing is constructed and has proved realizations, but the asserted motivic origin remains explicitly conjectural; the authors continue to describe it as speculative. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
},
{
"url": "https://doi.org/10.4171/DM/X15",
"label": "generalized Beilinson geometric height pairing"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | For homologically trivial cycles on a smooth projective variety over a function field, does the generalized Beilinson étale height pairing arise from a motivic pairing with values in the rational Picard group of the base? | For homologically trivial cycles on a smooth projective variety over a function field, does the constructed etale height pairing arise from a motivic pairing with values in the rational Picard group of the base? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,167 | OWR-16941-008 | Prismatic Cohomology from Topological Cyclic Homology | Let $R$ be an $S_n$-algebra. Do the groups
$$
\operatorname{Ext}_{TP_0(R/S_n^{\otimes2})}^j\bigl(TP_0(R/S_n),TP_i(R/S_n)\bigr)
$$
identify with the prismatic cohomology of $R$, and is the spectral sequence
$$
\operatorname{Ext}_{TP_0(R/S_n^{\otimes2})}^j\bigl(TP_0(R/S_n),TP_i(R/S_n)\bigr)\Longrightarrow TP_{i-j}(R)
$$
... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-008",
"literature-status:open",
"owr-year:2019"
] | The proposed identification of the displayed Ext groups with prismatic cohomology and of the spectral sequence with the BMS spectral sequence is stated as a conjecture, and no primary source located settles this exact construction in the stated generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | Let $R$ be an $S_n$-algebra. Do the groups
$$
\operatorname{Ext}_{TP_0(R/S_n^{\otimes2})}^j\bigl(TP_0(R/S_n),TP_i(R/S_n)\bigr)
$$
identify with the prismatic cohomology of $R$, and is the spectral sequence
$$
\operatorname{Ext}_{TP_0(R/S_n^{\otimes2})}^j\bigl(TP_0(R/S_n),TP_i(R/S_n)\bigr)\Longrightarrow TP_{i-j}(R)
$$
... | In the topological periodic cyclic homology setup for R over S_n, are the indicated Ext groups isomorphic to the prismatic cohomology of R, and is the associated Adams-type spectral sequence the BMS spectral sequence? | 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 | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,168 | OWR-16941-009 | Prismatic Cohomology of Local Complete Intersections | Let $Y\subset\mathbb P^n_{\mathbb Z_p}$ be closed with $Y_{\mathbb F_p}$ a local complete intersection, and let $T_n$ denote the ambient infinitesimal object in the relative periodic-cyclic-homology setup. Is
$$
\operatorname{Ext}_{\mathrm{P\text{-}Mod}}^j\bigl(TP_0(\mathcal O_Y/\mathcal O_{T_n}),TP_0(\mathcal O_Y/\mat... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-009",
"literature-status:open",
"owr-year:2019"
] | The conjectured identification for the locally complete-intersection Ext spectral sequence with prismatic cohomology and BMS remains unresolved in the exact form extracted. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | Let $Y\subset\mathbb P^n_{\mathbb Z_p}$ be closed with $Y_{\mathbb F_p}$ a local complete intersection, and let $T_n$ denote the ambient infinitesimal object in the relative periodic-cyclic-homology setup. Is
$$
\operatorname{Ext}_{\mathrm{P\text{-}Mod}}^j\bigl(TP_0(\mathcal O_Y/\mathcal O_{T_n}),TP_0(\mathcal O_Y/\mat... | For a locally complete-intersection scheme Y in the stated periodic cyclic homology setup, are the indicated Ext groups isomorphic to the prismatic cohomology of Y, with the displayed spectral sequence identified with the BMS spectral sequence? | 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 | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,169 | OWR-16941-010 | Zariski Descent for the Milnor–Witt Rost–Schmid Complex | Does the Bloch–Levine–Rost–Schmid complex $C^*(-,K_q^{MW},q)$ satisfy Zariski descent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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-16941-010",
"literature-status:open",
"owr-year:2019"
] | The BLRS complex gives a cycle model for Milnor--Witt motivic cohomology in important cases, but the analogue of Levine localization and hence Zariski descent is explicitly left as a question; later work proves restricted equivalences rather than the full extracted assertion. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
},
{
"url": "https://arxiv.org/abs/1811.01541",
"label": "Bachmann--Yakerson on the BLRS framework"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | Does the Bloch–Levine–Rost–Schmid complex $C^*(-,K_q^{MW},q)$ satisfy Zariski descent? | Does the Bloch-Levine-Rost-Schmid complex C^*( - ,K_q^{MW},q) satisfy Zariski descent? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,170 | OWR-16941-011 | Sheaf Models for Modular Category O | Can the modular representation category O, formed as the stated Serre quotient, be described as an appropriate category of sheaves? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790](https://doi.org/10.4171/owr/2019/29)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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 immediately answers this rhetorical question by giving the motivic-sheaf model and its categorical equivalence. No separ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16941-011",
"literature-status:open",
"owr-year:2019"
] | Geometric and graded realizations of modular category O have been constructed, but the extracted broad equivalence with an unspecified category of sheaves is not a precise theorem and remains open as stated. | [
{
"url": "https://doi.org/10.4171/owr/2019/29",
"label": "OWR primary report"
},
{
"url": "https://arxiv.org/abs/1609.05956",
"label": "geometric modular category O"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/29 | null | null | null | null | Can the modular representation category O, formed as the stated Serre quotient, be described as an appropriate category of sheaves? | unrecoverable | The official report immediately answers this rhetorical question by giving the motivic-sheaf model and its categorical equivalence. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraic K-theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/29, pp. 1737--1790 |
30,004,171 | OWR-16942-001 | Marked Length Spectrum Rigidity | Let a group $G$ act by isometries on metric spaces $X$ and $Y$, and define the marked length spectrum by $\ell_X(g)=\inf_{x\in X}d(x,gx)$. Under which hypotheses does $\ell_X=\ell_Y$ imply that $X$ and $Y$ are $G$-equivariantly isometric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-16942-001",
"literature-status:partially-solved",
"owr-year:2019"
] | Marked length-spectrum rigidity is proved for irreducible CAT(0) cube complexes under essentiality, no-free-face, minimality, and related hypotheses, but the extracted question does not impose those hypotheses and is not solved in full generality. | [
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "OWR primary report"
},
{
"url": "https://doi.org/10.1112/jlms.12489",
"label": "CAT(0) cube length-spectrum rigidity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | Let a group $G$ act by isometries on metric spaces $X$ and $Y$, and define the marked length spectrum by $\ell_X(g)=\inf_{x\in X}d(x,gx)$. Under which hypotheses does $\ell_X=\ell_Y$ imply that $X$ and $Y$ are $G$-equivariantly isometric? | Given two actions G on X and G on Y in a specified class of metric spaces and actions, does equality of their marked length data imply that X and Y are equivariantly isometric? | 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 | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,172 | OWR-16942-002 | Tangent Flows and Type-Two Blow-Ups | When can tangent flows be related to blow-downs of Type II blow-ups in zero-Maslov Lagrangian mean curvature flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-16942-002",
"literature-status:partially-solved",
"owr-year:2019"
] | There are strong results relating Type II blow-ups, tangent flows, and blow-downs, including exactness and rigidity theorems for zero-Maslov or almost calibrated flows, but no general criterion for the relation or uniqueness requested in the extracted question is established. | [
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "OWR primary report"
