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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,816 | OWR-16164-009 | Bijection Between Eulerian Orientations and Bicolored Trees | Find a bijective proof that rooted planar Eulerian orientations are equinumerous with the corresponding class of bicolored trees. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-009",
"literature-status:open",
"owr-year:2018"
] | The generating functions for planar Eulerian orientations are known, but the report explicitly leaves open a bijective proof of equinumerosity with the corresponding bicoloured trees. Later refined enumerations do not supply that bijection. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2503.15046",
"label": "refined Eulerian-orientation enumeration"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | Find a bijective proof that rooted planar Eulerian orientations are equinumerous with the corresponding class of bicolored trees. | Find a bijective proof that rooted planar Eulerian orientations are equinumerous with the corresponding class of bicoloured trees. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,817 | OWR-16164-010 | Prevalence of Wilf Equivalence and Exponential Collapse | In natural families of finite structures, how common are Wilf equivalences? In particular, is exponential Wilf collapse typical, and what structural mechanism explains the prevalence of Wilf-equivalent objects? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-010",
"literature-status:open",
"owr-year:2018"
] | This is a broad conceptual question about explaining Wilf-equivalences rather than a single formal assertion. The report gives no general theorem answering it, so the extracted problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | In natural families of finite structures, how common are Wilf equivalences? In particular, is exponential Wilf collapse typical, and what structural mechanism explains the prevalence of Wilf-equivalent objects? | Explain how surprising Wilf-equivalences are in natural universes of finite structures; in particular, determine whether exponential Wilf-collapse is the typical behaviour and thereby explain the prevalence of Wilf-equivalent objects. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,818 | OWR-16164-012 | Brownian First-Visit Cell Lengths on the Circle | Choose starting points $p_1,\ldots,p_k$ on the unit circle and run independent Brownian motions from them. If $B_i$ is the set of points first visited by the motion started at $p_i$, determine the joint distribution of $(|B_1|,\ldots,|B_k|)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-012",
"literature-status:open",
"owr-year:2018"
] | The stated Brownian first-visit Voronoi problem asks for the joint law of all cell lengths on the circle. No paper resolving this exact distribution was found; the original report records it as unpublished and unknown. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | Choose starting points $p_1,\ldots,p_k$ on the unit circle and run independent Brownian motions from them. If $B_i$ is the set of points first visited by the motion started at $p_i$, determine the joint distribution of $(|B_1|,\ldots,|B_k|)$. | Choose k starting points on the unit circle and run independent Brownian motions from them; if B_i is the set of points first visited by the particle from p_i, determine the joint probability distribution of the vector (|B_1|,\ldots,|B_k|). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,819 | OWR-16164-013 | Stanley Rank-Size Bounds for Differential Posets | For every $r$-differential poset with rank sizes $p_n$, improve the bound $$p_n\leq1+r\sum_{k=0}^{n-2}p_k+(r-1)p_{n-1}$$ toward Stanley's conjectured inequality $p_n\leq rp_{n-1}+p_{n-2}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-013",
"literature-status:open",
"owr-year:2018"
] | The report states Stanley's upper bound p_n \leq r p_{n-1}+p_{n-2} is still open. Later work proves strict rank growth, but does not prove this upper-bound conjecture or the requested improvement to Byrnes' inequality. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1806.03509",
"label": "rank gaps in differential posets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | For every $r$-differential poset with rank sizes $p_n$, improve the bound $$p_n\leq1+r\sum_{k=0}^{n-2}p_k+(r-1)p_{n-1}$$ toward Stanley's conjectured inequality $p_n\leq rp_{n-1}+p_{n-2}$. | For every r-differential poset with rank sizes p_n, improve the known bound p_n\leq 1+r\sum_{k=0}^{n-2}p_k+(r-1)p_{n-1} so as to approach Stanley's conjectured inequality p_n\leq rp_{n-1}+p_{n-2}. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,820 | OWR-16164-014 | Positive Polynomial Comparisons for Unitriangular Conjugacy Classes | Put $T=q-1$ and define $A_n(T)$ by $$\sum_{n\geq0}A_n(T)\frac{x^n}{n!}=(1-\sin(Tx))^{-1/T}.$$ For an infinite family of prime powers $q$ for which the number $k(U_n(\mathbb F_q))$ of conjugacy classes in $U_n(\mathbb F_q)$ is polynomial in $q$, is $$k(U_n(\mathbb F_{T+1}))-A_n(T)\in\mathbb N[T]$$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-014",
"literature-status:open",
"owr-year:2018"
] | The conjectured nonnegative-polynomial comparison for conjugacy classes of unitriangular groups was verified only through n=16. Current primary literature still treats the underlying Higman polynomiality question as unresolved and offers no proof or counterexample for this stronger claim. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1507.00411",
"label": "Pak--Soffer on Higman's conjecture"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | Put $T=q-1$ and define $A_n(T)$ by $$\sum_{n\geq0}A_n(T)\frac{x^n}{n!}=(1-\sin(Tx))^{-1/T}.$$ For an infinite family of prime powers $q$ for which the number $k(U_n(\mathbb F_q))$ of conjugacy classes in $U_n(\mathbb F_q)$ is polynomial in $q$, is $$k(U_n(\mathbb F_{T+1}))-A_n(T)\in\mathbb N[T]$$? | Let T=q-1 and define A_n(T) by \sum_{n\geq0}A_n(T)x^n/n!=(1-\sin(Tx))^{-1/T}. Prove or disprove that, for an infinite family of primes q for which k(U_n(\mathbb{F}_q)) is polynomial in q, the difference k(U_n(\mathbb{F}_{T+1}))-A_n(T) belongs to \mathbb{N}[T]. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,821 | OWR-16164-019 | Pattern-Avoidance Inequalities on Digitally Convex Shapes | Let $\lambda\subset\mathbb Z^2$ be a digitally convex shape of side $n$, and let $S_\lambda$ consist of the permutations $\sigma\in S_n$ whose graph lies in $\lambda$. Let $A_\lambda$ count the permutations in $S_\lambda$ that avoid every increasing triple $i_1<i_2<i_3$ for which both $(i_1,\sigma_{i_3})$ and $(i_3,\si... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | partially_solved | null | 2,018 | 2 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-28T00:00:00 | 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 | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-09-28",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16164-019",
"literature-status:open",
"owr-year:2018"
] | Ferudun’s band $\lambda=\{(x,y)\in[7]^2:-3\le y-x\le4\}$ has $A_\lambda=536>B_\lambda=515$. Independent enumeration from the record’s pattern definitions reproduces both counts. Swapping the red and blue conventions bijects the colourings and leaves the count unchanged. The manuscript is an unrefereed preprint produced... | [
{
"url": "https://doi.org/10.5281/zenodo.23006715",
"label": "Alper Ferudun (2026), A Counterexample to a Conjecture of Sportiello on Coloured Permutations in Convex Shapes — unrefereed preprint"
},
{
"url": "https://eulersolve.org/papers/owr-16164-019/",
"label": "EulerSolve manuscript, source,... | 2026-09-28T00:00:00 | Alper Ferudun (2026), A Counterexample to a Conjecture of Sportiello on Coloured Permutations in Convex Shapes — unrefereed preprint: https://doi.org/10.5281/zenodo.23006715
EulerSolve manuscript, source, and verification materials: https://eulersolve.org/papers/owr-16164-019/
Enumerative Combinatorics (2019), Oberwolf... | https://doi.org/10.4171/owr/2018/23 | null | null | null | Let $\lambda\subset\mathbb Z^2$ be a digitally convex shape of side $n$, and let $S_\lambda$ consist of the permutations $\sigma\in S_n$ whose graph lies in $\lambda$. Let $A_\lambda$ count the permutations in $S_\lambda$ that avoid every increasing triple $i_1<i_2<i_3$ for which both $(i_1,\sigma_{i_3})$ and $(i_3,\si... | For every digitally-convex shape \lambda, prove the conjecture B_\lambda\geq A_\lambda, where A_\lambda counts the specified uncoloured pattern-avoiding permutations in \lambda and B_\lambda counts the corresponding specified two-coloured pattern-avoiding permutations. | 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 | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,822 | OWR-16164-020 | Catalan-Power Divisibility of a Set-Partition Transition Determinant | Let $A=(a_{ij})_{1\leq i,j\leq n}$. For set partitions $P$ of $X=\{x_1,\ldots,x_n\}$ and $Q$ of $Y=\{y_1,\ldots,y_n\}$, call a set $S$ of edges $x_i y_j$ a transition from $P$ to $Q$ if adjoining $S$ to spanning trees on the blocks of $P$ produces a spanning forest of $X\cup Y$ in which every component meets $Y$ and th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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 | {
"source_url": "https://zenodo.org/records/23298482",
"checked_at": "2026-10-11",
"kind": "claim",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 unrefereed claim, 2026-10-11] I have released an unrefereed preprint, **On a Determinant of Teufl and Wagner Related to Set Partitions: Divisibility by the Catalan Power of det A** (Alper Ferudun, Mercury Software GmbH). (https://zenodo.org/records/23298482) | [
"owr",
"oberwolfach-reports",
"OWR-16164-020",
"literature-status:open",
"owr-year:2018"
] | The determinant divisibility statement was supported experimentally only through small n in the report, and no general proof or counterexample was found in the subsequent literature search. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | Let $A=(a_{ij})_{1\leq i,j\leq n}$. For set partitions $P$ of $X=\{x_1,\ldots,x_n\}$ and $Q$ of $Y=\{y_1,\ldots,y_n\}$, call a set $S$ of edges $x_i y_j$ a transition from $P$ to $Q$ if adjoining $S$ to spanning trees on the blocks of $P$ produces a spanning forest of $X\cup Y$ in which every component meets $Y$ and th... | For the matrix T in the conjectured uniform presentation of the pure braid group, determine whether (\det A)C_n always divides \det T, where C_n=\frac{1}{n+1}\binom{2n}{n} is the n-th Catalan number. | 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 | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,823 | OWR-16164-021 | Uniform Presentations of Pure Reflection Braid Groups | Let $W$ be a finite reflection group with pure braid group $P_c(W)$, let $T$ be the set of squares of the reflection generators, and let $\Delta$ be the full twist. Is $$P_c(W)=\langle T:\operatorname{Red}_T(\Delta)\rangle$$ a presentation for every finite reflection group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464](https://doi.org/10.4171/owr/2018/23)
## Literature review (checked 2026-08-21)
**Status:** ... | 3 | open | null | 2,018 | 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-16164-021",
"literature-status:open",
"owr-year:2018"
] | The proposed uniform full-twist presentation for pure braid groups is proved in several Coxeter types, including A, B, D, H3, I2(m), and F4, but remains open for the remaining exceptional types; the universal claim is therefore open. | [
{
"url": "https://doi.org/10.4171/owr/2018/23",
"label": "original OWR report"
},
{
"url": "https://math.mit.edu/research/highschool/primes/materials/2025/Liu-Williams.pdf",
"label": "Liu--Williams full-twist presentations"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/23 | null | null | null | Let $W$ be a finite reflection group with pure braid group $P_c(W)$, let $T$ be the set of squares of the reflection generators, and let $\Delta$ be the full twist. Is $$P_c(W)=\langle T:\operatorname{Red}_T(\Delta)\rangle$$ a presentation for every finite reflection group? | For a finite reflection group W with pure braid group P_c(W), prove or disprove the uniform presentation P_c(W)=\langle T:\operatorname{Red}_T(\Delta)\rangle, where T consists of the squares of the reflection generators and \Delta is the full twist. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Enumerative Combinatorics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/23, pp. 1381--1464 |
30,003,824 | OWR-16165-003 | Derived Decomposition of Fixed-Determinant Bundle Moduli | Let $C$ be a smooth projective curve of genus $g$, let $L$ be a line bundle of degree one, and let $M_C(2,L)$ be the moduli space of rank-two bundles with determinant $L$. Does its bounded derived category admit the semiorthogonal decomposition
$$
D^b(M_C(2,L))=\left\langle D^b(k),D^b(k),D^b(C),D^b(C),\ldots,D^b(\opera... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515](https://doi.org/10.4171/owr/2018/24)
## Literature ... | 3 | partially_solved | null | 2,018 | 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 | {
"source_url": "https://doi.org/10.1215/00127094-2024-0016",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes; the generation step is in an unpublished preprint)**. P. Belmans (OWR 24/2018, p. 1475, Conjecture 7): for a curve C of genus g ≥ 2 and deg L = 1, D^b(M_C(2, L)) decomposes semiorthogonally into two copies of D^b(Sym^i C) for i = 0, …, g − 2 and one of D^b(Sy... | [
"owr",
"oberwolfach-reports",
"OWR-16165-003",
"literature-status:open",
"owr-year:2018"
] | Substantial partial semiorthogonal decompositions containing the expected symmetric-power components are known, but the complement required by the conjectured full decomposition is still not proved to be trivial. | [
{
"url": "https://doi.org/10.4171/owr/2018/24",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1017/fms.2023.14",
"label": "current moduli-space decomposition results"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/24 | null | null | null | Let $C$ be a smooth projective curve of genus $g$, let $L$ be a line bundle of degree one, and let $M_C(2,L)$ be the moduli space of rank-two bundles with determinant $L$. Does its bounded derived category admit the semiorthogonal decomposition
$$
D^b(M_C(2,L))=\left\langle D^b(k),D^b(k),D^b(C),D^b(C),\ldots,D^b(\opera... | For a smooth projective curve C of genus g and a degree-one line bundle L, conjecture that the derived category of the rank-two fixed-determinant moduli space has a semiorthogonal decomposition with two copies of Db(Sym^i C) for i=0,\ldots,g-2 and one copy of Db(Sym^{g-1}C), together with the indicated exceptional Db(\... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515 |
30,003,825 | OWR-16165-006 | Ideals in the Positive Witt Algebra | For the positive Witt algebra $W_+$ with $[e_i,e_j]=(j-i)e_{i+j}$, prove or disprove that every nonzero ideal $I$ of $U(W_+)$ gives a quotient of finite Gelfand–Kirillov dimension, and that the two-sided ideals of $U(W_+)$ satisfy the ascending chain condition. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515](https://doi.org/10.4171/owr/2018/24)
## Literature ... | 3 | partially_solved | null | 2,018 | 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 | {
"source_url": null,
"checked_at": "2026-09-29",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **partially_solved**. S. J. Sierra (joint with A. Petukhov; OWR 24/2018, p. 1503) conjectures that (1) U(W_+) has just infinite GK-dimension and (2) its two-sided ideals satisfy the ACC. | [
"owr",
"oberwolfach-reports",
"OWR-16165-006",
"literature-status:open",
"owr-year:2018"
] | The two conjectures that every nonzero quotient of U(W-plus) has finite Gelfand-Kirillov dimension and that its two-sided ideals satisfy ACC were explicitly left unproved; later work located gives partial results, not a resolution. | [
{
"url": "https://doi.org/10.4171/owr/2018/24",
"label": "original OWR report"
},
{
"url": "https://webhomes.maths.ed.ac.uk/~ssierra/preprints.html",
"label": "Sierra current research list"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/24 | null | null | null | For the positive Witt algebra $W_+$ with $[e_i,e_j]=(j-i)e_{i+j}$, prove or disprove that every nonzero ideal $I$ of $U(W_+)$ gives a quotient of finite Gelfand–Kirillov dimension, and that the two-sided ideals of $U(W_+)$ satisfy the ascending chain condition. | For the positive Witt algebra W_+ with [e_i,e_j]=(j-i)e_{i+j}, prove or disprove that every nonzero ideal I of U(W_+) gives a quotient of finite Gelfand--Kirillov dimension, and that the two-sided ideals of U(W_+) satisfy the ascending chain condition. | 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 | Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515 |