},
{
"url": "https://doi.org/10.1007/s10240-023-00143-5",
"label": "ancient solutions and translators"
},
{
"url": "https://doi.org/10.1016/j.jfa.2025.111032",
"label": "Type II singularities with zero Masl... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | When can tangent flows be related to blow-downs of Type II blow-ups in zero-Maslov Lagrangian mean curvature flow? | When can tangent flows be related to blow-downs of Type II blow-ups in zero-Maslov Lagrangian mean curvature flow? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,173 | OWR-16942-003 | Ancient Lagrangian Mean-Curvature Flows with Planar Blow-Downs | Can one classify the exact, almost calibrated, ancient solutions to Lagrangian mean curvature flow in $\mathbb{C}^2$ whose blow-down is a pair of planes intersecting in a line? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-16942-003",
"literature-status:partially-solved",
"owr-year:2019"
] | For the stated blow-down configuration, a theorem proves that every almost calibrated exact ancient solution is a translator, but this reduction is not a complete classification of all such translators and hence only partially resolves the extracted question. | [
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "OWR primary report"
},
{
"url": "https://doi.org/10.1007/s10240-023-00143-5",
"label": "ancient solutions and translators"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | Can one classify the exact, almost calibrated, ancient solutions to Lagrangian mean curvature flow in $\mathbb{C}^2$ whose blow-down is a pair of planes intersecting in a line? | Can one classify the exact, almost calibrated, ancient solutions to Lagrangian mean curvature flow in \mathbb{C}^2 whose blow-down is a pair of planes intersecting in a line? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,174 | OWR-16942-005 | Log K-Stability versus Geometric Invariant Theory | For a K-polystable Fano variety $X$ and sufficiently large $\beta$, is log K-polystability of the pair $(X,(1-\beta)D)$ equivalent to geometric invariant theory stability for the natural $\operatorname{Aut}(X)$-action on $H^0(X,K_X^{-l})$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-16942-005",
"literature-status:partially-solved",
"owr-year:2019"
] | Zhou proves the GIT--log K-stability equivalence for K-polystable Fano varieties under additional log-canonicity and small-coefficient hypotheses; the unrestricted formulation for arbitrary plurianticanonical divisors remains unresolved. | [
{
"url": "https://arxiv.org/abs/2102.07458",
"label": "Zhou, Log K-stability of GIT-stable divisors"
},
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | For a K-polystable Fano variety $X$ and sufficiently large $\beta$, is log K-polystability of the pair $(X,(1-\beta)D)$ equivalent to geometric invariant theory stability for the natural $\operatorname{Aut}(X)$-action on $H^0(X,K_X^{-l})$? | For any K-polystable Fano variety X and sufficiently large beta, is log K-polystability of (X,(1-beta)D) equivalent to GIT stability for the natural Aut(X)-action on the plurianticanonical sections containing D? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,175 | OWR-16942-006 | Uniqueness of Scalar-Flat Kähler ALE Metrics | For an ALE Kähler manifold admitting scalar-flat Kähler metrics, is the scalar-flat Kähler metric in a given Kähler class unique? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,019 | 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-16942-006",
"literature-status:open",
"owr-year:2019"
] | The record contains only the assertion that a problem is completely open and omits the mathematical statement, so no stronger classification is justified. | [
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | For an ALE Kähler manifold admitting scalar-flat Kähler metrics, is the scalar-flat Kähler metric in a given Kähler class unique? | For an ALE Kahler manifold admitting scalar-flat Kahler metrics, is the scalar-flat Kahler metric in a given Kahler class unique? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,176 | OWR-16942-007 | Short-Time PIC1 Ricci Flow | Let $(M,g_0)$ be a smooth complete $n$-dimensional manifold with $n\geq3$ satisfying PIC1. Does there exist $T>0$ and a smooth PIC1 Ricci flow $g(t)$ on $M$ for $0\leq t<T$ such that $g(0)=g_0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839](https://doi.org/10.4171/owr/2019/30)
## Literature review (checked 2026-08-22)
**Stat... | 3 | partially_solved | null | 2,019 | 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-16942-007",
"literature-status:partially-solved",
"owr-year:2019"
] | Ricci-flow existence with suitable weak PIC1 pinching is proved in dimensions at least four, while the corresponding conjecture remains open in dimension three; thus the all-dimensional claim is only partially resolved. | [
{
"url": "https://arxiv.org/abs/2309.00596",
"label": "Ricci flow and PIC1"
},
{
"url": "https://doi.org/10.4171/owr/2019/30",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/30 | null | null | null | Let $(M,g_0)$ be a smooth complete $n$-dimensional manifold with $n\geq3$ satisfying PIC1. Does there exist $T>0$ and a smooth PIC1 Ricci flow $g(t)$ on $M$ for $0\leq t<T$ such that $g(0)=g_0$? | If (M,g_0) is a smooth complete n-dimensional manifold with n\geq 3 satisfying the PIC1 condition, does there exist a smooth PIC1 Ricci flow g(t) on M for t\in[0,T) with T>0 and g(0)=g_0? | 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 | Differentialgeometrie im Großen (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/30, pp. 1791--1839 |
30,004,177 | OWR-17127-001 | Birkhoff Rigidity Conjecture for Convex Billiards | Are the completely integrable billiards inside smooth strictly convex planar domains exactly the billiards inside ellipses? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"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-17127-001",
"literature-status:partially-solved",
"owr-year:2019"
] | The general Birkhoff rigidity question remains open, but global results for centrally symmetric tables and strong local results near almost every ellipse rule out many possible counterexamples. | [
{
"url": "https://annals.math.princeton.edu/2022/196-1/p02",
"label": "Bialy--Mironov, centrally symmetric tables"
},
{
"url": "https://doi.org/10.1007/s00222-025-01397-y",
"label": "Koval, local strong Birkhoff conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Are the completely integrable billiards inside smooth strictly convex planar domains exactly the billiards inside ellipses? | Are the integrable Birkhoff billiards exactly the billiards in ellipses? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,178 | OWR-17127-002 | Local Birkhoff Rigidity Near Elliptical Billiards | Let a smooth strictly convex planar billiard have invariant caustics with every rotation number in $(0,\delta)$ for some $\delta>0$. Under what hypotheses does this boundary foliation force the billiard table to be an ellipse? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"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-17127-002",
"literature-status:partially-solved",
"owr-year:2019"
] | The local boundary-foliation version is proved for perturbations of almost every ellipse, while the unrestricted question for arbitrary convex billiard tables and arbitrary small rotation intervals remains open. | [
{
"url": "https://doi.org/10.1007/s00222-025-01397-y",
"label": "Koval, local strong Birkhoff conjecture"
},
{
"url": "https://annals.math.princeton.edu/2018/188-1/p06",
"label": "Kaloshin--Sorrentino, local Birkhoff conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/31",
"lab... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Let a smooth strictly convex planar billiard have invariant caustics with every rotation number in $(0,\delta)$ for some $\delta>0$. Under what hypotheses does this boundary foliation force the billiard table to be an ellipse? | For a smooth strictly convex billiard whose invariant caustics occur only in a small boundary neighborhood, with rotation numbers in (0,delta), what rigidity follows, and under suitable near-ellipse hypotheses must the domain be an ellipse? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,179 | OWR-17127-005 | Zero-Entropy Surface Dynamics and Their Bifurcations | Classify surface diffeomorphisms with zero topological entropy and describe the mechanisms by which they bifurcate to positive-entropy dynamics. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
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"slug": "dynamical-systems",
"order_index": 11,
"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-17127-005",
"literature-status:open",
"owr-year:2019"
] | The extracted record poses broad classification and bifurcation questions for zero-entropy surface diffeomorphisms; available theorems cover restricted classes and do not settle the general questions. | [
{
"url": "https://arxiv.org/abs/2005.14278",
"label": "Crovisier--Pujals--Tresser, zero entropy"
},
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Classify surface diffeomorphisms with zero topological entropy and describe the mechanisms by which they bifurcate to positive-entropy dynamics. | How can one describe the dynamics of surface diffeomorphisms with zero topological entropy, and how do they bifurcate to systems with positive entropy? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,180 | OWR-17127-006 | Period Structure of Dissipative Disk Diffeomorphisms | For every dissipative diffeomorphism of the disk, does there exist $n_0$ such that every period belongs to $$\{n2^k:n\leq n_0,\ k\in\mathbb N\},$$ and, if there are infinitely many periods, must they contain $\{n2^k:k\in\mathbb N\}$ for some $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
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"slug": "dynamical-systems",
"order_index": 11,
"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-17127-006",
"literature-status:partially-solved",
"owr-year:2019"
] | The period-doubling conclusion is proved for mildly dissipative disc diffeomorphisms, including the relevant Hénon regime, but the exact conjecture for every dissipative disc diffeomorphism remains open. | [
{
"url": "https://arxiv.org/abs/2005.14278",
"label": "Crovisier--Pujals--Tresser, zero entropy"
},
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | For every dissipative diffeomorphism of the disk, does there exist $n_0$ such that every period belongs to $$\{n2^k:n\leq n_0,\ k\in\mathbb N\},$$ and, if there are infinitely many periods, must they contain $\{n2^k:k\in\mathbb N\}$ for some $n$? | For any dissipative diffeomorphism of the disc, does there exist n_0 such that its periods lie in \{n 2^k:n\leq n_0, k\in\mathbb{N}\}, and, if infinite, contain \{n 2^k:k\in\mathbb{N}\} for some n? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,181 | OWR-17127-007 | Boundary of Zero-Entropy Dissipative Systems | Within the space of mildly dissipative disk diffeomorphisms, is the boundary of the zero-topological-entropy locus exactly the set of infinitely renormalizable zero-entropy systems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,019 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
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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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"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-17127-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The inclusion of the zero-entropy boundary in the infinitely renormalizable class is proved for mildly dissipative disc maps, but equality and the unrestricted dissipative setting are not established. | [
{
"url": "https://arxiv.org/abs/2005.14278",
"label": "Crovisier--Pujals--Tresser, zero entropy"
},
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Within the space of mildly dissipative disk diffeomorphisms, is the boundary of the zero-topological-entropy locus exactly the set of infinitely renormalizable zero-entropy systems? | In the class of mild dissipative disc diffeomorphisms, is the boundary of the zero-entropy systems equal to the infinitely renormalizable zero-entropy systems? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,182 | OWR-17127-008 | Ranks of Reeb Action Spectra | Which additive ranks can occur for the action spectrum of a contact form on a closed $3$-manifold? If the rank is $2$, must the Reeb flow have exactly two geometrically distinct periodic orbits? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 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,
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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-17127-008",
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] | Rank one contact forms are understood, and two-or-infinity results are known in important three-dimensional cases, but the possible ranks and the rank-two orbit classification asked here remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
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{
"url": "https://doi.org/10.2140/gt.2019.23.3601",
"label": "Cristofaro-Gardiner--Hutchings--Pomerleano"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Which additive ranks can occur for the action spectrum of a contact form on a closed $3$-manifold? If the rank is $2$, must the Reeb flow have exactly two geometrically distinct periodic orbits? | For a contact form on a closed three-manifold, what ranks can its Reeb action spectrum have, and in rank two must there be exactly two geometrically distinct Reeb orbits? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,183 | OWR-17127-009 | Arnold Fixed Point Bound by Cup Length | Does every Hamiltonian diffeomorphism of a closed connected symplectic manifold $M$ have at least $\operatorname{cl}(M)$ fixed points, where $\operatorname{cl}(M)$ denotes its cup length? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** open
*... | 3 | open | null | 2,019 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "topology",
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"created_at": "2026-07-31T15:26:25.671Z"
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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-17127-009",
"literature-status:open",
"owr-year:2019"
] | The record is an incomplete exposition of the Arnold conjecture and its Hamiltonian-homeomorphism applications, not a complete problem statement; the intended general claim cannot be identified without speculation. | [
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
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{
"url": "https://arxiv.org/abs/1810.03139",
"label": "Le Roux--Seyfaddini--Viterbo, barcodes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | Does every Hamiltonian diffeomorphism of a closed connected symplectic manifold $M$ have at least $\operatorname{cl}(M)$ fixed points, where $\operatorname{cl}(M)$ denotes its cup length? | Does every Hamiltonian diffeomorphism of a closed connected symplectic manifold have at least cl(M) fixed points, where cl(M) is the cup length of M? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,184 | OWR-17127-010 | Transversal Foliations and Global Sections for Reeb Flows | If a Reeb flow on a closed $3$-manifold admits a transverse foliation and has zero topological entropy, must it admit a global surface of section after removing finitely many invariant tori? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917](https://doi.org/10.4171/owr/2019/31)
## Literature review (checked 2026-08-22)
**Status:** partial... | 3 | partially_solved | null | 2,019 | 11 | 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-17127-010",
"literature-status:partially-solved",
"owr-year:2019"
] | Transversal-foliation methods yield symbolic dynamics and a global surface of section under non-degeneracy and zero-entropy assumptions, but the broad question about all resulting Reeb flows is not settled. | [
{
"url": "https://doi.org/10.4171/owr/2019/31",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4171/JEMS/1220",
"label": "Hryniewicz--Salomao--Wysocki, global sections"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/31 | null | null | null | If a Reeb flow on a closed $3$-manifold admits a transverse foliation and has zero topological entropy, must it admit a global surface of section after removing finitely many invariant tori? | If a three-dimensional Reeb flow admits a transversal foliation, what additional dynamical structure follows; in particular, does zero topological entropy force a global surface of section up to finitely many invariant tori? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Dynamische Systeme (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/31, pp. 1855--1917 |