30,003,826 | OWR-16165-007 | Ideal Theory of Witt and Virasoro Enveloping Algebras | For the full Witt algebra $W$ and the Virasoro algebra $V$, do their enveloping algebras have the following properties: every nonzero ideal has a quotient of finite Gelfand–Kirillov dimension, two-sided ideals satisfy the ascending chain condition, and an ideal containing a quadratic expression in the generators has a ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515](https://doi.org/10.4171/owr/2018/24)
## Literature ... | 3 | open | null | 2,018 | 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-16165-007",
"literature-status:open",
"owr-year:2018"
] | The proposed analogues for the full Witt algebra and the Virasoro algebra were stated as future work, and no proof of those analogues was found in the current primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2018/24",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/24 | null | null | null | For the full Witt algebra $W$ and the Virasoro algebra $V$, do their enveloping algebras have the following properties: every nonzero ideal has a quotient of finite Gelfand–Kirillov dimension, two-sided ideals satisfy the ascending chain condition, and an ideal containing a quadratic expression in the generators has a ... | For the full Witt algebra W and the Virasoro algebra V, do analogues of the three assertions hold for their enveloping algebras: every nonzero ideal has a quotient of finite GK-dimension, two-sided ideals satisfy the ascending chain condition, and an ideal containing a quadratic expression in the generators has a quoti... | 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 | Interactions between Algebraic Geometry and Noncommutative Algebra (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/24, pp. 1465--1515 |
30,003,827 | OWR-16166-001 | Brauer–Manin Obstruction for Rationally Connected Varieties | Let $X$ be a smooth, proper, geometrically irreducible, rationally connected variety over a number field $k$. Is $X(k)$ dense in the Brauer–Manin set $X(\mathbb A_k)^{\operatorname{Br}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 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-16166-001",
"literature-status:open",
"owr-year:2018"
] | The fragment refers to Colliot-Thelene's conjecture that the Brauer-Manin obstruction is the only obstruction for smooth proper rationally connected varieties over number fields. Fibration methods prove important special cases, but the general conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2018/25",
"label": "original OWR report"
},
{
"url": "https://annals.math.princeton.edu/2016/183-1/p05",
"label": "fibration method for rational points"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | Let $X$ be a smooth, proper, geometrically irreducible, rationally connected variety over a number field $k$. Is $X(k)$ dense in the Brauer–Manin set $X(\mathbb A_k)^{\operatorname{Br}}$? | Let X be a smooth proper geometrically irreducible rationally connected variety over a number field k. Is X(k) dense in the Brauer-Manin set X(\mathbb{A}_k)^{\mathrm{Br}}? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,828 | OWR-16166-002 | Split Values of Linear and Quadratic Polynomials | Theorem-level partial result: Conjecture 6 on split values of polynomials holds for n=2 when k=k_1=\mathbb{Q} and k_2 is a quadratic extension of \mathbb{Q}, equivalently for one linear and one quadratic polynomial. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Answered in the source or not an open problem (solved (a theorem, not a problem)) | null | null | [Discussion #4 literature review, 2026-10-02] **solved (a theorem, not a problem)**. The record is Theorem 10 of D. Schindler's abstract (OWR 25/2018, p. 1537): the Harpaz–Wittenberg conjecture on split values of polynomials (Conjecture 6 there; Conjecture 9.1 of [Ann. of Math. 183 (2016)](https://doi.org/10.4007/annal... | [
"owr",
"oberwolfach-reports",
"OWR-16166-002",
"literature-status:open",
"owr-year:2018"
] | The extracted text records a proved one-quadratic/one-linear case of Harpaz--Wittenberg Conjecture 6 and further special cubic cases, but the general conjecture remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://doi.org/10.1093/imrn/rnx252",
"label": "Browning--Schindler"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | null | Theorem-level partial result: Conjecture 6 on split values of polynomials holds for n=2 when k=k_1=\mathbb{Q} and k_2 is a quadratic extension of \mathbb{Q}, equivalently for one linear and one quadratic polynomial. | unrecoverable | The official report labels this statement as Theorem 10 and presents it as a proved special case of the split-values conjecture, not as an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,829 | OWR-16166-004 | Milnor K-Theory Reconstruction of Function Fields and Varieties | In reconstruction from Milnor $K$-theory, can field-reconstruction counterexamples arise from function fields of curves over algebraically closed or finite fields? Can reconstruction be extended to function fields of transcendence degree at least $2$ over more general base fields? What minimal data determine a normal, ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 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-16166-004",
"literature-status:open",
"owr-year:2018"
] | The record asks for extensions beyond the proved finitely generated regular function-field cases and for non-birational reconstruction up to isomorphism; these broader questions remain unresolved. | [
{
"url": "https://webusers.imj-prg.fr/~anna.cadoret/K2.pdf",
"label": "Cadoret--Pirutka"
},
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | In reconstruction from Milnor $K$-theory, can field-reconstruction counterexamples arise from function fields of curves over algebraically closed or finite fields? Can reconstruction be extended to function fields of transcendence degree at least $2$ over more general base fields? What minimal data determine a normal, ... | For Milnor-K-theoretic reconstruction, can a counterexample to field reconstruction arise from function fields of curves over algebraically closed or finite fields; can the applications be extended to function fields of transcendence degree at least two over more general base fields; and what minimal data determine a n... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,830 | OWR-16166-007 | Decidability of Finite Field Extensions | Is every finite extension of a decidable field necessarily decidable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem (solved (no; answered in the source)) | null | null | [Discussion #4 literature review, 2026-10-02] **solved (no; answered in the source)**. J. Koenigsmann (OWR 25/2018, p. 1556, Question 2, raised in his [Israel J. Math. 214 (2016)](https://doi.org/10.1007/s11856-016-1367-9) paper) asks whether every finite extension of a decidable field is decidable, and reports a negat... | [
"owr",
"oberwolfach-reports",
"OWR-16166-007",
"literature-status:open",
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] | The cited list remains a frontier for complete first-order decidability; only restricted fragments and related languages have been settled. | [
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://doi.org/10.2140/ant.2016.10.665",
"label": "Anscombe--Fehm"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | null | Is every finite extension of a decidable field necessarily decidable? | unrecoverable | The official report answers the question negatively by constructing a decidable field with an undecidable finite extension, so the extraction is not an unresolved problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,831 | OWR-16166-008 | Computing Galois Closures over Rational Function Fields | Let $k$ be a field, let $a_1,\ldots,a_n$ be algebraically independent over $k$, set $K=k(a_1,\ldots,a_n)$, and let $L/K$ be an explicitly given finite separable extension. Construct an algorithm that computes the Galois group of the Galois closure of $L/K$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 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-16166-008",
"literature-status:open",
"owr-year:2018"
] | The excerpt is a general algorithmic problem statement and is truncated before a claim or resolution; existing work treats special polynomial and geometric families, not the full problem. | [
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://arxiv.org/abs/1805.05454",
"label": "Entin"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | Let $k$ be a field, let $a_1,\ldots,a_n$ be algebraically independent over $k$, set $K=k(a_1,\ldots,a_n)$, and let $L/K$ be an explicitly given finite separable extension. Construct an algorithm that computes the Galois group of the Galois closure of $L/K$. | Given a field k, independent variables a_1,\ldots,a_n, K=k(a_1,\ldots,a_n), and an explicit finite separable extension L/K, can one compute the Galois group of the Galois closure of L over K? | 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 | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,832 | OWR-16166-009 | Square Discriminants and Minimal Ramification of Alternating Group Powers | Let $$\mathcal M_n=\left\{X^n+\sum_{i=0}^{n-1}\varepsilon_iX^i:\varepsilon_i\in\{\pm1\}\right\}.$$ Does the proportion of polynomials in $\mathcal M_n$ with square discriminant tend to zero as $n\to\infty$, and can the number of such polynomials be bounded by $O(1)$? Separately, for $G=A_5^n$, is the Boston–Markin pred... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 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-16166-009",
"literature-status:open",
"owr-year:2018"
] | The square-discriminant asymptotic and the A5-product minimal-ramification conjecture remain open; later work gives related bounds and lower bounds but no resolution of either target. | [
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://doi.org/10.1112/blms.13049",
"label": "Bary-Soroker--Ben-Porath--Matei"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | Let $$\mathcal M_n=\left\{X^n+\sum_{i=0}^{n-1}\varepsilon_iX^i:\varepsilon_i\in\{\pm1\}\right\}.$$ Does the proportion of polynomials in $\mathcal M_n$ with square discriminant tend to zero as $n\to\infty$, and can the number of such polynomials be bounded by $O(1)$? Separately, for $G=A_5^n$, is the Boston–Markin pred... | For M_n=\{f=X^n+\sum_{i=0}^{n-1}\epsilon_iX^i:\epsilon_i\in\{\pm1\}\}, does the number of polynomials whose discriminant is a square tend to zero as n tends to infinity, and can the relevant upper bound be improved to O(1)? In addition, for G=A_5^n, is the Boston-Markin conjecture m(G)=\max\{d(G/[G,G]),1\} true, in par... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,833 | OWR-16166-010 | Inverse-Galois and Decidability Problems for Profinite Groups | Let $G$ be a finite group and let $C_1,\ldots,C_{m(G)+r}$ be conjugacy classes of cyclic subgroups that generate $G$. Is there a tamely ramified extension $L/\mathbb Q$ with Galois group $G$ and inertia groups $C_1,\ldots,C_{m(G)+r}$? Can every finite $p$-group occur as a regular Galois group over $\mathbb Q(t)$? For $... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577](https://doi.org/10.4171/owr/2018/25)
## Literature review (checked 2026-08-21)
**Status:** open
**A... | 3 | open | null | 2,018 | 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"
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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-16166-010",
"literature-status:open",
"owr-year:2018"
] | This bundle contains unresolved tame inverse-Galois, regular p-group realization, profinite, and decidability questions; known solvable and simple-group cases do not settle the general claims. | [
{
"url": "https://ems.press/content/serial-article-files/46747",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/25 | null | null | null | Let $G$ be a finite group and let $C_1,\ldots,C_{m(G)+r}$ be conjugacy classes of cyclic subgroups that generate $G$. Is there a tamely ramified extension $L/\mathbb Q$ with Galois group $G$ and inertia groups $C_1,\ldots,C_{m(G)+r}$? Can every finite $p$-group occur as a regular Galois group over $\mathbb Q(t)$? For $... | Given a finite group G and conjugacy classes of cyclic subgroups C_1,\ldots,C_{m(G)+r} generating G, does there exist a tame extension L/\mathbb{Q} with Galois group G and inertia groups C_1,\ldots,C_{m(G)+r}? Can every finite p-group be realized as a regular Galois group Gal(K/\mathbb{Q}(t)) with K\cap\mathbb{Q}=\math... | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Field Arithmetic (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/25, pp. 1517--1577 |
30,003,834 | OWR-16167-003 | Finiteness Properties of Hyperbolic Tessellation Groups | Let $\Delta$ be a tessellation of the hyperbolic plane, let $S_\infty$ be the finitary symmetric group, and suppose that $\phi(\Delta)/S_\infty$ is isomorphic to Thompson's group $V$. Do $\phi(\Delta)$ and $\phi(\Delta)/S_\infty$ have the same finiteness properties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-003",
"literature-status:open",
"owr-year:2018"
] | The equality of finiteness properties for phi(Delta)/S_infty and phi(Delta) remains an open general question; known results cover special Euclidean and Houghton-type cases. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://doi.org/10.4171/JCA/91",
"label": "Farley--Hughes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Let $\Delta$ be a tessellation of the hyperbolic plane, let $S_\infty$ be the finitary symmetric group, and suppose that $\phi(\Delta)/S_\infty$ is isomorphic to Thompson's group $V$. Do $\phi(\Delta)$ and $\phi(\Delta)/S_\infty$ have the same finiteness properties? | For a hyperbolic-plane tessellation \Delta, with S_\infty the finitary symmetric group and phi(\Delta)/S_\infty isomorphic to Thompson's group V, do phi(\Delta)/S_\infty and phi(\Delta) have the same finiteness properties? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,835 | OWR-16167-004 | Smoothability of Group Actions on One-Manifolds | Let $M$ be a connected one-dimensional manifold and let $G<\operatorname{Homeo}^+(M)$ act on $M$. Does the abstract group $G$ admit a faithful action by $C^r$ diffeomorphisms on $M$? Is the given action topologically conjugate to a $C^r$ action, and what obstructs such actions on one-dimensional manifolds? Also, does a... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-004",
"literature-status:open",
"owr-year:2018"
] | The bundle has partial smoothability and rigidity theorems, but faithful countable property-T circle actions and amenability of F remain unresolved; hence the extracted bundle is open. | [
{
"url": "https://doi.org/10.1112/topo.12151",
"label": "Lodha--Matte Bon--Triestino"
},
{
"url": "https://arxiv.org/abs/2011.12861",
"label": "Duchesne"
},
{
"url": "https://doi.org/10.4171/JCA/110",
"label": "Guba"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Let $M$ be a connected one-dimensional manifold and let $G<\operatorname{Homeo}^+(M)$ act on $M$. Does the abstract group $G$ admit a faithful action by $C^r$ diffeomorphisms on $M$? Is the given action topologically conjugate to a $C^r$ action, and what obstructs such actions on one-dimensional manifolds? Also, does a... | Let M be a connected 1-manifold and let G<\operatorname{Homeo}^+(M) act on M. Does the underlying group admit a faithful action by C^r diffeomorphisms on M; is the given action topologically conjugate to a C^r action; and what obstructs C^r actions on 1-manifolds? Also, does an infinite Kazhdan group admit a faithful a... | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,836 | OWR-16167-005 | $C^1$ Smoothability of Monod and Lodha–Moore Groups | Are the Monod groups $H(A)$ and the Lodha–Moore group $G_0$ smoothable by $C^1$ diffeomorphisms, or do they admit faithful $C^1$ actions on the real line or a closed interval? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-005",
"literature-status:open",
"owr-year:2018"
] | The groups are not identified in the truncated record; available smoothability results cover special classes only, so the exact question is unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://doi.org/10.1112/topo.12151",
"label": "Lodha--Matte Bon--Triestino"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Are the Monod groups $H(A)$ and the Lodha–Moore group $G_0$ smoothable by $C^1$ diffeomorphisms, or do they admit faithful $C^1$ actions on the real line or a closed interval? | Are the Monod groups H(A) and the Lodha-Moore group G_0 smoothable by C^1 diffeomorphisms, or do they admit faithful C^1 actions on the real line or a closed interval? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,837 | OWR-16167-006 | Zimmer Rigidity for Homeomorphism Actions | Does Zimmer's conjecture remain true for actions by homeomorphisms, rather than diffeomorphisms: namely, do higher-rank lattices have only virtually trivial actions on closed manifolds below the prescribed dimension bound? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-006",