30,004,185 | OWR-17128-001 | Higher-Dimensional Frenkel–Kontorova Traveling Waves | Extend the one-dimensional Frenkel–Kontorova existence theorem for traveling heteroclinic waves in smooth anharmonic two-well potentials to higher spatial dimensions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979](https://doi.org/10.4171/owr/2019/32)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,019 | 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",
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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-17128-001",
"literature-status:open",
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] | The higher-dimensional extension of the heteroclinic Frenkel--Kontorova theorem is posed as a question, and the cited primary work establishes only the one-dimensional-chain result. | [
{
"url": "https://doi.org/10.1016/j.matpur.2019.01.002",
"label": "Buffoni--Schwetlick--Zimmer, heteroclinic waves"
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{
"url": "https://doi.org/10.4171/owr/2019/32",
"label": "original OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/32 | null | null | null | Extend the one-dimensional Frenkel–Kontorova existence theorem for traveling heteroclinic waves in smooth anharmonic two-well potentials to higher spatial dimensions. | Can the one-dimensional Frenkel-Kontorova theorem guaranteeing traveling heteroclinic waves for suitable smooth anharmonic two-well potentials be extended to higher spatial dimensions? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979 |
30,004,186 | OWR-17128-002 | Stability of Peaked Reduced Ostrovsky Waves | For the reduced Ostrovsky equation, are the peaked periodic traveling waves $$U_*(z)=\frac{3z^2-\pi^2}{18},$$ extended periodically, nonlinearly stable or unstable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979](https://doi.org/10.4171/owr/2019/32)
## Literature review (checked 2026-08-22)
**S... | 3 | partially_solved | null | 2,019 | 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-17128-002",
"literature-status:partially-solved",
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] | Linear and spectral instability, together with uniqueness, are proved for the peaked periodic wave, but nonlinear instability and the full nonlinear stability question remain open. | [
{
"url": "https://doi.org/10.1137/18M117978X",
"label": "Geyer--Pelinovsky, linear instability"
},
{
"url": "https://doi.org/10.1090/proc/14937",
"label": "Geyer--Pelinovsky, spectral instability"
},
{
"url": "https://doi.org/10.4171/owr/2019/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/32 | null | null | null | For the reduced Ostrovsky equation, are the peaked periodic traveling waves $$U_*(z)=\frac{3z^2-\pi^2}{18},$$ extended periodically, nonlinearly stable or unstable? | For the reduced Ostrovsky equation, are the peaked periodic traveling-wave solutions U_*(z)=(3z^2-\pi^2)/18, periodically extended, stable? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979 |
30,004,187 | OWR-17128-003 | Nonlocal Water Waves with Generalized Vorticity | Extend the nonlocal interface formulation of the water-wave problem from constant vorticity to general vorticity, and determine whether the extension yields additional conservation laws. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979](https://doi.org/10.4171/owr/2019/32)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,019 | 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-17128-003",
"literature-status:open",
"owr-year:2019"
] | The record states a conjectural extension of conservation laws to generalized vorticity; existing vorticity laws do not establish this particular water-wave extension. | [
{
"url": "https://doi.org/10.4171/owr/2019/32",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1017/S002211208100222X",
"label": "Mobbs, vorticity conservation laws"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/32 | null | null | null | Extend the nonlocal interface formulation of the water-wave problem from constant vorticity to general vorticity, and determine whether the extension yields additional conservation laws. | Does the nonlocal interface formulation of the water-wave problem extend from constant vorticity to generalized vorticity, potentially yielding new conservation laws? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979 |
30,004,188 | OWR-17128-004 | Long-Time Dynamics of Fractional Dispersive Equations | For the fractional dispersive equation $$\partial_tu=\partial_x\!\left(|\partial_x|^\alpha u-u^p\right)\quad\text{on }\mathbb R,$$ determine how the parameters $\alpha$ and $p$ govern global behavior, singularity formation, and the stability of solitary waves. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979](https://doi.org/10.4171/owr/2019/32)
## Literature review (checked 2026-08-22)
**S... | 3 | open | null | 2,019 | 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-17128-004",
"literature-status:open",
"owr-year:2019"
] | This is a motivational formulation of the unresolved long-time-dynamics problem for a dispersive nonlinear PDE, not a theorem or a uniquely specified conjecture. | [
{
"url": "https://doi.org/10.4171/owr/2019/32",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/32 | null | null | null | For the fractional dispersive equation $$\partial_tu=\partial_x\!\left(|\partial_x|^\alpha u-u^p\right)\quad\text{on }\mathbb R,$$ determine how the parameters $\alpha$ and $p$ govern global behavior, singularity formation, and the stability of solitary waves. | For the dispersive equation \partial_tu=\partial_x(|\partial_x|^\alpha u-u^p) on \mathbb{R}, how does the balance between nonlinearity and dispersion determine the long-time dynamics, including solitary-wave stability? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Theory of Water Waves (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/32, pp. 1919--1979 |
30,004,189 | OWR-17129-001 | Adaptive Refinement and Global Optimization of Topological Shapes | For adaptive topology optimization using level-set and state-variable discretizations, determine reliable refinement and coarsening strategies, methods for escaping local minima, efficient hierarchical B-spline gradient schemes, couplings with isogeometric shape optimization, and algorithms for extracting surface or vo... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Foundations of Isogeometric Analysis (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/33, pp. 1981--2032](https://doi.org/10.4171/owr/2019/33)
## Literature review (checked 2... | 3 | open | null | 2,019 | 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 | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-17129-001",
"literature-status:open",
"owr-year:2019"
] | The record lists six methodological research questions about adaptive topology optimization; they are posed as future work and no complete general answers are supplied. | [
{
"url": "https://doi.org/10.4171/owr/2019/33",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/33 | null | null | null | For adaptive topology optimization using level-set and state-variable discretizations, determine reliable refinement and coarsening strategies, methods for escaping local minima, efficient hierarchical B-spline gradient schemes, couplings with isogeometric shape optimization, and algorithms for extracting surface or vo... | In adaptive topology optimization with level-set and state-variable discretizations, how should refinement and coarsening be scheduled; can one robustly find a global rather than local minimum; can hierarchical B-splines accelerate gradient methods; can adaptive topology optimization be efficiently fused with isogeomet... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical Foundations of Isogeometric Analysis (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/33, pp. 1981--2032 |
30,004,190 | OWR-17130-003 | Mean-Curvature Blowup Limits of Wings and Pitchfork Translators | Do the finite-entropy $\Delta-wings$ and pitchfork translators of mean curvature flow arise as blow-up limits of mean curvature flows? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-003",
"literature-status:open",
"owr-year:2019"
] | The translators and their uniqueness are established, but occurrence of pitchfork translators as blowup limits of closed mean curvature flows remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1903.04617",
"label": "Scherk-like Translators for Mean Curvature Flow"
},
{
"url": "https://arxiv.org/abs/2310.06980",
"label": "Uniqueness of Semigraphical Tran... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Do the finite-entropy $\Delta-wings$ and pitchfork translators of mean curvature flow arise as blow-up limits of mean curvature flows? | Do the finite-entropy \Delta-wings and pitchfork translators of mean curvature flow arise as blow-up limits of mean curvature flows? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,191 | OWR-17130-006 | Explicit Cheeger Sets and Constants of Bounded Domains | Given a bounded domain $\Omega\subset\mathbb R^n$, explicitly describe its Cheeger sets $E\subseteq\Omega$, with $\lvert E\rvert>0$, minimizing $P(E)/\lvert E\rvert$, and compute
$$h(\Omega)=\inf_{E\subseteq\Omega}\frac{P(E)}{\lvert E\rvert}.$$
Can the minimizing sets and the value of this infimum be determined expl... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 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-17130-006",
"literature-status:partially-solved",
"owr-year:2019"
] | Explicit Cheeger sets and constants are known for important classes such as Jordan domains without necks, but no general description or computation for arbitrary domains is known. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1704.07253",
"label": "The Cheeger Constant of a Jordan Domain Without Necks"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Given a bounded domain $\Omega\subset\mathbb R^n$, explicitly describe its Cheeger sets $E\subseteq\Omega$, with $\lvert E\rvert>0$, minimizing $P(E)/\lvert E\rvert$, and compute
$$h(\Omega)=\inf_{E\subseteq\Omega}\frac{P(E)}{\lvert E\rvert}.$$
Can the minimizing sets and the value of this infimum be determined expl... | Given a bounded open domain \Omega\subset\mathbb{R}^n, n\ge2, can one explicitly describe its Cheeger sets E minimizing P(E)/|E| and compute the Cheeger constant h(\Omega)=\inf_{E\subset\Omega, |E|>0}P(E)/|E|? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,192 | OWR-17130-008 | $C^1$ Regularity of Planar Convex Variational Minimizers | If $F$ is strictly convex, is every Lipschitz minimizer of
$$\int_{B_1}F(\nabla u)\,dx$$
in dimension $n=2$ of class $C^1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-008",
"literature-status:open",
"owr-year:2019"
] | The finite-degeneracy planar case is proved, but the extracted strictly convex two-dimensional regularity question in full generality remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1903.03103",
"label": "Minimizers of Convex Functionals with Small Degeneracy Set"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | If $F$ is strictly convex, is every Lipschitz minimizer of
$$\int_{B_1}F(\nabla u)\,dx$$
in dimension $n=2$ of class $C^1$? | Prove or disprove that, when F is strictly convex, every Lipschitz minimizer of \int_{B_1}F(\nabla u) dx in dimension n=2 is C^1. | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,193 | OWR-17130-009 | Martinez–Maure Support Functions as Singular Minimizers | Is the support function $R$ of the Martínez–Maure example a Lipschitz singular minimizer of
$$\int_{B_1}F(\nabla u)\,dx$$
for some integrand $F$ whose singular set $D_F$ consists exactly of the four noncoplanar cusps? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-009",
"literature-status:open",
"owr-year:2019"
] | The Martinez--Maure support-function example remains a conjectural singular minimizer; no proof or counterexample to this specific conjecture was found. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1903.03103",
"label": "Minimizers of Convex Functionals with Small Degeneracy Set"
},
{
"url": "https://www.inspe-paris.fr/system/files/2021-06/cras2001.pdf",
"la... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Is the support function $R$ of the Martínez–Maure example a Lipschitz singular minimizer of
$$\int_{B_1}F(\nabla u)\,dx$$
for some integrand $F$ whose singular set $D_F$ consists exactly of the four noncoplanar cusps? | Is the support function R of the Martinez-Maure example a Lipschitz singular minimizer of a functional \int_{B_1}F(\nabla u) dx whose singular set D_F consists exactly of the four non-coplanar cusps? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,194 | OWR-17130-010 | Persistence of Euler Vortex Filaments Under Binormal Flow | For the three-dimensional Euler equations with initial vorticity concentrated along a smooth spatial curve, does the vorticity remain concentrated around a curve for finite times, and can it remain close for a significant time to a filament evolving by binormal flow? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-010",
"literature-status:open",
"owr-year:2019"
] | Rigorous concentrated-filament results exist for special geometries, but the general Euler vortex-filament construction near binormal flow remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1603.00227",
"label": "On the Vortex Filament Conjecture for Euler Flows"
},
{
"url": "https://doi.org/10.1016/j.jde.2024.11.044",
"label": "helical-symmetry spec... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | For the three-dimensional Euler equations with initial vorticity concentrated along a smooth spatial curve, does the vorticity remain concentrated around a curve for finite times, and can it remain close for a significant time to a filament evolving by binormal flow? | For the three-dimensional Euler equations with initial vorticity concentrated along a smooth spatial curve, does the vorticity remain concentrated around a curve for finite times, and can it remain close for a significant time to a filament evolving by binormal flow? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,195 | OWR-17130-011 | Hausdorff Absolute Continuity of PDE-Constrained Measures | Let
$$A=\partial_{x_1}^3+\partial_{x_2}^3+\partial_{x_3}^3.$$
If a real Radon measure $\mu$ on $\mathbb R^3$ satisfies $A\mu=0$ distributionally, must $\mu\ll\mathcal H^2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-011",
"literature-status:open",
"owr-year:2019"
] | The cited dimension and rectifiability theory leaves this third-order operator conjecture unresolved; no later proof or counterexample was found. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3782/OWR_2019_34.pdf?isAllowed=y&sequence=1",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00039-019-00497-1",
"label": "Dimensional Estimates and Rectifiability for Measures Satisfying Linear PDE Constrai... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Let
$$A=\partial_{x_1}^3+\partial_{x_2}^3+\partial_{x_3}^3.$$
If a real Radon measure $\mu$ on $\mathbb R^3$ satisfies $A\mu=0$ distributionally, must $\mu\ll\mathcal H^2$? | For A=\partial_{x_1}^3+\partial_{x_2}^3+\partial_{x_3}^3 on C^\infty(\mathbb{R}^3), does every real Radon measure \mu satisfying A\mu=0 in the distributional sense obey \mu\ll\mathcal{H}^2? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,196 | OWR-17130-012 | Ancient Ovals as Post-Singularity Limit Flows | Can ancient ovals arise as limit flows at singularities of a mean curvature flow after the first singular time? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | open | null | 2,019 | 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-17130-012",
"literature-status:open",
"owr-year:2019"
] | Mean-convex-neighborhood and ancient-flow classification results have advanced, but whether ancient ovals arise at subsequent singularities remains explicitly unresolved. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3782/OWR_2019_34.pdf?isAllowed=y&sequence=1",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1810.08467",
"label": "Ancient Low Entropy Flows, Mean Convex Neighborhoods, and Uniqueness"
},
{