"literature-status:open",
"owr-year:2018"
] | Zimmer-type rigidity for homeomorphism actions remains open in the C0 setting, despite substantial smooth and singular-diffeomorphism results. | [
{
"url": "https://doi.org/10.1090/noti2252",
"label": "Zimmer program survey"
},
{
"url": "https://doi.org/10.1112/topo.12151",
"label": "Lodha--Matte Bon--Triestino"
},
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Does Zimmer's conjecture remain true for actions by homeomorphisms, rather than diffeomorphisms: namely, do higher-rank lattices have only virtually trivial actions on closed manifolds below the prescribed dimension bound? | Does Zimmer's conjecture remain true for actions by homeomorphisms, rather than diffeomorphisms: namely, do higher-rank lattices have only virtually trivial actions on closed manifolds below the prescribed dimension bound? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,838 | OWR-16167-007 | Automaticity of Thompson's Group $F$ | Is Thompson's group $F$ automatic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-007",
"literature-status:open",
"owr-year:2018"
] | Automaticity of Thompson's group F remains unresolved; autostackability and other weaker structures do not provide an automatic structure. | [
{
"url": "https://doi.org/10.1016/j.jalgebra.2019.04.004",
"label": "Corwin--Golan--Hermiller--Johnson--Sunic"
},
{
"url": "https://arxiv.org/abs/1501.04313",
"label": "Elder--Taback"
},
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Repor... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Is Thompson's group $F$ automatic? | Is Thompson's group F automatic? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,839 | OWR-16167-008 | Graph-Automatic Structures for Thompson's Group $F$ | Why should Thompson's group $F$ fail to be automatic, and does $F$ admit a graph-automatic structure? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-008",
"literature-status:open",
"owr-year:2018"
] | F has 1-counter and 3-counter graph-automatic structures, but ordinary automaticity and graph automaticity in the stated finite-state sense remain unresolved. | [
{
"url": "https://arxiv.org/abs/1501.04313",
"label": "Elder--Taback"
},
{
"url": "https://arxiv.org/abs/1501.04315",
"label": "Taback--Younes"
},
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Why should Thompson's group $F$ fail to be automatic, and does $F$ admit a graph-automatic structure? | Why should Thompson's group F fail to be automatic, and does F admit a graph-automatic structure? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,840 | OWR-16167-010 | Conjugacy in Braided Thompson Groups | Is the conjugacy problem decidable for the braided Thompson groups $F_{\mathrm{br}}$ and $T_{\mathrm{br}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-010",
"literature-status:open",
"owr-year:2018"
] | The 2018 result settles V_br but explicitly leaves conjugacy for F_br and T_br as open follow-up questions; no later general solution was found. | [
{
"url": "https://ems.press/content/serial-article-files/46748",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://arxiv.org/abs/1210.2931",
"label": "Bux--Flueck--Witzel"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Is the conjugacy problem decidable for the braided Thompson groups $F_{\mathrm{br}}$ and $T_{\mathrm{br}}$? | Is the conjugacy problem decidable for the braided Thompson groups F_{br} and T_{br}? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,841 | OWR-16167-011 | Closed Spraiges in the Braided Thompson Group | A closed spraige is a closed split–braid–merge band diagram representing conjugacy data in the braided Thompson group $V_{\mathrm{br}}$. Beyond its use in studying conjugacy, what structural or dynamical information about $V_{\mathrm{br}}$ can be recovered from closed spraiges? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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"
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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-16167-011",
"literature-status:open",
"owr-year:2018"
] | The record poses a broad follow-up about further invariants of closed spraiges; the cited conjugacy result does not settle it. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | A closed spraige is a closed split–braid–merge band diagram representing conjugacy data in the braided Thompson group $V_{\mathrm{br}}$. Beyond its use in studying conjugacy, what structural or dynamical information about $V_{\mathrm{br}}$ can be recovered from closed spraiges? | What further information about the braided Thompson group V_{br} can be extracted from closed spraiges? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,842 | OWR-16167-012 | Subgroups of Piecewise-Projective Homeomorphism Groups | Is Thompson's group $F$ the only structurally significant subgroup of the group $\operatorname{PL}_o(I)$ of orientation-preserving piecewise-linear homeomorphisms of the interval? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-012",
"literature-status:open",
"owr-year:2018"
] | The phrase interesting subgroup is not a precise theorem, and the subgroup structure of PLo(I) remains poorly understood in the primary literature. | [
{
"url": "https://arxiv.org/abs/math/0501085",
"label": "Brin"
},
{
"url": "https://ems.press/content/serial-article-files/46748",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Is Thompson's group $F$ the only structurally significant subgroup of the group $\operatorname{PL}_o(I)$ of orientation-preserving piecewise-linear homeomorphisms of the interval? | Is Thompson's group F the only interesting subgroup of the group of piecewise-projective homeomorphisms PLo(I)? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,843 | OWR-16167-013 | Empty Regions in the Biembeddability Poset | In the poset of biembeddability classes of finitely generated subgroups of $\operatorname{PL}_o(I)$, are all three of the following regions empty: elementary-amenable classes incomparable with $F$, non-elementary-amenable classes incomparable with $F$, and non-elementary-amenable subgroups of $F$ into which $F$ does no... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-013",
"literature-status:open",
"owr-year:2018"
] | The emptiness of Regions 2,4,6 remains unresolved; later work still describes the corresponding Brin--Sapir boundary as unknown. | [
{
"url": "https://ems.press/content/serial-article-files/46748",
"label": "Oberwolfach Report 2019"
},
{
"url": "https://oa.tib.eu/renate/server/api/core/bitstreams/13a65f3d-fc78-4e5e-8baf-43e2dfd9102a/content",
"label": "Oberwolfach Report 2020"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | In the poset of biembeddability classes of finitely generated subgroups of $\operatorname{PL}_o(I)$, are all three of the following regions empty: elementary-amenable classes incomparable with $F$, non-elementary-amenable classes incomparable with $F$, and non-elementary-amenable subgroups of $F$ into which $F$ does no... | In the poset of biembeddability classes of finitely generated subgroups of PLo(I), are the regions consisting respectively of elementary-amenable classes incomparable with F, non-elementary-amenable classes incomparable with F, and non-elementary-amenable subgroups of F in which F does not embed all empty? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,844 | OWR-16167-014 | Fast Generators for F-Less Homeomorphism Groups | Does every finitely generated subgroup $H<\operatorname{PL}_o(I)$ that contains no copy of Thompson's group $F$ have a finite fast generating set $A$ with the same biembeddability class? Can fast subgroups of $\operatorname{PL}_o(I)$ that contain no copy of $F$ be characterized? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-014",
"literature-status:open",
"owr-year:2018"
] | The Brin--Sapir conjecture remains open in general; restricted analyses of elementary amenable subgroups and fast generating sets give partial structure but not a proof. | [
{
"url": "https://arxiv.org/abs/math/0501085",
"label": "Brin"
},
{
"url": "https://doi.org/10.4171/JCA/49",
"label": "Bleak--Brin--Moore"
},
{
"url": "https://ems.press/content/serial-article-files/46748",
"label": "Oberwolfach Report 2019"
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] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Does every finitely generated subgroup $H<\operatorname{PL}_o(I)$ that contains no copy of Thompson's group $F$ have a finite fast generating set $A$ with the same biembeddability class? Can fast subgroups of $\operatorname{PL}_o(I)$ that contain no copy of $F$ be characterized? | Does every finitely generated F-less subgroup H of PLo(I) have a finite fast generating set A with the same biembeddability class, and can fast F-less subgroups of PLo(I) be usefully 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,845 | OWR-16167-015 | Well-Quasi-Ordering of Thompson Subgroups | Are the biembeddability classes of subgroups of Thompson's group $F$ well-quasi-ordered, and are there subgroups of $\operatorname{PL}_o(I)$ whose classes violate well-quasi-ordering? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-015",
"literature-status:open",
"owr-year:2018"
] | Bleak--Brin--Moore prove a long well-ordered restricted family and incomparable examples, but the full biembeddability WQO question and the PLo(I) violation question remain open. | [
{
"url": "https://doi.org/10.4171/JCA/49",
"label": "Bleak--Brin--Moore"
},
{
"url": "https://ems.press/content/serial-article-files/46748",
"label": "Oberwolfach Report 2019"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Are the biembeddability classes of subgroups of Thompson's group $F$ well-quasi-ordered, and are there subgroups of $\operatorname{PL}_o(I)$ whose classes violate well-quasi-ordering? | Are the biembeddability classes of subgroups of Thompson's group F well quasi-ordered, and are there examples in PLo(I) that violate well-quasi-ordering? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,846 | OWR-16167-016 | Finiteness and Rigidity of Fast Bump Groups | For every $n>1$, are all groups generated by $n$ fast one-bump functions, apart from nontrivial direct sums and wreath products, of type $F_\infty$? Are all such groups isomorphic? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-016",
"literature-status:open",
"owr-year:2018"
] | Questions 71--72 remain unresolved in general: the report records affirmative answers only for n=2,3 and conjectural behavior for n>3, with no later primary resolution found. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | For every $n>1$, are all groups generated by $n$ fast one-bump functions, apart from nontrivial direct sums and wreath products, of type $F_\infty$? Are all such groups isomorphic? | For every n>1, are all groups generated by n fast 1-bump functions, excluding nontrivial direct sums and wreath products, of type F_\infty; and are all such groups isomorphic? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,847 | OWR-16167-018 | Biembeddability and the Golden-Ratio Thompson Group | For the poset [X] of biembeddability classes of finitely generated subgroups of PLo(I), can the structure of [X] be understood further, and does Cleary's golden-ratio Thompson group F_\tau embed in F? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | partially_solved | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | {
"source_url": "https://doi.org/10.4171/ggd/708",
"checked_at": "2026-10-02",
"kind": "partial",
"evidence": "published"
} | Unrecoverable OWR statement (The official report shows that this extraction merges two independent numbered questions, one about the biembeddability poset and another ab) | null | null | [Discussion #4 literature review, 2026-10-02] **partially_solved** (the specific question is answered: no). M. G. Brin (joint with C. Bleak and J. T. Moore; OWR 26/2018, p. 1611) asks the general Question 74, whether more can be said about the poset [X] of biembeddability classes of finitely generated subgroups of PL₊(... | [
"owr",
"oberwolfach-reports",
"OWR-16167-018",
"literature-status:open",
"owr-year:2018"
] | The embedding question for F_{\tau} is answered negatively by Hyde--Moore, but the extracted record also contains an incomplete structural question; the combined record therefore remains open. | [
{
"url": "https://arxiv.org/abs/2103.14911",
"label": "Hyde--Moore, Subgroups of PL+ I"
},
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | null | For the poset [X] of biembeddability classes of finitely generated subgroups of PLo(I), can the structure of [X] be understood further, and does Cleary's golden-ratio Thompson group F_\tau embed in F? | unrecoverable | The official report shows that this extraction merges two independent numbered questions, one about the biembeddability poset and another about embedding the golden-ratio Thompson group. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,848 | OWR-16167-020 | Quasi-Retracts of Thompson's Group $F$ | Does Thompson's group $F$ have any interesting proper nonabelian quasi-retracts; in particular, is $F$ a quasi-retract of $T$, or is $F\times F$ a quasi-retract of $F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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"
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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-16167-020",
"literature-status:open",
"owr-year:2018"
] | The report poses both quasi-retract questions as open, and no later primary resolution of either question was found. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Does Thompson's group $F$ have any interesting proper nonabelian quasi-retracts; in particular, is $F$ a quasi-retract of $T$, or is $F\times F$ a quasi-retract of $F$? | Does Thompson's group F have any interesting proper nonabelian quasi-retracts; in particular, is F a quasi-retract of T, or is F\times F a quasi-retract of F? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,849 | OWR-16167-021 | Homology and Hopficity of Braided Thompson Groups | Is the braided Thompson group V_{br} hopfian, and what about F_{br}; is V_{br} acyclic, and what about the Brin-Thompson groups nV; and can the Stein-Farley cube complex for T recover Ghys-Sergiescu's computation of H_*(T;\mathbb{Q})? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report shows that this extraction merges three independent numbered questions concerning Hopficity, acyclicity, and a Stein–Far) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16167-021",
"literature-status:open",
"owr-year:2018"
] | Known type F_\infty and bounded-cohomology results for related braided groups do not settle the Hopfian, acyclicity, Brin--Thompson, or Stein--Farley questions in the record. | [
{
"url": "https://arxiv.org/abs/1210.2931",
"label": "Bux--Flossner--Meyer--Witzel, braided Thompson groups"
},
{
"url": "https://doi.org/10.2140/agt.2024.24.1601",
"label": "Fournier-Facio--Lodha--Zaremsky, braided Thompson groups"
},
{
"url": "https://ems.press/content/serial-article-f... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | null | Is the braided Thompson group V_{br} hopfian, and what about F_{br}; is V_{br} acyclic, and what about the Brin-Thompson groups nV; and can the Stein-Farley cube complex for T recover Ghys-Sergiescu's computation of H_*(T;\mathbb{Q})? | unrecoverable | The official report shows that this extraction merges three independent numbered questions concerning Hopficity, acyclicity, and a Stein–Farley complex computation. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,850 | OWR-16167-022 | Nonamenable Groups without Free Subgroups | Does there exist a nonamenable group G with a finite K(G,1) and no free subgroups, or at least finite virtual cohomological dimension and no free subgroups? Can Wajnryb-Witowicz-regular relations for the amenable Brin-Navas group B be used to prove that Thompson's group F has such relations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | partially_solved | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report shows that this extraction merges two independent numbered questions concerning nonamenable groups and Wajnryb–Witowicz ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16167-022",
"literature-status:partially-solved",
"owr-year:2018"
] | The Lodha--Moore construction gives a type F_\infty non-amenable group with no non-abelian free subgroups, settling the existence question; the Wajnryb--Witowicz question about F remains open after the proposed proof failed. | [
{
"url": "https://arxiv.org/abs/1408.3127",
"label": "Lodha, A nonamenable type F_\\infty group"
},
{
"url": "https://gcc.episciences.org/11315/pdf",
"label": "Guba, How to solve equations in groups?"
},
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | null | Does there exist a nonamenable group G with a finite K(G,1) and no free subgroups, or at least finite virtual cohomological dimension and no free subgroups? Can Wajnryb-Witowicz-regular relations for the amenable Brin-Navas group B be used to prove that Thompson's group F has such relations? | unrecoverable | The official report shows that this extraction merges two independent numbered questions concerning nonamenable groups and Wajnryb–Witowicz relations. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,851 | OWR-16167-023 | A Nonamenable Extension Beyond Thompson's Group | Let $\alpha(t)=t+1/2$ and let $\beta$ be the piecewise-projective homeomorphism of $\mathbb R$ defined by $\beta(t)=t$ for $t\leq0$, $\beta(t)=t/(1-t)$ for $0\leq t\leq1/2$, $\beta(t)=3-1/t$ for $1/2\leq t\leq1$, and $\beta(t)=t+1$ for $t\geq1$. Is the subgroup $\langle\alpha,\beta\rangle$ of Monod's group nonamenable,... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-023",
"literature-status:open",
"owr-year:2018"
] | The report's question about whether the subgroup generated by alpha and beta is the simplest non-amenable example beyond F, and why 1/2 is essential, remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Let $\alpha(t)=t+1/2$ and let $\beta$ be the piecewise-projective homeomorphism of $\mathbb R$ defined by $\beta(t)=t$ for $t\leq0$, $\beta(t)=t/(1-t)$ for $0\leq t\leq1/2$, $\beta(t)=3-1/t$ for $1/2\leq t\leq1$, and $\beta(t)=t+1$ for $t\geq1$. Is the subgroup $\langle\alpha,\beta\rangle$ of Monod's group nonamenable,... | For the subgroup \langle\alpha,\beta\rangle of Monod's group generated by the displayed piecewise-projective homeomorphisms, is this the simplest example that goes slightly beyond Thompson's group F and is non-amenable, and why is the coefficient 1/2 important? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,852 | OWR-16167-024 | Finitely Presented Piecewise-Projective Groups | Is every finitely presented subgroup of PLo(I) generated by a fast set of one-bump generators of type F^{\infty}? Does the Higman group \langle a,b,c,d\mid b^a=b^2, c^b=c^2, d^c=d^2, a^d=a^2\rangle embed into a Lodha--Moore group, or at least into Monod's group H(\mathbb R)? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report shows that this extraction merges two independent numbered questions concerning fast one-bump groups and an embedding of) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16167-024",
"literature-status:open",
"owr-year:2018"
] | The two universal finiteness and embedding questions in the record remain open; known F_\infty results for particular Lodha--Moore groups do not settle either statement. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
},
{
"url": "https://ems.press/journals/ggd/articles/13662",
"label": "Lodha, A nonamenable type F_\\infty group"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | null | Is every finitely presented subgroup of PLo(I) generated by a fast set of one-bump generators of type F^{\infty}? Does the Higman group \langle a,b,c,d\mid b^a=b^2, c^b=c^2, d^c=d^2, a^d=a^2\rangle embed into a Lodha--Moore group, or at least into Monod's group H(\mathbb R)? | unrecoverable | The official report shows that this extraction merges two independent numbered questions concerning fast one-bump groups and an embedding of the Higman group. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,853 | OWR-16167-025 | Abelianizations of Finitely Presented Thompson $F$ Subgroups | Does every finitely presented subgroup of Thompson's group $F$ have torsion-free abelianization? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | open | null | 2,018 | 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-16167-025",
"literature-status:open",
"owr-year:2018"
] | Rover's example disproves the analogous finitely generated statement, but the report explicitly leaves the finitely presented-subgroup question open; no later primary proof or counterexample was found. | [
{
"url": "https://ems.press/content/serial-article-files/46748?nt=1",
"label": "Oberwolfach Report 26/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | Does every finitely presented subgroup of Thompson's group $F$ have torsion-free abelianization? | Does every finitely presented subgroup of Thompson's group F have torsion-free abelianisation? | 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 | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,854 | OWR-16167-026 | Finiteness Properties of Lodha–Moore Kernels | For the Lodha--Moore groups, is the kernel of the natural map to \mathbb Z of type F^{\infty}? More broadly, can the family of Thompson-like groups contain a group that is not finitely presentable but is of type FP_2? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633](https://doi.org/10.4171/owr/2018/26)
## Literatur... | 3 | partially_solved | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report shows that this extraction merges two independent numbered questions concerning a Lodha–Moore kernel and a non-finitely-) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16167-026",
"literature-status:partially-solved",
"owr-year:2018"
] | Lodha--Zaremsky solve the Lodha--Moore kernel question by determining the higher BNSR invariants and proving the relevant finitely presented normal subgroups are type F_\infty; the separately appended FP_2 question remains open. | [
{
"url": "https://arxiv.org/abs/2007.12518",
"label": "Lodha--Zaremsky, The BNSR invariants of the Lodha--Moore groups"
},
{
"url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/04297B3A2B295AB357EA34BA136473C5/S0305004122000111a.pdf",
"label": "Cambridge University Pr... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/26 | null | null | null | null | For the Lodha--Moore groups, is the kernel of the natural map to \mathbb Z of type F^{\infty}? More broadly, can the family of Thompson-like groups contain a group that is not finitely presentable but is of type FP_2? | unrecoverable | The official report shows that this extraction merges two independent numbered questions concerning a Lodha–Moore kernel and a non-finitely-presentable group of type $FP_2$. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Cohomological and Metric Properties of Groups of Homeomorphisms of R (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/26, pp. 1579--1633 |
30,003,855 | OWR-16168-004 | Sharp Normalized Steklov Supremum in Higher Dimensions | Among smooth bounded domains $\Omega\subset\mathbb R^n$ with $n\geq3$, determine the supremum of $$\sigma_1(\Omega)|\partial\Omega|^{1/(n-1)}$$ and characterize the domain, or degenerating sequence of domains, on which it is attained. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684](https://doi.org/10.4171/owr/2018/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16168-004",
"literature-status:open",
"owr-year:2018"
] | Sharp Weinstock-type bounds are known for restricted classes such as convex domains, but the unrestricted higher-dimensional sharp supremum question in the record remains open. | [
{
"url": "https://arxiv.org/abs/1710.04587",
"label": "Bucur--Ferone--Nitsch--Trombetti, Weinstock inequality for convex domains"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0001870819301410",
"label": "Fraser--Schoen, Shape optimization for the Steklov problem"
},
{
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/27 | null | null | null | Among smooth bounded domains $\Omega\subset\mathbb R^n$ with $n\geq3$, determine the supremum of $$\sigma_1(\Omega)|\partial\Omega|^{1/(n-1)}$$ and characterize the domain, or degenerating sequence of domains, on which it is attained. | For smooth bounded domains \Omega\subset\mathbb R^n with n\ge 3, on which domain, or in the limit of which sequence of domains, is the supremum of the normalized first Steklov eigenvalue \sigma_1(\Omega)|\partial\Omega|^{1/(n-1)} attained? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684 |
30,003,856 | OWR-16168-005 | Bipolar Comparison and Transport Continuity | Does $(4,1)$-bipolar comparison imply the transport continuity property, and are these two properties equivalent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684](https://doi.org/10.4171/owr/2018/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16168-005",
"literature-status:open",
"owr-year:2018"
] | Lebedeva--Petrunin--Zolotov relate bipolar comparison to CTIL and MTW, but the implication or equivalence with TCP remains a conjecture and no later primary proof was found. | [
{
"url": "https://arxiv.org/abs/1711.09423",
"label": "Lebedeva--Petrunin--Zolotov, Bipolar comparison"
},
{
"url": "https://ems.press/content/serial-article-files/46749?nt=1",
"label": "Oberwolfach Report 27/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/27 | null | null | null | Does $(4,1)$-bipolar comparison imply the transport continuity property, and are these two properties equivalent? | Does (4,1)-bipolar comparison imply the transport continuity property (TCP), or are these properties equivalent? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684 |
30,003,857 | OWR-16168-007 | Positive Curvature on Higher Rank Symmetric Spaces | Does any compact, simply connected Riemannian symmetric space of rank greater than $1$ admit a metric of positive sectional curvature? In particular, does $S^2\times S^2$ admit such a metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684](https://doi.org/10.4171/owr/2018/27)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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"
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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-16168-007",
"literature-status:open",
"owr-year:2018"
] | Known symmetry-rank results provide evidence against positive curvature on higher-rank symmetric spaces, but the generalized Hopf conjecture and the requested classification remain unresolved. | [
{
"url": "https://arxiv.org/abs/1209.4627",
"label": "Kennard, Positively curved metrics on symmetric spaces"
},
{
"url": "https://annals.math.princeton.edu/2006/163-2/p07",
"label": "Wilking, Positively curved manifolds with symmetry"
},
{
"url": "https://ems.press/content/serial-articl... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/27 | null | null | null | Does any compact, simply connected Riemannian symmetric space of rank greater than $1$ admit a metric of positive sectional curvature? In particular, does $S^2\times S^2$ admit such a metric? | Does any compact simply connected Riemannian symmetric space of rank greater than one admit a metric with positive sectional curvature? The conjecture is that none does, including the Hopf case S^2\times S^2. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684 |
30,003,858 | OWR-16168-008 | Detection and Uniqueness of Expanding Harmonic-Map Flows | For harmonic-map-flow solutions emerging from a $0$-homogeneous map $u_0:S^{n-1}\to N$, characterize which solutions are expanders and formulate and prove an appropriate uniqueness theorem for expanding solutions. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684](https://doi.org/10.4171/owr/2018/27)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,018 | 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-16168-008",
"literature-status:partially-solved",
"owr-year:2018"
] | Existence is proved for homotopically trivial Lipschitz data and relative entropy gives generic uniqueness, but the general detection and uniqueness questions remain unsettled; 2026 work also exhibits nonuniqueness in a hemisphere setting. | [
{
"url": "https://arxiv.org/abs/1801.08012",
"label": "Deruelle--Lamm, Expanding Ricci solitons"
},
{
"url": "https://doi.org/10.1080/03605302.2019.1646280",
"label": "Deruelle, Relative entropy and uniqueness"
},
{
"url": "https://arxiv.org/abs/2602.08932",
"label": "Li, Nonuniquene... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/27 | null | null | null | For harmonic-map-flow solutions emerging from a $0$-homogeneous map $u_0:S^{n-1}\to N$, characterize which solutions are expanders and formulate and prove an appropriate uniqueness theorem for expanding solutions. | For harmonic-map-flow solutions emerging from a 0-homogeneous map u_0:S^{n-1}\to N, how can one detect an expanding solution among the solutions, and in what terms should uniqueness of such expanding solutions be stated and expected? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Geometrie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/27, pp. 1635--1684 |
30,003,859 | OWR-16169-001 | Rigidity of Hirzebruch–Kummer Coverings | Let $L$ be a rigid line configuration and let $S(n,L)$ be its Hirzebruch–Kummer covering. Is $S(n,L)$ rigid for all sufficiently large exponents $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,018 | 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-16169-001",
"literature-status:partially-solved",
"owr-year:2018"
] | The complete-quadrangle case is solved, with S(n,CQ) rigid exactly for n\geq4, but the conjecture for arbitrary rigid line configurations remains open. | [
{
"url": "https://arxiv.org/abs/1803.02984",
"label": "Bauer--Catanese, On the rigidity of line arrangements"
},
{
"url": "https://arxiv.org/abs/1609.08128",
"label": "Bauer--Catanese, Line arrangements and rigidity"
},
{
"url": "https://ems.press/content/serial-article-files/46750",
... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | Let $L$ be a rigid line configuration and let $S(n,L)$ be its Hirzebruch–Kummer covering. Is $S(n,L)$ rigid for all sufficiently large exponents $n$? | Given a rigid line configuration L and its Hirzebruch--Kummer covering S(n,L), is the surface S(n,L) rigid for all sufficiently large exponents n? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,860 | OWR-16169-003 | Explicit Generators for Higher-Dimensional Cremona Groups | For the Cremona group $Bir(\mathbb{P}^n)$ in dimensions $n\ge 4$, can one find a simple explicit generating set, i.e. an analogue of the Noether–Castelnuovo theorem? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,018 | 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-16169-003",
"literature-status:open",
"owr-year:2018"
] | The dimension-three characteristic-zero case is known, but no general satisfactory generating theorem is known in dimensions n\geq4; the extracted higher-dimensional problem remains open. | [
{
"url": "https://perso.univ-rennes1.fr/serge.cantat/Articles/hudson-pan-derksen.pdf",
"label": "Cantat--Hudson--D\\'eserti, Generators for the Cremona group"
},
{
"url": "https://www.insmi.cnrs.fr/fr/cnrsinfo/groupes-de-cremona-en-dimension-superieure",
"label": "CNRS, Cremona groups in higher ... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | For the Cremona group $Bir(\mathbb{P}^n)$ in dimensions $n\ge 4$, can one find a simple explicit generating set, i.e. an analogue of the Noether–Castelnuovo theorem? | For the Cremona group Bir(\mathbb P^n) in dimensions n\ge 4, can one find a simple explicit generating set, i.e. an analogue of the Noether--Castelnuovo theorem? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,861 | OWR-16169-004 | Mirror Families from Log Calabi–Yau Pairs | For a simple normal-crossings Calabi–Yau pair $(Y,D_Y)$ with maximal boundary and $D_Y$ supporting an ample divisor, does the Gross–Hacking–Keel curve-counting algebra construction produce a flat family of affine log Calabi–Yau varieties whose torus quotient depends only on $U=Y\setminus D_Y$ and is its mirror family? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,018 | 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-16169-004",
"literature-status:open",
"owr-year:2018"
] | The extracted record ends mid-conjecture and does not state a complete mathematical claim, so it cannot be verified as solved; under the queue rule it is classified open. | [
{
"url": "https://ems.press/content/serial-article-files/46750",
"label": "Oberwolfach Report 28/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | For a simple normal-crossings Calabi–Yau pair $(Y,D_Y)$ with maximal boundary and $D_Y$ supporting an ample divisor, does the Gross–Hacking–Keel curve-counting algebra construction produce a flat family of affine log Calabi–Yau varieties whose torus quotient depends only on $U=Y\setminus D_Y$ and is its mirror family? | For a simple normal-crossings Calabi--Yau pair (Y,D_Y) with maximal boundary and D_Y supporting an ample divisor, does the Gross--Hacking--Keel curve-counting algebra construction produce a flat family of affine log Calabi--Yau varieties whose torus quotient depends only on U=Y\setminus D_Y and is its mirror family? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,862 | OWR-16169-009 | Polar Cylinders and Affine Complements of Del Pezzo Surfaces | For a del Pezzo surface $S$ in its ambient weighted projective space $P$, is the absence of a $(-K_S)$-polar cylinder equivalent to the affine complement $P\setminus S$ being non-cylindrical? The implication from no polar cylinder to non-cylindricity is known. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,018 | 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-16169-009",
"literature-status:partially-solved",
"owr-year:2018"
] | For del Pezzo hypersurfaces, the implication from absence of a polar cylinder to non-cylindricity is proved, but the converse in the extracted equivalence remains a conjecture. | [
{
"url": "https://ems.press/content/serial-article-files/46750",
"label": "Park, Automorphism groups of complements"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | For a del Pezzo surface $S$ in its ambient weighted projective space $P$, is the absence of a $(-K_S)$-polar cylinder equivalent to the affine complement $P\setminus S$ being non-cylindrical? The implication from no polar cylinder to non-cylindricity is known. | For a del Pezzo surface S in its ambient weighted projective space P, is the absence of a (-K_S)-polar cylinder equivalent to the affine complement P\setminus S being non-cylindrical? The implication from no polar cylinder to non-cylindricity is known. | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,863 | OWR-16169-010 | Polar Cylinders and Complement Automorphisms | For a del Pezzo surface $S$, does $S$ contain no $(-K_S)$-polar cylinder if and only if $\operatorname{Aut}(P\setminus S)=\operatorname{Aut}(P,S)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,018 | 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-16169-010",
"literature-status:open",
"owr-year:2018"
] | The proposed equality of automorphism groups is stated as Conjecture 5; known results cover some degrees and rule out connected groups in others, but the general assertion remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46750",