"url": "htt... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Can ancient ovals arise as limit flows at singularities of a mean curvature flow after the first singular time? | Can ancient ovals arise as limit flows at singularities of a mean curvature flow after the first singular time? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,197 | OWR-17130-013 | Instantaneously Complete Yamabe Flow in Higher Dimensions | Does the theory of instantaneously complete Yamabe flows on noncompact surfaces extend to higher-dimensional noncompact manifolds? For conformally hyperbolic Yamabe flows, is
$$g(t)\geq m(m-1)t\,g_H$$
equivalent to instantaneous completeness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097](https://doi.org/10.4171/owr/2019/34)
## Literature review (checked 2026-08-22)
**Statu... | 3 | partially_solved | null | 2,019 | 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-17130-013",
"literature-status:partially-solved",
"owr-year:2019"
] | Instantaneously complete Yamabe flow is proved for hyperbolic space in arbitrary dimension and for rotationally symmetric data, but the full higher-dimensional equivalence and generalization remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2019/34",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1007/s00526-019-1634-9",
"label": "Instantaneously Complete Yamabe Flow on Hyperbolic Space"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/34 | null | null | null | Does the theory of instantaneously complete Yamabe flows on noncompact surfaces extend to higher-dimensional noncompact manifolds? For conformally hyperbolic Yamabe flows, is
$$g(t)\geq m(m-1)t\,g_H$$
equivalent to instantaneous completeness? | Does the theory of instantaneously complete Yamabe flows on noncompact surfaces generalize to higher-dimensional noncompact manifolds, and is the lower bound g(t)\ge m(m-1)t g_H equivalent to instantaneous completeness for conformally hyperbolic Yamabe flows? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Partial Differential Equations (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/34, pp. 2033--2097 |
30,004,198 | OWR-17132-001 | Normed Algebra Lifts of the Motivic Tau Cofiber | Can the motivic cofiber $S^0/\tau$, regarded as a commutative algebra in the $2$-complete motivic stable homotopy category over $\mathbb C$, be lifted to a normed algebra? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,019 | 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-17132-001",
"literature-status:open",
"owr-year:2019"
] | The motivic cofiber has a unique E-infinity ring structure, but a lift to the normed-algebra category remains an open question. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.4171/DM/642",
"label": "The Motivic Cofiber of tau"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Can the motivic cofiber $S^0/\tau$, regarded as a commutative algebra in the $2$-complete motivic stable homotopy category over $\mathbb C$, be lifted to a normed algebra? | Can the motivic cofiber S^0/\tau, regarded as a commutative algebra in the 2-complete motivic stable homotopy category over \mathbb{C}, be lifted to a normed algebra? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,199 | OWR-17132-004 | Generalized Smith Questions for Compact Lie Groups | Given reduced homology theories $h_*$ and $h'_*$ and a compact Lie group $G$, when does there exist a finite based $G$-CW complex $X$ such that $h_*(X)=0$ but $h'_*(X^G)\neq0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-004",
"literature-status:partially-solved",
"owr-year:2019"
] | The generalized Smith question is solved for abelian compact Lie groups and several other cases, but no general classification for arbitrary compact Lie groups is known. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1810.04698",
"label": "On the Balmer Spectrum for Compact Lie Groups"
},
{
"url": "https://arxiv.org/abs/2008.00330",
"label": "Chromatic Fixed Point Theory for E... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Given reduced homology theories $h_*$ and $h'_*$ and a compact Lie group $G$, when does there exist a finite based $G$-CW complex $X$ such that $h_*(X)=0$ but $h'_*(X^G)\neq0$? | Given generalized reduced homology theories h_* and h'_* and a compact Lie group G, does there exist a finite based G-CW complex X with h_*(X)=0 but h'_*(X^G)\ne0? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,200 | OWR-17132-005 | Realizable Type Functions of Equivariant Spectra | Which functions $$\operatorname{Sub}(G)\longrightarrow\mathbb N\cup\{\infty\}$$ occur as the chromatic type function of a finite $p$-local $G$-spectrum? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-005",
"literature-status:partially-solved",
"owr-year:2019"
] | The type-function realization problem is classified for abelian compact Lie groups, while the full nonabelian classification remains unresolved. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1709.04828",
"label": "Balmer Spectrum for Finite Abelian Groups"
},
{
"url": "https://arxiv.org/abs/1810.04698",
"label": "Balmer Spectrum for Compact Lie Groups... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Which functions $$\operatorname{Sub}(G)\longrightarrow\mathbb N\cup\{\infty\}$$ occur as the chromatic type function of a finite $p$-local $G$-spectrum? | Which functions Sub(G)\to\mathbb{N}\cup\{\infty\} can be realized as the type function of a finite p-local G-spectrum? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,201 | OWR-17132-006 | Chromatic Fixed-Point Implications for Finite p-Groups | Let $H<G$ be subgroups of a finite $p$-group and let $m,n$ be nonnegative integers. For which pairs $(m,n)$ does $$K(m)_*(\Phi^H X)=0\quad\Longrightarrow\quad K(n)_*(\Phi^G X)=0$$ hold for every finite $G$-spectrum $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-006",
"literature-status:partially-solved",
"owr-year:2019"
] | Blue-shift bounds and many subgroup cases are known, but the complete list of pairs for arbitrary finite p-groups remains open. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1709.04828",
"label": "Balmer Spectrum for Finite Abelian Groups"
},
{
"url": "https://arxiv.org/abs/2008.00330",
"label": "Chromatic Fixed Point Theory for Extra... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Let $H<G$ be subgroups of a finite $p$-group and let $m,n$ be nonnegative integers. For which pairs $(m,n)$ does $$K(m)_*(\Phi^H X)=0\quad\Longrightarrow\quad K(n)_*(\Phi^G X)=0$$ hold for every finite $G$-spectrum $X$? | For a subgroup H<G of a finite p-group G, and integers m,n, for which pairs does K(m)_*(\Phi^H X)=0 imply K(n)_*(\Phi^G X)=0 for every finite G-spectrum X? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,202 | OWR-17132-007 | Realizing Chromatic Types at Nested Fixed Points | Let $H<G$ be subgroups of a finite $p$-group. For which pairs $(m,n)$ does there exist a finite $G$-spectrum $X$ such that $\Phi^H X$ has chromatic type $m$ and $\Phi^G X$ has chromatic type $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-007",
"literature-status:partially-solved",
"owr-year:2019"
] | The realization problem is solved in broad abelian and selected nonabelian cases, but not for all subgroup pairs and heights. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1709.04828",
"label": "Balmer Spectrum for Finite Abelian Groups"
},
{
"url": "https://arxiv.org/abs/2008.00330",
"label": "Chromatic Fixed Point Theory for Extra... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Let $H<G$ be subgroups of a finite $p$-group. For which pairs $(m,n)$ does there exist a finite $G$-spectrum $X$ such that $\Phi^H X$ has chromatic type $m$ and $\Phi^G X$ has chromatic type $n$? | For a subgroup H<G of a finite p-group G, for which pairs (m,n) does there exist a finite G-spectrum X whose geometric fixed points \Phi^G X and \Phi^H X have types n and m, respectively? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,203 | OWR-17132-008 | Small-Genus Cohomology of High-Dimensional Diffeomorphism Groups | For $$W_{g,1}=D^{2n}\mathbin{\#}_g(S^n\times S^n),\qquad 2n\geq6,$$ determine the rational cohomology ring $$H^*(B\operatorname{Diff}_\partial(W_{g,1});\mathbb Q)$$ at small genus, particularly $g=1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-008",
"literature-status:partially-solved",
"owr-year:2019"
] | The rational cohomology is computed in a stable low-degree range and unstable classes are known, but the requested small-genus full cohomology is not determined. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/1908.04724",
"label": "The Cohomology of Torelli Groups Is Algebraic"