"label": "Park, Automorphism groups of complements"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | For a del Pezzo surface $S$, does $S$ contain no $(-K_S)$-polar cylinder if and only if $\operatorname{Aut}(P\setminus S)=\operatorname{Aut}(P,S)$? | For a del Pezzo surface S, does S contain no (-K_S)-polar cylinder if and only if Aut(P\setminus S)=Aut(P,S)? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,864 | OWR-16169-012 | Hodge Numbers from Landau–Ginzburg Fiber Components | If $X$ is a smooth Fano variety of dimension $n$ with toric Landau–Ginzburg model $f_X$, and $k_{f_X}$ is the number of components of reducible compactification fibers minus the number of reducible fibers, is $h^{1,n-1}(X)=k_{f_X}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | partially_solved | null | 2,018 | 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-16169-012",
"literature-status:partially-solved",
"owr-year:2018"
] | The Hodge-number mirror relation is proved for several classes, and a 2025 paper proves the KKP conjecture for smooth Fano threefolds; the extracted all-smooth-Fano statement remains open in higher dimensions. | [
{
"url": "https://doi.org/10.4213/tm4452",
"label": "Cheltsov--Przyjalkowski, KKP for Fano threefolds"
},
{
"url": "https://ems.press/content/serial-article-files/46750",
"label": "Przyjalkowski, KKP conjectures in lower dimensions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | If $X$ is a smooth Fano variety of dimension $n$ with toric Landau–Ginzburg model $f_X$, and $k_{f_X}$ is the number of components of reducible compactification fibers minus the number of reducible fibers, is $h^{1,n-1}(X)=k_{f_X}$? | If X is a smooth Fano variety of dimension n with toric Landau--Ginzburg model f_X, and k_{f_X} is the number of components of reducible compactification fibers minus the number of reducible fibers, is h^{1,n-1}(X)=k_{f_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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,865 | OWR-16169-013 | A Serre-Style Proof of the Jordan Property | Can the Jordan property for rationally connected varieties over a field of characteristic zero be proved by extending Serre's Minkowski-style method for finite subgroups of rank-two Cremona groups, rather than by using the boundedness argument of Prokhorov and Shramov? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,018 | 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-16169-013",
"literature-status:open",
"owr-year:2018"
] | The Jordan property for rationally connected varieties is known, but the extracted question asks for a particular alternative proof following the cited approach; no such general proof was identified. | [
{
"url": "https://ems.press/content/serial-article-files/46750",
"label": "Oberwolfach Report 28/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | Can the Jordan property for rationally connected varieties over a field of characteristic zero be proved by extending Serre's Minkowski-style method for finite subgroups of rank-two Cremona groups, rather than by using the boundedness argument of Prokhorov and Shramov? | Can one give an alternative proof of the Jordan property for rationally connected varieties over a field of characteristic zero, following the approach of Serre rather than the existing approach? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,866 | OWR-16169-016 | Maximum Simple Singularities of Plane Curves | For a plane curve of degree $d$, what is the largest $k$ for which an $A_k$ singularity can occur? More generally, for $(a,b)\in\mathbb N^2$, what is the largest $k$ for which a curve in $\mathbb A^2(\mathbb C)$ of bidegree $(a,b)$ can have an $A_k$ singularity? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743](https://doi.org/10.4171/owr/2018/28)
## Literature review (checked 2026-08-21)
**Status:*... | 3 | open | null | 2,018 | 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-16169-016",
"literature-status:open",
"owr-year:2018"
] | The cited work gives formulas and tables in small bidegrees, while the requested general extremal function for arbitrary a and b is not determined. | [
{
"url": "https://arxiv.org/abs/1808.05133",
"label": "Schneider, Plane curves and A_k-singularities"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/28 | null | null | null | For a plane curve of degree $d$, what is the largest $k$ for which an $A_k$ singularity can occur? More generally, for $(a,b)\in\mathbb N^2$, what is the largest $k$ for which a curve in $\mathbb A^2(\mathbb C)$ of bidegree $(a,b)$ can have an $A_k$ singularity? | For a plane curve of degree d, what is the maximal k for which an A_k singularity can occur, and more generally, for (a,b)\in\mathbb N^2, what is the maximal k for which a curve in \mathbb A^2(\mathbb C) of bidegree (a,b) has an A_k singularity? | 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 | Subgroups of Cremona Groups (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/28, pp. 1685--1743 |
30,003,867 | OWR-16170-001 | Statistical Recovery of High-Dimensional Network Structure | Given observations from a high-dimensional network model, how can the underlying network structure, including its edge-generation rule, be statistically estimated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783](https://d... | 3 | open | null | 2,018 | 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-16170-001",
"literature-status:open",
"owr-year:2018"
] | The extracted network-estimation question is underspecified and no general theorem settling it follows from the report; under the required rule, the unresolved claim is classified as open. | [
{
"url": "https://ems.press/content/serial-article-files/46753",
"label": "Oberwolfach Report 29/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/29 | null | null | null | Given observations from a high-dimensional network model, how can the underlying network structure, including its edge-generation rule, be statistically estimated? | Given observations from a high-dimensional network model, how can the underlying network structure, including its edge-generation rule, be statistically estimated? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783 |
30,003,868 | OWR-16170-002 | Local Algorithms for Semidefinite Programming | How accurately can local algorithms solve or approximate semidefinite programs, particularly SDP relaxations for random graph problems? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783](https://d... | 3 | open | null | 2,018 | 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-16170-002",
"literature-status:open",
"owr-year:2018"
] | Local algorithms have rigorous SDP guarantees for particular random graph models, but the general question of how well they solve semidefinite programs remains unresolved. | [
{
"url": "https://arxiv.org/abs/1610.05350",
"label": "Fan--Montanari, SDP and local algorithms"
},
{
"url": "https://doi.org/10.1145/3055399.3055451",
"label": "STOC 2017 version"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/29 | null | null | null | How accurately can local algorithms solve or approximate semidefinite programs, particularly SDP relaxations for random graph problems? | How accurately can local algorithms solve or approximate semidefinite programs, particularly SDP relaxations for random graph problems? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783 |
30,003,869 | OWR-16170-003 | Local Approximation of Random-Graph Semidefinite Programs | For a large class of random graph models, can semidefinite programs be approximately solved by local algorithms, with comparable performance for problems such as minimum bisection and community detection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783](https://d... | 3 | open | null | 2,018 | 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-16170-003",
"literature-status:open",
"owr-year:2018"
] | Results cover several random graph and community-detection models, but no theorem gives the requested local-algorithm SDP approximation for a large general class. | [
{
"url": "https://arxiv.org/abs/1610.05350",
"label": "Fan--Montanari, SDP and local algorithms"
},
{
"url": "https://arxiv.org/abs/1911.01960",
"label": "Banks--Mohanty--Raghavendra, local statistics"
},
{
"url": "https://arxiv.org/abs/2311.09017",
"label": "Ivkov--Schramm, local st... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/29 | null | null | null | For a large class of random graph models, can semidefinite programs be approximately solved by local algorithms, with comparable performance for problems such as minimum bisection and community detection? | For a large class of random graph models, can semidefinite programs be approximately solved by local algorithms, with comparable performance for problems such as minimum bisection and community detection? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783 |
30,003,870 | OWR-16170-004 | Polynomial-Time Estimation in Binary Latent-Variable Models | Under general identifiability conditions for binary latent-variable models, do statistically consistent procedures exist for estimating the parameter matrix $W$ in time polynomial in the number $d$ of hidden variables? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783](https://d... | 3 | open | null | 2,018 | 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-16170-004",
"literature-status:open",
"owr-year:2018"
] | The spectral method is statistically consistent in the treated setting but has exponential dependence on the hidden dimension; a generally identifiable polynomial-time estimator is left open. | [
{
"url": "https://proceedings.mlr.press/v80/jaffe18a.html",
"label": "Jaffe et al., ICML 2018"
},
{
"url": "https://arxiv.org/abs/1802.09656",
"label": "Jaffe et al., preprint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/29 | null | null | null | Under general identifiability conditions for binary latent-variable models, do statistically consistent procedures exist for estimating the parameter matrix $W$ in time polynomial in the number $d$ of hidden variables? | Under general identifiability conditions for binary latent-variable models, do statistically consistent procedures exist for estimating the parameter matrix W with running time polynomial in the number d of hidden variables? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Matrix Estimation Meets Statistical Network Analysis: Extracting low-dimensional structures in high dimension (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/29, pp. 1745--1783 |
30,003,871 | OWR-16171-001 | $p$-Adic Riemann–Hilbert and de Rham Compatibility | Let $X$ be a smooth algebraic variety over a number field $E$, let $L$ be a geometric $p$-adic étale local system on $X$, and let $\sigma:E\hookrightarrow\mathbb C$. Are the tensor functors that associate to $L$ a regular integrable connection on $X_\sigma$ through the complex Riemann–Hilbert correspondence and through... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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... | [
"OWR-16171-002"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16171-001",
"literature-status:open",
"owr-year:2018"
] | The p-adic logarithmic Riemann--Hilbert comparison conjecture and its Hodge-theoretic compatibility are presented as out of reach except in special cases; no general proof was identified. | [
{
"url": "https://arxiv.org/abs/1803.05786",
"label": "Logarithmic Riemann--Hilbert correspondences"
},
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Oberwolfach Report 30/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Let $X$ be a smooth algebraic variety over a number field $E$, let $L$ be a geometric $p$-adic étale local system on $X$, and let $\sigma:E\hookrightarrow\mathbb C$. Are the tensor functors that associate to $L$ a regular integrable connection on $X_\sigma$ through the complex Riemann–Hilbert correspondence and through... | Let X be a smooth algebraic variety over a number field E and let L be a geometric p-adic etale local system on X. The tensor functors that associate to L the regular integrable connection on \sigma X via the complex Riemann--Hilbert correspondence and via algebraic de Rham theory are conjectured to be canonically isom... | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,872 | OWR-16171-002 | Canonical Comparison of Geometric Local-System Realizations | For a smooth algebraic variety X over a number field E and a geometric p-adic etale local system L on X, the Riemann--Hilbert and algebraic de Rham tensor functors to regular integrable connections on \sigma X should be canonically isomorphic, and the filtered de Rham realization should be a complex variation of Hodge ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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 that this is a duplicate extraction of the same conjecture retained in OWR-16171-001. No separate clean stateme) | [
"OWR-16171-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16171-002",
"literature-status:open",
"owr-year:2018"
] | The extracted relative Fontaine--Mazur-type assertion is explicitly described as out of reach; existing results do not establish it in general. | [
{
"url": "https://arxiv.org/abs/1803.05786",
"label": "Logarithmic Riemann--Hilbert correspondences"
},
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Oberwolfach Report 30/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | null | For a smooth algebraic variety X over a number field E and a geometric p-adic etale local system L on X, the Riemann--Hilbert and algebraic de Rham tensor functors to regular integrable connections on \sigma X should be canonically isomorphic, and the filtered de Rham realization should be a complex variation of Hodge ... | unrecoverable | The official report confirms that this is a duplicate extraction of the same conjecture retained in OWR-16171-001. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,873 | OWR-16171-003 | Resolvent Degrees of Universal Polynomials | Hilbert's conjecture asserts that for $n\geq 6$ the resolvent degree of the universal degree-$n$ polynomial cover $\widetilde{P}_n\to P_n$ satisfies $\operatorname{RD}(\widetilde{P}_n\to P_n)\geq 2$; for $n=6,7,8,9$ the values are conjectured to be $2,3,4,4$, respectively. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-003",
"literature-status:open",
"owr-year:2018"
] | The stated lower bounds for the resolvent degree of the generic polynomial remain conjectural; the literature supplies upper bounds and reformulations but not the claimed general lower bound. | [
{
"url": "https://arxiv.org/abs/2406.15954",
"label": "Edens--Reichstein, Hilbert's 13th problem"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb--Wolfson, resolvent degree"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Hilbert's conjecture asserts that for $n\geq 6$ the resolvent degree of the universal degree-$n$ polynomial cover $\widetilde{P}_n\to P_n$ satisfies $\operatorname{RD}(\widetilde{P}_n\to P_n)\geq 2$; for $n=6,7,8,9$ the values are conjectured to be $2,3,4,4$, respectively. | Hilbert's conjecture asserts that for n\geq 6 the resolvent degree of the universal degree-n polynomial cover \widetilde{P}_n\to P_n satisfies RD(\widetilde{P}_n\to P_n)\geq 2; for n=6,7,8,9 the values are conjectured to be 2,3,4,4, respectively. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,874 | OWR-16171-004 | Resolvent Degrees of Lines and Bitangents | Conjecturally, the resolvent degree of the 27-sheeted cover parametrizing lines on smooth cubic surfaces is $\operatorname{RD}(H_{3,3}^{(1)}\to H_{3,3})=3$, and the resolvent degree of the 28-sheeted cover parametrizing bitangents to smooth plane quartics is $\operatorname{RD}(H_{4,2}^{(1)}\to H_{4,2})=\dim H_{4,2}=6$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-004",
"literature-status:open",
"owr-year:2018"
] | The conjectural resolvent degrees for the moduli of cubic surfaces and genus-two curves are not proved; current work provides partial geometric interpretations and bounds. | [
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb--Wolfson, resolvent degree"
},
{
"url": "https://escholarship.org/content/qt0598s939/qt0598s939.pdf",
"label": "Recent resolvent-degree study"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Conjecturally, the resolvent degree of the 27-sheeted cover parametrizing lines on smooth cubic surfaces is $\operatorname{RD}(H_{3,3}^{(1)}\to H_{3,3})=3$, and the resolvent degree of the 28-sheeted cover parametrizing bitangents to smooth plane quartics is $\operatorname{RD}(H_{4,2}^{(1)}\to H_{4,2})=\dim H_{4,2}=6$. | Conjecturally, the resolvent degree of the 27-sheeted cover parametrizing lines on smooth cubic surfaces is RD(H_{3,3}^{(1)}\to H_{3,3})=3, and the resolvent degree of the 28-sheeted cover parametrizing bitangents to smooth plane quartics is RD(H_{4,2}^{(1)}\to H_{4,2})=\dim H_{4,2}=6. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,875 | OWR-16171-005 | Resolvent Degree of Abelian-Variety Torsion Covers | If $(g,p)\neq(2,2)$, then the resolvent degree of the $p$-torsion cover of the moduli space $A_g$ of principally polarized abelian varieties is $\operatorname{RD}(A_{g,p}\to A_g)=\dim A_g=g(g+1)/2$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-005",
"literature-status:open",
"owr-year:2018"
] | The proposed maximal resolvent degree for principally polarized abelian varieties is still a conjectural lower-bound statement; no general proof was identified. | [
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Oberwolfach Report 30/2018"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb--Wolfson, resolvent degree"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | If $(g,p)\neq(2,2)$, then the resolvent degree of the $p$-torsion cover of the moduli space $A_g$ of principally polarized abelian varieties is $\operatorname{RD}(A_{g,p}\to A_g)=\dim A_g=g(g+1)/2$. | If (g,p)\neq(2,2), then the resolvent degree of the p-torsion cover of the moduli space A_g of principally polarized abelian varieties is RD(A_{g,p}\to A_g)=\dim A_g=g(g+1)/2. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,876 | OWR-16171-006 | Lower Bounds for Symplectic Resolvent Degrees | For $n\geq6$, choose an embedding $A_n\hookrightarrow\operatorname{Sp}_{2g}(\mathbb F_2)$ for which $A_n\cap U$ is a maximal elementary abelian $2$-subgroup of $A_n$, where $U$ is the unipotent radical of the Siegel parabolic, and put $e_{A_n}=\operatorname{rank}_{\mathbb F_2}(A_n\cap U)$. Let $\widetilde A_{g,2}\to A_... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-006",
"literature-status:open",
"owr-year:2018"
] | The asserted lower bound involving the exponent of the abelianization is presented as a conjecture and remains unproved in general, so the implied Hilbert conjecture is not established. | [
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Oberwolfach Report 30/2018"
},
{
"url": "https://arxiv.org/abs/1803.04063",
"label": "Farb--Wolfson, resolvent degree"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | For $n\geq6$, choose an embedding $A_n\hookrightarrow\operatorname{Sp}_{2g}(\mathbb F_2)$ for which $A_n\cap U$ is a maximal elementary abelian $2$-subgroup of $A_n$, where $U$ is the unipotent radical of the Siegel parabolic, and put $e_{A_n}=\operatorname{rank}_{\mathbb F_2}(A_n\cap U)$. Let $\widetilde A_{g,2}\to A_... | For n\geq 6, let A_n\hookrightarrow Sp_{2g}(\mathbb F_2) be as in the report and let e_{A_n} be the rank of its intersection with the unipotent radical. Conjecturally RD(\widetilde A_{g,2}\to A^{A_n})\geq e_{A_n}. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,877 | OWR-16171-007 | Beilinson's Regulator Conjecture | Let $X$ be a variety over $\mathbb Q$ and let $m<2i$. Does the regulator map carry the appropriate integral subspace of motivic cohomology to a $\mathbb Q$-structure on Deligne cohomology, with determinant equal to the special value predicted by Beilinson's conjecture? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-007",
"literature-status:open",
"owr-year:2018"
] | The extracted regulator-formula claim is truncated and does not identify a settled theorem; the surrounding Beilinson-type conjectural statements remain unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Oberwolfach Report 30/2018"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Let $X$ be a variety over $\mathbb Q$ and let $m<2i$. Does the regulator map carry the appropriate integral subspace of motivic cohomology to a $\mathbb Q$-structure on Deligne cohomology, with determinant equal to the special value predicted by Beilinson's conjecture? | Beilinson's conjecture predicts that for a variety X over \mathbb Q and m<2i, an integral subspace of motivic cohomology maps under the regulator to a \mathbb Q-structure on Deligne cohomology and that the determinant of the regulator has the predicted value. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,878 | OWR-16171-008 | Rank-One Equivalences for Elliptic Curves | For an elliptic curve $E/\mathbb{Q}$ and $r\in\{0,1\}$, the following are conjectured equivalent: $\operatorname{rank}E(\mathbb{Q})=r$ and the Tate–Shafarevich group $\operatorname{Sha}(E/\mathbb{Q})$ is finite; $\operatorname{corank}_{\mathbb{Z}_p}\operatorname{Sel}_{p^\infty}(E/\mathbb{Q})=r$; and $\operatorname{ord}... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-008",
"literature-status:partially-solved",
"owr-year:2018"
] | For elliptic curves, the rank-zero and rank-one implications and many p-converse and p-part BSD results are proved under hypotheses, but the universal equivalence stated for every curve and a prime p is not proved. | [
{
"url": "https://arxiv.org/abs/2409.01350",
"label": "Zeta elements for elliptic curves and BSD"
},
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Wan, BSD formula for elliptic curves"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | For an elliptic curve $E/\mathbb{Q}$ and $r\in\{0,1\}$, the following are conjectured equivalent: $\operatorname{rank}E(\mathbb{Q})=r$ and the Tate–Shafarevich group $\operatorname{Sha}(E/\mathbb{Q})$ is finite; $\operatorname{corank}_{\mathbb{Z}_p}\operatorname{Sel}_{p^\infty}(E/\mathbb{Q})=r$; and $\operatorname{ord}... | For an elliptic curve E/\mathbb Q and r\in\{0,1\}, the following are conjectured equivalent: rank E(\mathbb Q)=r and the Tate--Shafarevich group \Sha(E/\mathbb Q) is finite; corank_{\mathbb Z_p}\operatorname{Sel}_{p^\infty}(E/\mathbb Q)=r; and ord_{s=1}L(s,E/\mathbb Q)=r. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,879 | OWR-16171-009 | Birch–Swinnerton-Dyer Conjecture | The Birch–Swinnerton-Dyer conjecture asserts for every elliptic curve $E/\mathbb{Q}$ that $\operatorname{ord}_{s=1}L(E,s)=\operatorname{rank}E(\mathbb{Q})$, together with a formula for the leading Taylor coefficient in terms of arithmetic invariants; the rank part remains largely open when the rank is at least 2. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-009",
"literature-status:partially-solved",
"owr-year:2018"
] | The rank part of BSD in analytic rank zero and one is known in broad settings, and substantial p-primary and full-formula families are proved, but the full BSD formula is not established for all elliptic curves of ranks zero and one. | [
{
"url": "https://arxiv.org/abs/2409.01350",
"label": "Zeta elements for elliptic curves and BSD"
},
{
"url": "https://ems.press/content/serial-article-files/46751",
"label": "Wan, BSD formula for elliptic curves"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | The Birch–Swinnerton-Dyer conjecture asserts for every elliptic curve $E/\mathbb{Q}$ that $\operatorname{ord}_{s=1}L(E,s)=\operatorname{rank}E(\mathbb{Q})$, together with a formula for the leading Taylor coefficient in terms of arithmetic invariants; the rank part remains largely open when the rank is at least 2. | The Birch--Swinnerton-Dyer conjecture asserts for every elliptic curve E/\mathbb Q that ord_{s=1}L(E,s)=\operatorname{rank}E(\mathbb Q), together with a formula for the leading Taylor coefficient in terms of arithmetic invariants; the rank part remains largely open when the rank is at least 2. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,880 | OWR-16171-011 | Parametrization of Supersingular Cohomology Modules | Let $G = \mathrm{GL}_n(\mathbb{Q}_p)$ (or a reductive $p$-adic group), let $B_s^b$ be a Deligne--Lusztig-type or Bruhat--Tits stratum in the $p$-adic period domain, and let $H_s^{(1)}$ be the pro-$p$ Iwahori--Hecke algebra at a supersingular parameter $s$. Can the supersingular $H_s^{(1)}$-modules appearing in the $\bm... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-011",
"literature-status:partially-solved",
"owr-year:2018"
] | The report proves realization with multiplicity one for simple supersingular modules in dimensions n less than or equal to 3, but no general parametrization by t is established. | [
{
"url": "https://doi.org/10.4171/owr/2018/30",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Let $G = \mathrm{GL}_n(\mathbb{Q}_p)$ (or a reductive $p$-adic group), let $B_s^b$ be a Deligne--Lusztig-type or Bruhat--Tits stratum in the $p$-adic period domain, and let $H_s^{(1)}$ be the pro-$p$ Iwahori--Hecke algebra at a supersingular parameter $s$. Can the supersingular $H_s^{(1)}$-modules appearing in the $\bm... | Can the supersingular H_s^{(1)}-modules appearing in the cohomology of B_s^{b} be parametrized by the parameter t? | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,881 | OWR-16171-012 | Images of Infinite Galois Representations | Let $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(A)$ be a continuous representation that is irreducible, is not induced from a character of an index-two subgroup, and has infinite image. What is the structure of $\operatorname{Im}\rho$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-012",
"literature-status:partially-solved",
"owr-year:2018"
] | The broad image-classification question remains unresolved, while Conti--Lang--Medvedovsky prove strong congruence-subgroup results under substantial hypotheses for two-dimensional pseudorepresentations and related Galois representations. | [
{
"url": "https://arxiv.org/abs/1904.10519",
"label": "Conti--Lang--Medvedovsky, Big images"
},
{
"url": "https://doi.org/10.4171/owr/2018/30",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Let $\rho:G_{\mathbb Q}\to\operatorname{GL}_2(A)$ be a continuous representation that is irreducible, is not induced from a character of an index-two subgroup, and has infinite image. What is the structure of $\operatorname{Im}\rho$? | Let \rho:G_{\mathbb Q}\to GL_2(A) be a continuous representation that is irreducible, not induced from a character of an index-two subgroup, and has infinite image. What is the structure of \operatorname{Im}\rho? | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,882 | OWR-16171-013 | Stark Units in Abelian Towers | Prove the Gross–Popescu conjecture describing the behavior of Stark units in towers of abelian extensions of number fields. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-013",
"literature-status:partially-solved",
"owr-year:2018"
] | Gross's tower-of-fields order-of-vanishing conjecture has been proved and Gross--Stark units have been constructed cohomologically, but the full Stark-unit behavior described in the extracted record is not settled. | [
{
"url": "https://doi.org/10.4171/JEMS/821",
"label": "Dasgupta--Spiess, JEMS"
},
{
"url": "https://annals.math.princeton.edu/2018/188-3/p03",
"label": "Dasgupta--Kakde--Ventullo, Annals"
},
{
"url": "https://doi.org/10.4171/owr/2018/30",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Prove the Gross–Popescu conjecture describing the behavior of Stark units in towers of abelian extensions of number fields. | Prove the Gross--Popescu conjecture describing the behavior of Stark units in towers of abelian extensions of number fields. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,883 | OWR-16171-014 | Kontsevich's Period Conjecture | Kontsevich's period conjecture asserts that the evaluation map from the algebra of formal periods over $\mathbb{Q}$ to the algebra of actual periods is injective. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | open | null | 2,018 | 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-16171-014",
"literature-status:open",
"owr-year:2018"
] | The extracted claim is Kontsevich's injectivity conjecture for the evaluation map from formal periods to periods; it is widely open, with only important restricted cases known. | [
{
"url": "https://arxiv.org/abs/1105.0865",
"label": "Huber--Muller-Stach, formal periods"
},
{
"url": "https://d-nb.info/1216560587/34",
"label": "Huber, Galois theory of periods"
},
{
"url": "https://doi.org/10.4171/owr/2018/30",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | Kontsevich's period conjecture asserts that the evaluation map from the algebra of formal periods over $\mathbb{Q}$ to the algebra of actual periods is injective. | Kontsevich's period conjecture asserts that the evaluation map from the algebra of formal periods over \mathbb Q to the algebra of actual periods is injective. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,884 | OWR-16171-015 | Period Conjecture for Nori Motives | For every motive $M$ in Nori's category, is the evaluation map from the formal period algebra $\widetilde P_{\langle M\rangle}$ to the period algebra $P_{\langle M\rangle}$ injective? Equivalently, does the associated formal period scheme have the conjectured connectedness and transcendence-degree dimension? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844](https://doi.org/10.4171/owr/2018/30)
## Literature review (checked 2026-08-21)
**Status:**... | 3 | partially_solved | null | 2,018 | 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-16171-015",
"literature-status:partially-solved",
"owr-year:2018"
] | The general period conjecture in the excerpt remains open, but the cited 1-motive case and equivalent formulations for restricted motivic subcategories are proved. | [
{
"url": "https://arxiv.org/abs/1105.0865",
"label": "Huber--Muller-Stach, formal periods"
},
{
"url": "https://d-nb.info/1216560587/34",
"label": "Huber, Galois theory of periods"
},
{
"url": "https://doi.org/10.4171/owr/2018/30",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/30 | null | null | null | For every motive $M$ in Nori's category, is the evaluation map from the formal period algebra $\widetilde P_{\langle M\rangle}$ to the period algebra $P_{\langle M\rangle}$ injective? Equivalently, does the associated formal period scheme have the conjectured connectedness and transcendence-degree dimension? | For every motive M in Nori's category, the evaluation map from its formal period algebra \widetilde P_{\langle M\rangle} to its period algebra P_{\langle M\rangle} is injective; equivalently, the associated formal period scheme has the conjectured connectedness and transcendence-degree dimension. | 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 | Algebraische Zahlentheorie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/30, pp. 1785--1844 |
30,003,885 | OWR-16406-002 | Infinite Rank and Torsion in Integral Homology Cobordism | Does the integral homology cobordism group $\Theta^3_{\mathbb Z}$ contain a direct sum of infinitely many copies of $\mathbb Z$? Does it contain any nontrivial torsion? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,018 | 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-16406-002",
"literature-status:partially-solved",
"owr-year:2018"
] | Manolescu disproved the splitting condition underlying the high-dimensional triangulation conjecture, but the excerpt also records unresolved questions about the structure of the homology-cobordism group, including torsion and infinite-rank summands. | [
{
"url": "https://doi.org/10.1090/jams829",
"label": "Manolescu, JAMS"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | Does the integral homology cobordism group $\Theta^3_{\mathbb Z}$ contain a direct sum of infinitely many copies of $\mathbb Z$? Does it contain any nontrivial torsion? | For the integral homology cobordism group \Theta^3_{\mathbb Z}, it remains open whether the group contains a direct sum of infinitely many copies of \mathbb Z or has any nontrivial torsion. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,886 | OWR-16406-003 | Cannon’s Hyperbolic Three-Space Conjecture | If a hyperbolic group $G$ has boundary homeomorphic to $S^2$, must $G$ act properly, cocompactly, and isometrically on $\mathbb H^3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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... | [
"OWR-16406-004"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16406-003",
"literature-status:open",
"owr-year:2018"
] | The stable Cannon conjecture remains a conjecture; the stable manifold-model theorem in the literature does not imply the asserted realization by a hyperbolic 3-manifold. | [
{
"url": "https://arxiv.org/abs/1804.00738",
"label": "Ferry--Luck--Weinberger, stable Cannon"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | If a hyperbolic group $G$ has boundary homeomorphic to $S^2$, must $G$ act properly, cocompactly, and isometrically on $\mathbb H^3$? | Cannon's conjecture: if G is a hyperbolic group whose boundary is homeomorphic to S^2, then G acts properly, cocompactly, and isometrically on three-dimensional hyperbolic space. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,887 | OWR-16406-004 | Duplicate Cannon-Conjecture Extraction | If G is a hyperbolic group with boundary homeomorphic to S^2, then G acts properly, cocompactly, and isometrically on three-dimensional hyperbolic space. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (This record restates Cannon’s conjecture, represented canonically by OWR-16406-003 in the same report. No separate clean statement is promot) | [
"OWR-16406-003"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16406-004",
"literature-status:open",
"owr-year:2018"
] | The Cannon conjecture for hyperbolic groups with 2-sphere boundary is still unresolved, although many conditional and relative versions are known. | [
{
"url": "https://arxiv.org/abs/1205.5747",
"label": "Markovic, criterion for Cannon's conjecture"
},
{
"url": "https://arxiv.org/abs/2405.20428",
"label": "Relatively hyperbolic groups with planar boundaries"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach r... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | null | If G is a hyperbolic group with boundary homeomorphic to S^2, then G acts properly, cocompactly, and isometrically on three-dimensional hyperbolic space. | unrecoverable | This record restates Cannon’s conjecture, represented canonically by OWR-16406-003 in the same report. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,888 | OWR-16406-005 | Equivalence of Affine-Space Embeddings Under Automorphisms | Given embeddings $f,g:\mathbb C^d\hookrightarrow\mathbb C^n$, does there exist an automorphism $\Psi:\mathbb C^n\to\mathbb C^n$ such that $\Psi\circ f=g$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16406-005",
"literature-status:open",
"owr-year:2018"
] | This is the higher-dimensional affine-space embedding or Abhyankar--Sathaye problem; it is proved in low-dimensional cases but remains open in general. | [
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach report"
},
{
"url": "https://www.sciencedirect.com/science/article/pii/S0021869300986770",
"label": "Jelonek, embeddings of hypersurfaces"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | Given embeddings $f,g:\mathbb C^d\hookrightarrow\mathbb C^n$, does there exist an automorphism $\Psi:\mathbb C^n\to\mathbb C^n$ such that $\Psi\circ f=g$? | Given embeddings f,g:\mathbb C^d\hookrightarrow\mathbb C^n, does there exist an automorphism \Psi:\mathbb C^n\to\mathbb C^n such that \Psi\circ f=g? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,889 | OWR-16406-006 | Minimal Dimensions of Manifold Thickenings | Let $X$ be a finite aspherical complex with nonzero $k$th $L^2$-Betti number. Must every manifold thickening of $X$ have dimension at least $2k$? Equivalently, what is the minimum possible dimension of such a thickening? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16406-006",
"literature-status:open",
"owr-year:2018"
] | The minimal-thickening question is linked in the primary source to the Davis--Okun and Singer conjectures, neither of which is resolved in the stated generality. | [
{
"url": "https://archive.mpim-bonn.mpg.de/id/eprint/3842/1/preprint_2014_44.pdf",
"label": "Okun--Schreve, action dimension and Singer"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | Let $X$ be a finite aspherical complex with nonzero $k$th $L^2$-Betti number. Must every manifold thickening of $X$ have dimension at least $2k$? Equivalently, what is the minimum possible dimension of such a thickening? | If X is a finite aspherical complex with nonzero k-th L^2-Betti number, must every manifold thickening of X have dimension at least 2k? Equivalently, determine the minimal dimension of a thickening of X. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,890 | OWR-16406-008 | Nonarithmetic Lattices in Higher-Dimensional Complex Hyperbolic Space | Do nonarithmetic lattices exist in $\operatorname{Isom}(\mathbb H_{\mathbb C}^n)\cong\operatorname{SU}(n,1)$ for $n\geq3$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** partially solved... | 3 | partially_solved | null | 2,018 | 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-16406-008",
"literature-status:partially-solved",
"owr-year:2018"
] | Non-arithmetic lattices are known in SU(2,1) and SU(3,1), while existence for SU(n,1) with n greater than or equal to 4 remains open; thus the n greater than or equal to 3 formulation is only partially resolved. | [
{
"url": "https://www.maths.ox.ac.uk/node/13849",
"label": "Parker, non-arithmetic lattices"
},
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC392706/",
"label": "Mostow, non-arithmetic lattice in SU(2,1)"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach r... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | Do nonarithmetic lattices exist in $\operatorname{Isom}(\mathbb H_{\mathbb C}^n)\cong\operatorname{SU}(n,1)$ for $n\geq3$? | Do non-arithmetic lattices exist in Isom(H_{\mathbb C}^n)\cong SU(n,1) for n\geq 3? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,891 | OWR-16406-010 | Generic Properties of Random Heegaard Three-Manifolds | What properties does a generic closed 3-manifold have when its Heegaard gluing map is chosen by a random walk on the mapping class group? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16406-010",
"literature-status:open",
"owr-year:2018"