},
{
"url": "https://arxiv.org/abs/2002.04647",
"label": "A Homological Approach to Pseudois... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | For $$W_{g,1}=D^{2n}\mathbin{\#}_g(S^n\times S^n),\qquad 2n\geq6,$$ determine the rational cohomology ring $$H^*(B\operatorname{Diff}_\partial(W_{g,1});\mathbb Q)$$ at small genus, particularly $g=1$. | For W_{g,1}=D^{2n}\#_g(S^n\times S^n) with 2n\ge6 and small g, for example g=1, what is the rational cohomology ring H^*(BDiff_\partial(W_{g,1});\mathbb{Q})? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,204 | OWR-17132-010 | Equivariant Topological Modular Forms Duality for Compact Lie Groups | Let $G$ be a compact Lie group with adjoint representation $L$. Is $\operatorname{TMF}^G$ a dualizable $\operatorname{TMF}$-module with dual $(\Sigma^{-L}\operatorname{TMF})^G$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-010",
"literature-status:partially-solved",
"owr-year:2019"
] | Dualizability is proved for finite groups, compact abelian groups, and torus times finite groups, while the conjecture for all compact Lie groups remains open. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1112/S0010437X23007509",
"label": "On Equivariant Topological Modular Forms"
},
{
"url": "https://arxiv.org/abs/2311.07958",
"label": "Comparing Tempered and Equivar... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Let $G$ be a compact Lie group with adjoint representation $L$. Is $\operatorname{TMF}^G$ a dualizable $\operatorname{TMF}$-module with dual $(\Sigma^{-L}\operatorname{TMF})^G$? | If G is a compact Lie group with adjoint representation L, is TMF^G a dualizable TMF-module with dual (\Sigma^{-L}TMF)^G? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,205 | OWR-17132-011 | Topological Modular Forms for Cyclic Groups | For a general positive integer $n$, calculate the spectrum $\operatorname{TMF}^{C_n}$ or determine its homotopy groups. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** partially ... | 3 | partially_solved | null | 2,019 | 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-17132-011",
"literature-status:partially-solved",
"owr-year:2019"
] | Later work computes or decomposes the cases for small cyclic groups such as C-two and C-three, but no calculation for general n is available. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2101.06841",
"label": "C-two-equivariant Topological Modular Forms"
},
{
"url": "https://arxiv.org/abs/2510.23602",
"label": "Genuine C-n-equivariant Topological ... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | For a general positive integer $n$, calculate the spectrum $\operatorname{TMF}^{C_n}$ or determine its homotopy groups. | Can one explicitly calculate TMF^{C_n}, or at least determine its homotopy groups? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,206 | OWR-17132-012 | Eta-Periodic Slice Spectral Sequences over General Fields | Let $k$ be a field of characteristic zero over which $\rho$ is nonnilpotent. Determine the differentials, extensions, and abutment of the $\eta$-periodic slice spectral sequence over $k$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256](https://doi.org/10.4171/owr/2019/36)
## Literature review (checked 2026-08-22)
**Status:** open
**As... | 3 | open | null | 2,019 | 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-17132-012",
"literature-status:open",
"owr-year:2019"
] | The profile over characteristic-zero fields with nonnilpotent rho, including the conjectured real-field profile, remains unresolved in the cited and later literature. | [
{
"url": "https://doi.org/10.4171/OWR/2019/36",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2204.05937",
"label": "R-motivic v-one-periodic homotopy"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/36 | null | null | null | Let $k$ be a field of characteristic zero over which $\rho$ is nonnilpotent. Determine the differentials, extensions, and abutment of the $\eta$-periodic slice spectral sequence over $k$. | For a characteristic-zero field k in which \rho is non-nilpotent, what is the profile of the \eta-periodic slice spectral sequence over k? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Homotopy Theory (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/36, pp. 2183--2256 |
30,004,207 | OWR-17133-001 | Equivalence of Nuclear Dimension, Z-Stability, and Strict Comparison | For simple, separable, nonelementary, nuclear $C^*$-algebras, are finite nuclear dimension, $\mathcal Z$-stability, and strict comparison equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332](https://doi.org/10.4171/owr/2019/37)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,019 | 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-17133-001",
"literature-status:open",
"owr-year:2019"
] | The UCT problem for separable nuclear C-star algebras remains unresolved; finite-complexity and groupoid subclasses are known to satisfy UCT. | [
{
"url": "https://doi.org/10.4171/OWR/2019/37",
"label": "original Oberwolfach report"
},
{
"url": "https://arxiv.org/abs/2104.10766",
"label": "The UCT for C-star Algebras with Finite Complexity"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/37 | null | null | null | For simple, separable, nonelementary, nuclear $C^*$-algebras, are finite nuclear dimension, $\mathcal Z$-stability, and strict comparison equivalent? | For simple, separable, non-elementary, nuclear C^*-algebras, are finite nuclear dimension, Z-stability, and strict comparison equivalent? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332 |
30,004,208 | OWR-17133-004 | The Dixmier Unitarisability Problem | Is every unitarisable discrete group amenable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332](https://doi.org/10.4171/owr/2019/37)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,019 | 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-17133-004",
"literature-status:open",
"owr-year:2019"
] | Amenable groups are unitarisable, but the converse remains unresolved for nonamenable groups without free subgroups; the cited literature gives progress rather than a proof or counterexample. | [
{
"url": "https://doi.org/10.4171/owr/2019/37",
"label": "Oberwolfach Report 37, Dixmier problem"
},
{
"url": "https://arxiv.org/abs/0812.2093",
"label": "Monod and Ozawa, non-unitarisable groups"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/37 | null | null | null | Is every unitarisable discrete group amenable? | Is every unitarisable discrete group amenable? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332 |
30,004,209 | OWR-17133-009 | Freely Complemented and Maximal Amenable MASAs | Let $p=(p_1,\ldots,p_d)$ be evaluated on a semicircular $d$-tuple $S$. Under what conditions does $p_1(S)$ generate a freely complemented masa? Is this generic? Are most masas in $L(F_d)$ maximal amenable, and is every maximal amenable masa freely complemented? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332](https://doi.org/10.4171/owr/2019/37)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,019 | 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-17133-009",
"literature-status:open",
"owr-year:2019"
] | The question for general polynomial images p sub 1 of a semicircular family remains open; known generator, radial, perturbative, and reassembly examples do not settle genericity or all maximal-amenability questions. | [
{
"url": "https://doi.org/10.4171/owr/2019/37",
"label": "Oberwolfach Report 37, MASA questions"
},
{
"url": "https://arxiv.org/abs/2411.05136",
"label": "Boschert et al., freely complemented MASAs"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/37 | null | null | null | Let $p=(p_1,\ldots,p_d)$ be evaluated on a semicircular $d$-tuple $S$. Under what conditions does $p_1(S)$ generate a freely complemented masa? Is this generic? Are most masas in $L(F_d)$ maximal amenable, and is every maximal amenable masa freely complemented? | For a polynomial p=(p_1,\ldots,p_d) evaluated on a semicircular d-tuple S, under what conditions does p_1(S) generate a freely complemented MASA; is this generic, are most MASAs in L(F_d) maximal amenable, and is every maximal amenable MASA freely complemented? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332 |