] | The question about the distribution and geometry of random Heegaard-splitting or fibred 3-manifolds has substantial asymptotic results but no complete characterization in the broad form stated. | [
{
"url": "https://www.cambridge.org/core/journals/compositio-mathematica/article/uniform-models-and-short-curves-for-random-3manifolds/08BED370D27937EADC9B1B5DDA187A2B",
"label": "Random 3-manifolds, Compositio Mathematica"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | What properties does a generic closed 3-manifold have when its Heegaard gluing map is chosen by a random walk on the mapping class group? | What properties does a generic closed 3-manifold have when its Heegaard gluing map is chosen by a random walk on the mapping class group? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,892 | OWR-16406-011 | Topological Characterization of Complex Algebraic Links | Which link types arise as $L=V\cap S^3$, where $V\subset\mathbb C^2$ is an algebraic curve and $S^3$ is the unit sphere, and what topological obstructions or characterizations detect such C-links? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910](https://doi.org/10.4171/owr/2018/31)
## Literature review (checked 2026-08-21)
**Status:** open
**Assessme... | 3 | open | null | 2,018 | 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-16406-011",
"literature-status:open",
"owr-year:2018"
] | The extracted question asks for general topological obstructions or characterizations of links of algebraic curves; known Heegaard-Floer and algebraic-geometric obstructions cover cases but do not settle the general problem. | [
{
"url": "https://arxiv.org/abs/1409.2111",
"label": "Borodzik--Hedden--Livingston, plane algebraic curves"
},
{
"url": "https://doi.org/10.4171/owr/2018/31",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/31 | null | null | null | Which link types arise as $L=V\cap S^3$, where $V\subset\mathbb C^2$ is an algebraic curve and $S^3$ is the unit sphere, and what topological obstructions or characterizations detect such C-links? | Which link types arise as L=V\cap S^3, where V\subset\mathbb C^2 is an algebraic curve and S^3 is the unit sphere, and what topological obstructions or characterizations detect such C-links? | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Topologie (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/31, pp. 1857--1910 |
30,003,893 | OWR-16407-003 | Delocalized Cyclic Pairings with Structure Sets | Let $(M,g)$ be a closed manifold with a metric of positive scalar curvature. Determine, in general, the pairing of delocalized continuous cyclic cocycles with the topological structure set; equivalently, compute the associated pairings $\tau_c\circ\rho(M,g)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981](https://doi.org/10.4171/owr/2018/32)
## Literature rev... | 3 | open | null | 2,018 | 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-16407-003",
"literature-status:open",
"owr-year:2018"
] | The computation of the pairing with the topological structure set is explicitly identified as an open problem; later work computes important special cases but not the stated general pairing. | [
{
"url": "https://ems.press/content/serial-article-files/46757?nt=1",
"label": "Xie--Yu Oberwolfach report"
},
{
"url": "https://doi.org/10.2140/akt.2023.8.531",
"label": "Chen--Wang--Xie--Yu, Annals of K-Theory"
},
{
"url": "https://doi.org/10.4171/owr/2018/32",
"label": "Oberwolfac... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/32 | null | null | null | Let $(M,g)$ be a closed manifold with a metric of positive scalar curvature. Determine, in general, the pairing of delocalized continuous cyclic cocycles with the topological structure set; equivalently, compute the associated pairings $\tau_c\circ\rho(M,g)$. | For a closed manifold (M,g) with a positive scalar curvature metric, determine in general the pairing of delocalized continuous cyclic cocycles with the topological structure set, equivalently compute the associated pairings \tau_c\circ\rho(M,g). | 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 | Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981 |
30,003,894 | OWR-16407-005 | Arithmetic Nature of Delocalized Eta Invariants | What values can delocalized eta invariants of Dirac operators on universal covers take in general; in particular, are they always algebraic numbers? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981](https://doi.org/10.4171/owr/2018/32)
## Literature rev... | 3 | open | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16407-005",
"literature-status:open",
"owr-year:2018"
] | The question whether delocalized eta invariants are always algebraic remains open in general; algebraicity is proved conditionally from rational Baum--Connes and related hypotheses. | [
{
"url": "https://doi.org/10.1093/imrn/rnz170",
"label": "Xie--Yu, IMRN"
},
{
"url": "https://doi.org/10.4171/owr/2018/32",
"label": "Oberwolfach report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/32 | null | null | null | What values can delocalized eta invariants of Dirac operators on universal covers take in general; in particular, are they always algebraic numbers? | What values can delocalized eta invariants of Dirac operators on universal covers take in general; in particular, are they always algebraic numbers? | 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 | Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981 |
30,003,895 | OWR-16407-007 | All-Order Expansion of the Noncommutative $\Phi^4$ Model | For the function $I_\lambda(a)$ arising from the boundary-value solution of the noncommutative $\Phi^4$ model, does the formal expansion
$$
I_\lambda(a)=\sum_{n\geq1}\frac{\lambda^n}{n!}\frac{d^{n-1}}{da^{n-1}}\bigl(-\log(1+a)\bigr)^n
-\lambda\sum_{n\geq1}\frac{\lambda^n}{n!}\frac{d^{n-1}}{da^{n-1}}\left[\frac{\bigl(-\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981](https://doi.org/10.4171/owr/2018/32)
## Literature rev... | 3 | solved | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s00220-019-03592-4",
"checked_at": "2026-09-29",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-29] **solved (yes)**. R. Wulkenhaar (joint with E. Panzer; OWR 32/2018, p. 1939) checks the Stirling-number formula (8) for I_λ(a), equivalently the record's (9), through order λ^10 and conjectures it to all orders. Panzer–Wulkenhaar prove it in the final version, [Commun. Math... | [
"owr",
"oberwolfach-reports",
"OWR-16407-007",
"literature-status:open",
"owr-year:2018"
] | The coefficient identity was checked through ten orders and then conjectured; the primary paper proves a Lambert-W resummation but still leaves the all-order combinatorial identity as a conjecture. | [
{
"url": "https://arxiv.org/abs/1807.02945",
"label": "Panzer--Wulkenhaar"
},
{
"url": "https://ivv5hpp.uni-muenster.de/u/raimar/publications/abstracts/owr18-raimar.pdf",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/32 | null | null | null | For the function $I_\lambda(a)$ arising from the boundary-value solution of the noncommutative $\Phi^4$ model, does the formal expansion
$$
I_\lambda(a)=\sum_{n\geq1}\frac{\lambda^n}{n!}\frac{d^{n-1}}{da^{n-1}}\bigl(-\log(1+a)\bigr)^n
-\lambda\sum_{n\geq1}\frac{\lambda^n}{n!}\frac{d^{n-1}}{da^{n-1}}\left[\frac{\bigl(-\... | For the function I_\lambda(a) arising in the boundary-value solution of the noncommutative \Phi^4-model, the explicit formal power-series expansion given for I_\lambda(a) is conjectured to hold to all orders in \lambda. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981 |
30,003,896 | OWR-16407-009 | Baum–Connes Assembly for Minimal Exact Crossed Products | For the minimal exact crossed-product functor $\rtimes_E$, understand the reformulated Baum–Connes assembly map $K_*^{\mathrm{top}}(G;A)\to K_*(A\rtimes_E G)$, including concrete realization and computation of the crossed product. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981](https://doi.org/10.4171/owr/2018/32)
## Literature rev... | 3 | partially_solved | null | 2,018 | 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-16407-009",
"literature-status:partially-solved",
"owr-year:2018"
] | The exact crossed-product reformulation was clarified by the minimal exact crossed product and agrees with the classical construction for trivial coefficients, but the Baum--Connes conjecture with general coefficients remains open. | [
{
"url": "https://arxiv.org/abs/1311.2343",
"label": "Baum--Guentner--Willett"
},
{
"url": "https://arxiv.org/abs/1804.02725",
"label": "Buss--Echterhoff--Willett"
},
{
"url": "https://doi.org/10.4171/owr/2018/32",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/32 | null | null | null | For the minimal exact crossed-product functor $\rtimes_E$, understand the reformulated Baum–Connes assembly map $K_*^{\mathrm{top}}(G;A)\to K_*(A\rtimes_E G)$, including concrete realization and computation of the crossed product. | For the minimal exact crossed-product functor \rtimes_E, understand the reformulated Baum--Connes assembly map K_*^{\mathrm{top}}(G;A)\to K_*(A\rtimes_E G), including concrete realization and computation of the crossed product. | 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 | Non-commutative Geometry, Index Theory and Mathematical Physics (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/32, pp. 1911--1981 |
30,003,897 | OWR-16408-002 | Green’s Canonical Syzygy Conjecture for Arbitrary Curves | For every nonhyperelliptic canonically embedded smooth curve $C$ of genus $g$, is
$$K_{i,1}(C,\omega_C)=0$$
equivalent to $i\geq g-\operatorname{Cliff}(C)-1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,018 | 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-16408-002",
"literature-status:open",
"owr-year:2018"
] | Voisin resolved the generic characteristic-zero case and later work covers broad generic positive-characteristic cases, but Green's conjecture for arbitrary smooth curves remains open. | [
{
"url": "https://www.cambridge.org/core/journals/compositio-mathematica/article/greens-canonical-syzygy-conjecture-for-generic-curves-of-odd-genus/65660027A237A4129796991EEC9C2CC1",
"label": "Voisin"
},
{
"url": "https://arxiv.org/abs/1810.11635",
"label": "Aprodu--Farkas--Papadima--Raicu--Weym... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | For every nonhyperelliptic canonically embedded smooth curve $C$ of genus $g$, is
$$K_{i,1}(C,\omega_C)=0$$
equivalent to $i\geq g-\operatorname{Cliff}(C)-1$? | Green's Conjecture asks whether, for every non-hyperelliptic canonically embedded smooth curve C of genus g, K_{i,1}(C,\omega_C)=0 exactly when i\ge g-\operatorname{Cliff}(C)-1; the conjecture remains open for arbitrary curves although it is known for general curves. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,898 | OWR-16408-004 | Debarre’s Minimal Cohomology-Class Conjecture | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety of dimension $g$, and let $X\subset A$ be a reduced pure $d$-dimensional subvariety with $1\leq d\leq g-2$ and minimal cohomology class
$$[X]=\frac{\theta^{g-d}}{(g-d)!}.$$
Must either $(A,\Theta)$ be the Jacobian of a curve $C$ with $X$ a tr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,018 | 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-16408-004",
"literature-status:partially-solved",
"owr-year:2018"
] | Matsusaka--Ran handles curves and classification results cover low dimensions and important special cases, but the higher-dimensional minimal-cohomology-class and regularity conjectures remain unresolved. | [
{
"url": "https://arxiv.org/abs/math/0610166",
"label": "Pareschi--Popa"
},
{
"url": "https://arxiv.org/abs/1602.06231",
"label": "Casalaina-Martin--Popa--Schreieder"
},
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety of dimension $g$, and let $X\subset A$ be a reduced pure $d$-dimensional subvariety with $1\leq d\leq g-2$ and minimal cohomology class
$$[X]=\frac{\theta^{g-d}}{(g-d)!}.$$
Must either $(A,\Theta)$ be the Jacobian of a curve $C$ with $X$ a tr... | Debarre's minimal-class conjecture states that a reduced pure-dimensional subvariety X\subset A of an indecomposable principally polarized abelian variety (A,\Theta) has minimal cohomology class if and only if it is a curve W_d(C) in a Jacobian or the Fano surface in the intermediate Jacobian of a cubic threefold. | corrected_verified | The official report was checked. The reconstruction restores the dimension range, minimal-class formula, and both classification alternatives. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,899 | OWR-16408-005 | Multiplicity Bounds for Principal Theta Divisors | For every point $x\in\Theta$ of the theta divisor of an indecomposable principally polarized abelian variety of dimension $g$, is
$$\operatorname{mult}_x\Theta\leq\frac{g+1}{2}$$
always hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,018 | 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-16408-005",
"literature-status:partially-solved",
"owr-year:2018"
] | The proposed theta-divisor multiplicity bound is proved for isolated singularities and other special cases, but the conjecture for arbitrary principally polarized abelian varieties with non-isolated singularities remains open. | [
{
"url": "https://arxiv.org/abs/1605.08088",
"label": "Mustata--Popa"
},
{
"url": "https://people.math.harvard.edu/~mpopa/papers/SI.pdf",
"label": "Hodge ideals"
},
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | For every point $x\in\Theta$ of the theta divisor of an indecomposable principally polarized abelian variety of dimension $g$, is
$$\operatorname{mult}_x\Theta\leq\frac{g+1}{2}$$
always hold? | For every point x\in\Theta in an indecomposable principally polarized abelian variety of dimension g, the conjecture is \operatorname{mult}_x\Theta\le (g+1)/2. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,900 | OWR-16408-006 | Implications Among Conjectures on Principally Polarized Abelian Varieties | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety, and let $X\subset A$ be a geometrically nondegenerate subvariety for which $\mathcal I_X(\Theta)$ is a generic-vanishing sheaf. Quantify a strengthening of this hypothesis sufficient to prove the bound
$$\operatorname{mult}_x\Theta\leq\frac{\... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,018 | 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-16408-006",
"literature-status:open",
"owr-year:2018"
] | The exact record is an incomplete cross-reference between two conjectures rather than a complete standalone claim; the referenced general classification remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | Let $(A,\Theta)$ be an indecomposable principally polarized abelian variety, and let $X\subset A$ be a geometrically nondegenerate subvariety for which $\mathcal I_X(\Theta)$ is a generic-vanishing sheaf. Quantify a strengthening of this hypothesis sufficient to prove the bound
$$\operatorname{mult}_x\Theta\leq\frac{\... | An \epsilon-strengthening of Conjecture 2 is conjectured to imply Conjecture 4, and Conjecture 4 is expected to help prove important special cases of Conjecture 2 concerning subvarieties of principally polarized abelian varieties. | corrected_verified | The official report was checked. The dangling conjecture numbers were replaced by the generic-vanishing classification and theta-divisor multiplicity statements to which they refer. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,901 | OWR-16408-008 | Expository Motivation for Nonreductive GIT | Why is non-reductive geometric invariant theory needed to construct moduli spaces of unstable curves and related unstable objects, even when the initial presentation involves a reductive group action? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,018 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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 motivational question by explaining why nonreductive geometric invariant theory enters the modu) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16408-008",
"literature-status:open",
"owr-year:2018"
] | The exact record is only the question Why does non-reductive GIT appear here and does not state a mathematical conjecture or theorem whose status can be assessed. | [
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | null | Why is non-reductive geometric invariant theory needed to construct moduli spaces of unstable curves and related unstable objects, even when the initial presentation involves a reductive group action? | unrecoverable | The official report immediately answers this motivational question by explaining why nonreductive geometric invariant theory enters the moduli construction; it is not left as an open problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,902 | OWR-16408-015 | Virtual Cohomological Dimension of Surface Automorphism Groups | For a Coble surface, an Enriques surface, or an elliptic K3 surface $S$, is
$$\operatorname{vcd}(\operatorname{Aut}S)=\max_f\operatorname{MW-rk}(f),$$
where the maximum ranges over genus-one fibrations $f:S\to\mathbb P^1$ and $\operatorname{MW-rk}(f)$ is the Mordell–Weil rank of the Jacobian fibration? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | partially_solved | null | 2,018 | 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-16408-015",
"literature-status:partially-solved",
"owr-year:2018"
] | The Mordell--Weil rank gives one direction and equality is known for important generic and special surfaces, but the reverse inequality in the full Coble, Enriques, and elliptic K3 setting remains open. | [
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
},
{
"url": "https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/292398/1/2024-24.pdf",
"label": "Recent K3 work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | For a Coble surface, an Enriques surface, or an elliptic K3 surface $S$, is
$$\operatorname{vcd}(\operatorname{Aut}S)=\max_f\operatorname{MW-rk}(f),$$
where the maximum ranges over genus-one fibrations $f:S\to\mathbb P^1$ and $\operatorname{MW-rk}(f)$ is the Mordell–Weil rank of the Jacobian fibration? | If S is a Coble surface, an Enriques surface, or an elliptic K3 surface, then \operatorname{vcd}(\operatorname{Aut}S)=\max_f\operatorname{MW-rk}(f), where the maximum is over genus-one fibrations f:S\to\mathbb{P}^1 and \operatorname{MW-rk}(f) is the Mordell--Weil rank of the Jacobian fibration. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,903 | OWR-16408-016 | Cohomological Dimension of Automorphism Groups of Singular K3 Surfaces | Does the automorphism group of every singular K3 surface of discriminant 7 or 8 have cohomological dimension 2? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031](https://doi.org/10.4171/owr/2018/33)
## Literature review (checked 2026-08-21)
**Status:... | 3 | open | null | 2,018 | 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-16408-016",
"literature-status:open",
"owr-year:2018"
] | Ujikawa's generators and Bertin--Lecacheux's elliptic-fibration classifications provide substantial data, but no proof of the stated cohomological-dimension equality was found; this special case remains open. | [
{
"url": "https://arxiv.org/abs/1307.4197",