30,004,210 | OWR-17133-010 | Stable Rank One for Simple Reduced Group $C^*$-Algebras | For every discrete group $G$ such that $C^*_{\lambda}(G)$ is simple, does $C^*_{\lambda}(G)$ have stable rank one? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332](https://doi.org/10.4171/owr/2019/37)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,019 | 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-17133-010",
"literature-status:open",
"owr-year:2019"
] | Stable rank one is known for important families, including free products and many acylindrically hyperbolic groups, but the general question for every discrete G with simple reduced group C*-algebra remains open. | [
{
"url": "https://doi.org/10.4171/owr/2019/37",
"label": "Oberwolfach Report 37, stable rank"
},
{
"url": "https://doi.org/10.1016/j.jfa.2020.108689",
"label": "Gerasimova and Osin, invertible elements"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/37 | null | null | null | For every discrete group $G$ such that $C^*_{\lambda}(G)$ is simple, does $C^*_{\lambda}(G)$ have stable rank one? | For every discrete group G such that C^*_{\lambda}(G) is simple, does C^*_{\lambda}(G) have stable rank one? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332 |
30,004,211 | OWR-17133-011 | Realizing Lower Semicontinuous Trace Functions by Positive Elements | Let $A$ be a separable, unital, simple, exact $C^*$-algebra, and let $f\in\operatorname{LAff}(T(A))_{++}$. Does there exist $a\in(A\otimes\mathcal K)^+$ such that
$$d_\tau([a])=f(\tau)$$
for every $\tau\in T(A)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332](https://doi.org/10.4171/owr/2019/37)
## Literature review (checked 2026-08-22)
**Status:** open
**Assess... | 3 | open | null | 2,019 | 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-17133-011",
"literature-status:open",
"owr-year:2019"
] | The rank map is realized in regular classes and is injective under strict comparison, but surjectivity for arbitrary separable unital simple exact C*-algebras remains an open rank problem. | [
{
"url": "https://doi.org/10.4171/owr/2019/37",
"label": "Oberwolfach Report 37, Cuntz semigroup"
},
{
"url": "https://doi.org/10.1016/j.jfa.2010.03.022",
"label": "Dadarlat and Toms, ranks of operators"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/37 | null | null | null | Let $A$ be a separable, unital, simple, exact $C^*$-algebra, and let $f\in\operatorname{LAff}(T(A))_{++}$. Does there exist $a\in(A\otimes\mathcal K)^+$ such that
$$d_\tau([a])=f(\tau)$$
for every $\tau\in T(A)$? | Given a separable, unital, simple, exact C^*-algebra A and f\in LAff(T(A))_{++}, does there exist a\in(A\otimes\mathcal K)^+ such that d_{\tau}([a])=f(\tau) for every \tau\in T(A)? | corrected_verified | The mathematical content was preserved while notation, typography, duplicate clauses, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | C*-Algebras (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/37, pp. 2257--2332 |
30,004,212 | OWR-17134-002 | Nonlinear Stability of Columnar Euler Vortices | What conditions, if any, ensure nonlinear stability of columnar vortices for the three-dimensional Euler equations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Aspects of Hydrodynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/38, pp. 2333--2393](https://doi.org/10.4171/owr/2019/38)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,019 | 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-17134-002",
"literature-status:open",
"owr-year:2019"
] | Spectral and asymptotic linear stability results are available for important columnar vortices, but they do not prove the requested nonlinear stability; that problem remains open. | [
{
"url": "https://arxiv.org/abs/1901.02815",
"label": "Gallay and Smets, stability of vortices"
},
{
"url": "https://arxiv.org/abs/2603.17268",
"label": "Miao, Ren, and Zhang, asymptotic linear stability"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/38 | null | null | null | What conditions, if any, ensure nonlinear stability of columnar vortices for the three-dimensional Euler equations? | What conditions, if any, ensure nonlinear stability of columnar vortices for the three-dimensional Euler equations? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mathematical Aspects of Hydrodynamics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/38, pp. 2333--2393 |
30,004,213 | OWR-17135-002 | Generating Gross Substitutes Valuations from Matroid Ranks | For every $n$, does there exist a finite $m\geq n$ such that every gross-substitutes valuation on $[n]$ can be generated from weighted matroid-rank valuations on $[m]$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | partially_solved | null | 2,019 | 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 | [Discussion #4 update, 2026-10-04] Literature status correction for **OWR-17135-002**: the finite-auxiliary matroid-based valuation question has a published negative answer. | [
"owr",
"oberwolfach-reports",
"OWR-17135-002",
"literature-status:partially-solved",
"owr-year:2019"
] | Tran disproved the matroid-based valuation generation conjecture when m equals n for n at least 4 and proved the cases n at most 3, while finite m generation for every n remains open. | [
{
"url": "https://doi.org/10.1137/19M1304295",
"label": "Tran, finite matroid-based valuation conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, gross substitutes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | For every $n$, does there exist a finite $m\geq n$ such that every gross-substitutes valuation on $[n]$ can be generated from weighted matroid-rank valuations on $[m]$? | For each number of good types n, does there exist a finite m\ge n such that every gross-substitutes valuation on [n] is generated by matroid-based valuations, namely weighted matroid ranks on [m]? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,214 | OWR-17135-004 | Realizability of Balanced Complexes as Tropical Varieties | Characterize the balanced polyhedral complexes and fans that arise as tropical varieties of classical ideals. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-004",
"literature-status:open",
"owr-year:2019"
] | The realizability question for balanced polyhedral complexes and tropical ideals remains open; concrete nonrealizability results exist, but no full characterization is known. | [
{
"url": "https://arxiv.org/abs/1903.00356",
"label": "Draisma and Rincon, nonrealizable Bergman fans"
},
{
"url": "https://doi.org/10.1016/j.aim.2022.108713",
"label": "Maclagan and Rincon, tropical varieties are balanced"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Characterize the balanced polyhedral complexes and fans that arise as tropical varieties of classical ideals. | Which balanced polyhedral complexes or fans are realizable by classical ideals as tropical varieties? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
30,004,215 | OWR-17135-006 | Grassmann Polytopes as Positive Geometries | Are all Grassmann polytopes positive geometries? Determine their topology and combinatorics in a form analogous to the theory of ordinary convex polytopes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472](https://doi.org/10.4171/owr/2019/39)
## Literature review (checked... | 3 | open | null | 2,019 | 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-17135-006",
"literature-status:open",
"owr-year:2019"
] | The assertion that all Grassmann polytopes, particularly amplituhedra, are positive geometries remains a conjecture; special cases and canonical-form results do not prove the general claim. | [
{
"url": "https://doi.org/10.1007/JHEP11%282017%29039",
"label": "Arkani-Hamed, Bai, and Lam, positive geometries"
},
{
"url": "https://doi.org/10.4171/owr/2019/39",
"label": "Oberwolfach Report 39, Grassmann polytopes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2019/39 | null | null | null | Are all Grassmann polytopes positive geometries? Determine their topology and combinatorics in a form analogous to the theory of ordinary convex polytopes. | Are Grassmann polytopes positive geometries, and what are their topology and combinatorics in analogy with ordinary convex polytopes? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometric, Algebraic, and Topological Combinatorics (2020), Oberwolfach Reports, DOI 10.4171/owr/2019/39, pp. 2395--2472 |
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