"label": "Ujikawa"
},
{
"url": "https://arxiv.org/abs/1304.7427",
"label": "Shimada"
},
{
"url": "https://ems.press/content/serial-article-files/46758?nt=1",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/33 | null | null | null | Does the automorphism group of every singular K3 surface of discriminant 7 or 8 have cohomological dimension 2? | The automorphism group of a singular K3 surface of discriminant 7 or 8 has cohomological dimension 2. | corrected_verified | The mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Classical Algebraic Geometry (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/33, pp. 1983--2031 |
30,003,904 | OWR-16409-004 | Geometric Reduction Types of Plane Quartics | Given a plane quartic F(x,y,z)=0 over a number field and a prime p dividing its discriminant, determine whether p is a prime of geometrically bad reduction; if not, decide whether the curve has potentially good hyperelliptic or non-hyperelliptic reduction. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076](https://doi.org/10.4171/owr/2018/34)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,018 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Unrecoverable OWR statement (The official report states that the authors answer these reduction-type questions and characterize the answer using Dixmier–Ohno invariants,) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16409-004",
"literature-status:open",
"owr-year:2018"
] | The exact record is only the question What can we say about the prime p and gives no definition of p or precise theorem whose status can be checked. | [
{
"url": "https://ems.press/content/serial-article-files/46754",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/34 | null | null | null | null | Given a plane quartic F(x,y,z)=0 over a number field and a prime p dividing its discriminant, determine whether p is a prime of geometrically bad reduction; if not, decide whether the curve has potentially good hyperelliptic or non-hyperelliptic reduction. | unrecoverable | The official report states that the authors answer these reduction-type questions and characterize the answer using Dixmier–Ohno invariants, so the extraction is a result summary rather than an open problem. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076 |
30,003,905 | OWR-16409-006 | Symplectic Models for Relative Class Group Distributions | After incorporating the contribution of unit groups, is the joint distribution over number fields of relative class-group $\ell$-parts and the two accompanying class-group invariants equal to the distribution predicted by the random symplectic-similitude model? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076](https://doi.org/10.4171/owr/2018/34)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,018 | 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-16409-006",
"literature-status:open",
"owr-year:2018"
] | The joint distribution over number fields is explicitly conjectural; the report gives function-field verification and numerical evidence but no proof for number fields. | [
{
"url": "https://ems.press/content/serial-article-files/46754",
"label": "OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/34 | null | null | null | After incorporating the contribution of unit groups, is the joint distribution over number fields of relative class-group $\ell$-parts and the two accompanying class-group invariants equal to the distribution predicted by the random symplectic-similitude model? | After accounting for unit groups, the joint distribution over number fields of relative class-group \ell-parts together with the two additional class-group invariants is conjectured to equal the distribution predicted by the random symplectic-similitude model. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076 |
30,003,906 | OWR-16409-008 | Malle Conjecture for Number Field Counts | For a number field $k$ and a transitive permutation group $G\subseteq S_n$, determine the asymptotic behavior of $$N_k(G,X)=\#\{K/k:\operatorname{Gal}(K/k)\simeq G,\ \operatorname{Disc}(K/k)<X\}.$$ In the cases where Malle's original logarithmic exponent is valid, is $$N_k(G,X)\sim C(G,k)X^{1/a(G)}(\log X)^{b(G,k)-1}$$... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076](https://doi.org/10.4171/owr/2018/34)
## Literature review (checked 2026-08-21)
**St... | 3 | open | null | 2,018 | 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-16409-008",
"literature-status:open",
"owr-year:2018"
] | The record is an incomplete fragment identifying Malle's conjecture rather than a complete proposition; current work proves substantial families and also exposes counterexamples to the original formulation, so no definite resolution follows for this extracted claim. | [
{
"url": "https://ems.press/content/serial-article-files/46754",
"label": "Wang--Lemke Oliver--Wood report"
},
{
"url": "https://doi.org/10.1515/crelle-2025-0074",
"label": "Alberts--Lemke Oliver--Wang--Wood 2025"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/34 | null | null | null | For a number field $k$ and a transitive permutation group $G\subseteq S_n$, determine the asymptotic behavior of $$N_k(G,X)=\#\{K/k:\operatorname{Gal}(K/k)\simeq G,\ \operatorname{Disc}(K/k)<X\}.$$ In the cases where Malle's original logarithmic exponent is valid, is $$N_k(G,X)\sim C(G,k)X^{1/a(G)}(\log X)^{b(G,k)-1}$$... | For a number field k and a permutation group G\subset S_n, determine the asymptotic behavior as X\to\infty of N_k(G,X)=\#\{K/k:\operatorname{Gal}(K/k)\simeq G,\operatorname{Disc}(K/k)<X\}, as asserted by Malle's conjecture. | 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 | Explicit Methods in Number Theory (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/34, pp. 2033--2076 |
30,003,907 | OWR-16410-007 | Uniqueness of Tangents for Multivalued Energy Minimizers | Let $u$ be a Dirichlet-energy-minimizing $q$-valued function and let $Y$ be a singular point. Is the tangent function obtained by blow-up at $Y$ independent of the sequence of scales $\rho_j\to0^+$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/35, pp. 2077--2156](https://doi.org/10.4171/owr/2018/35)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,018 | 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-16410-007",
"literature-status:partially-solved",
"owr-year:2018"
] | Uniqueness of cylindrical tangent functions is proved at H superscript n minus 2 almost every singular point, but uniqueness for every point or every blow-up sequence remains open. | [
{
"url": "https://arxiv.org/abs/1711.06222",
"label": "Krummel--Wickramasekera 2017"
},
{
"url": "https://doi.org/10.4171/owr/2018/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/35 | null | null | null | Let $u$ be a Dirichlet-energy-minimizing $q$-valued function and let $Y$ be a singular point. Is the tangent function obtained by blow-up at $Y$ independent of the sequence of scales $\rho_j\to0^+$? | For a Dirichlet-energy-minimizing q-valued function u and a singular point Y, is the tangent function obtained by blow-up unique independently of the sequence \rho_j\to0^+? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Calculus of Variations (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/35, pp. 2077--2156 |
30,003,908 | OWR-16410-008 | Almost Everywhere Regularity of Parametrized Stationary Varifolds | For a general parametrized integer stationary $n$-varifold, does the singular set have zero $n$-dimensional Hausdorff measure without additional hypotheses? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Calculus of Variations (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/35, pp. 2077--2156](https://doi.org/10.4171/owr/2018/35)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,018 | 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-16410-008",
"literature-status:open",
"owr-year:2018"
] | The source explicitly leaves almost-everywhere regularity in full generality open; later parametrized and constant-multiplicity results do not establish the unrestricted statement. | [
{
"url": "https://doi.org/10.1002/cpa.21927",
"label": "Pigati--Riviere regularity theorem"
},
{
"url": "https://doi.org/10.4171/owr/2018/35",
"label": "Oberwolfach Report 35"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/35 | null | null | null | For a general parametrized integer stationary $n$-varifold, does the singular set have zero $n$-dimensional Hausdorff measure without additional hypotheses? | Does almost-everywhere regularity hold for general parametrized integer stationary varifolds in full generality, equivalently does their singular set have zero n-dimensional Hausdorff measure without additional assumptions? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Calculus of Variations (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/35, pp. 2077--2156 |
30,003,909 | OWR-16411-001 | Axisymmetry of Spherical Near-Horizon Geometries | Is every solution of the near-horizon-geometry equations on $S^2$ axisymmetric and therefore induced by a degenerate Kerr metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | partially_solved | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"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 partially solved. P. T. Chruściel (with S. Szybka, P. Tod), OWR 36/2018, p. 2174, Conjecture 1: do all solutions of the near-horizon-geometry equations on S², not only the axisymmetric ones, come from degenerate Kerr metrics... | [
"owr",
"oberwolfach-reports",
"OWR-16411-001",
"literature-status:partially-solved",
"owr-year:2018"
] | Kerr near-horizon uniqueness is proved in a neighborhood of the Kerr family, including the non-axisymmetric perturbative classification, but a global uniqueness theorem without the symmetry restriction is not established. | [
{
"url": "https://doi.org/10.1088/1361-6382/aa90e7",
"label": "Chrusciel--Szybka--Tod 2018"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Is every solution of the near-horizon-geometry equations on $S^2$ axisymmetric and therefore induced by a degenerate Kerr metric? | Conjecture: every solution of the near-horizon-geometry equations on a two-dimensional sphere is axisymmetric in the sense that it arises from a degenerate Kerr metric, so the axisymmetry assumption in the known classification can be removed. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,910 | OWR-16411-002 | Weak Cosmic Censorship in Asymptotically Flat Spacetimes | Does weak cosmic censorship hold for black-hole spacetimes in asymptotically flat settings, and under which geometric and dimensional hypotheses can it be proved or disproved? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16411-002",
"literature-status:open",
"owr-year:2018"
] | Weak cosmic censorship remains unresolved in the stated higher-dimensional asymptotically flat setting; numerical studies provide evidence for violations but not a general rigorous resolution. | [
{
"url": "https://arxiv.org/abs/2011.03049",
"label": "Figueras--Kunesch--Tunyasuvunakool--Lehner 2020"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Does weak cosmic censorship hold for black-hole spacetimes in asymptotically flat settings, and under which geometric and dimensional hypotheses can it be proved or disproved? | Determine whether weak cosmic censorship holds for black-hole spacetimes in asymptotically flat spaces, and characterize the circumstances under which it is true or false. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,911 | OWR-16411-003 | Horizon Topology Changes and Stable Higher-Dimensional Black Holes | Is the Gregory–Laflamme instability the only mechanism by which general relativity changes horizon topology? In spacetime dimension $D>4$, is every stable black hole a Myers–Perry black hole satisfying $J/M^{D-3}=O(1)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16411-003",
"literature-status:open",
"owr-year:2018"
] | The two higher-dimensional black-hole stability and topology conjectures remain conjectural; known ultraspinning instabilities and additional black-hole branches provide substantial constraints but no general classification. | [
{
"url": "https://doi.org/10.1007/978-3-642-41992-8",
"label": "Emparan--Reall higher-dimensional black holes"
},
{
"url": "https://doi.org/10.1007/s10714-025-03398-x",
"label": "Black holes galore in D greater than 4"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Ober... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Is the Gregory–Laflamme instability the only mechanism by which general relativity changes horizon topology? In spacetime dimension $D>4$, is every stable black hole a Myers–Perry black hole satisfying $J/M^{D-3}=O(1)$? | Conjecture: the Gregory--Laflamme instability is the only mechanism by which general relativity changes horizon topology; and, in dimensions greater than four, the only stable black hole is a Myers--Perry black hole with J/M^{D-3}\leq O(1). | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,912 | OWR-16411-004 | Nonlinear Instability of Anti–de Sitter Spacetime | Can arbitrarily small perturbations of anti–de Sitter initial data, evolved by the vacuum Einstein equations with reflecting conformal-boundary conditions, form black-hole regions at sufficiently late times? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16411-004",
"literature-status:open",
"owr-year:2018"
] | The AdS instability conjecture in the stated vacuum reflecting-boundary setting remains open; rigorous instability is known for selected matter models and symmetries, not for the full claim. | [
{
"url": "https://arxiv.org/abs/1104.3702",
"label": "Bizon--Rostworowski 2011"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Can arbitrarily small perturbations of anti–de Sitter initial data, evolved by the vacuum Einstein equations with reflecting conformal-boundary conditions, form black-hole regions at sufficiently late times? | AdS instability conjecture: arbitrarily small perturbations of the initial data of anti-de Sitter spacetime, evolved by the vacuum Einstein equations with reflecting conformal-boundary conditions, can form black-hole regions at sufficiently late times; hence anti-de Sitter spacetime is nonlinearly unstable. | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,913 | OWR-16411-006 | Mass Curvature Relations in Asymptotically Hyperbolic Geometry | Extend conformal and Weyl mass covariants to broader classes of asymptotically hyperbolic manifolds, and establish a sharp relation between each mass and an associated curvature operator. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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-16411-006",
"literature-status:open",
"owr-year:2018"
] | The report asks for a broader curvature-operator interpretation of mass; existing asymptotically hyperbolic mass constructions do not settle the stated tight link, so the problem remains open. | [
{
"url": "https://arxiv.org/abs/math/0110035",
"label": "Chrusciel--Herzlich 2003"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | Extend conformal and Weyl mass covariants to broader classes of asymptotically hyperbolic manifolds, and establish a sharp relation between each mass and an associated curvature operator. | Can one extend the conformal and Weyl mass covariants to a broader asymptotically hyperbolic setting while establishing a tight relation between a given mass and an associated curvature operator? | corrected_verified | The mathematical content was preserved while notation, typography, and sentence structure were repaired for publication. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,914 | OWR-16411-007 | Reduction of Order for Perturbatively Corrected Equations | For perturbatively corrected partial differential equations, is there a systematic reduction-of-order procedure that remains accurate to leading perturbative order without introducing spurious degrees of freedom, coordinate dependence, runaway solutions, or ill-posedness? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 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... | [
"OWR-16411-008"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16411-007",
"literature-status:open",
"owr-year:2018"
] | The extracted sentence is an underspecified request about perturbative corrections, with no definite mathematical statement or complete resolution identifiable in the primary literature. | [
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | For perturbatively corrected partial differential equations, is there a systematic reduction-of-order procedure that remains accurate to leading perturbative order without introducing spurious degrees of freedom, coordinate dependence, runaway solutions, or ill-posedness? | For perturbative corrections to partial differential equations, is there a systematic reduction-of-order or related procedure that remains accurate to leading order without introducing spurious degrees of freedom, coordinate dependence, or ill-posedness? | 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 | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
30,003,915 | OWR-16411-008 | Well Posed Perturbative Einstein Field Equations | For perturbative modifications of Einstein or related field equations, determine whether they admit a well-posed initial-value formulation and, if so, what physical predictions they make without spurious solutions or degrees of freedom. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251](https://doi.org/10.4171/owr/2018/36)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,018 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"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 | Duplicate/merged OWR extraction (The official report contains one overarching open question about handling perturbatively corrected equations; this generic restatement adds ) | [
"OWR-16411-007"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-16411-008",
"literature-status:open",
"owr-year:2018"
] | The extracted statement is only the generic sentence that an open problem deserves attention and omits the mathematical claim; related C superscript 1 comma 1 singularity theorems therefore cannot resolve this exact record. | [
{
"url": "https://arxiv.org/abs/1706.08426",
"label": "Graf--Grant--Kunzinger--Steinbauer 2018"
},
{
"url": "https://doi.org/10.4171/owr/2018/36",
"label": "Oberwolfach Report 36"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2018/36 | null | null | null | null | For perturbative modifications of Einstein or related field equations, determine whether they admit a well-posed initial-value formulation and, if so, what physical predictions they make without spurious solutions or degrees of freedom. | unrecoverable | The official report contains one overarching open question about handling perturbatively corrected equations; this generic restatement adds no distinct problem beyond OWR-16411-007. No separate clean statement is promoted; the original record remains publicly visible for provenance. | null | null | null | null | null | Mathematical General Relativity (2019), Oberwolfach Reports, DOI 10.4171/owr/2018/36, pp. 2157--2251 |
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