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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,005,216 | OWR-11101919-003 | Universal Approximation by One-Lipschitz Spline Networks | Are weight-constrained neural networks with learnable one-Lipschitz spline activations universal approximators of one-Lipschitz functions? Does universality extend to vector-valued targets, and what depth-width structures are optimal? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266](https://doi.org/10.4171/owr/2022/38)
## Literature review (checked 2026-08... | 3 | open | null | 2,022 | 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-11101919-003",
"literature-status:open",
"owr-year:2022"
] | Deep spline networks with three-region one-Lipschitz activations are optimal within a restricted architecture class, but universality for all one-Lipschitz functions remains an explicitly open problem. | [
{
"url": "https://doi.org/10.1137/22M1504573",
"label": "Neumayer--Goujon--Bohra--Unser, deep splines"
},
{
"url": "https://doi.org/10.4171/owr/2022/38",
"label": "original Oberwolfach report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/38 | null | null | null | Are weight-constrained neural networks with learnable one-Lipschitz spline activations universal approximators of one-Lipschitz functions? Does universality extend to vector-valued targets, and what depth-width structures are optimal? | neural networks, for which naturally the question of expressiveness arises. Due to these observations, we propose to use learnable spline activation func- tions with at least 3 linear regions instead. However, it remains an open question whether such NNs are uni- versal approximators of 1-Lipschitz functions and our re... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Imaging and Surface Processing (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/38, pp. 2195--2266 |
30,005,217 | OWR-11101920-001 | Structure and Asymptotics of Finite Group Characters | How do tensor products of complex characters decompose; what are their vanishing sets and asymptotic behavior; and what are the dimensions of modular characters? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-001",
"literature-status:open",
"owr-year:2022"
] | The record lists broad unresolved questions on tensor products, vanishing sets, asymptotics, and modular character dimensions; current work resolves only restricted families, not the general problem. | [
{
"url": "https://doi.org/10.4171/owr/2022/39",
"label": "original Oberwolfach report"
},
{
"url": "https://doi.org/10.1016/j.aim.2024.109589",
"label": "Navarro--Ruhstorfer--Tiep--Vallejo, height-zero fields"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | How do tensor products of complex characters decompose; what are their vanishing sets and asymptotic behavior; and what are the dimensions of modular characters? | How does one decompose the tensor product of a pair of complex characters? Can we understand the vanishing sets of complex characters? What about the asymptotic behaviour of complex characters? What are the dimen- sions of the modular characters? These questions have been hailed as some of the definitive open problems ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,218 | OWR-11101920-002 | Positivity in Affine Kazhdan–Lusztig Theory | In affine type $A$, is the decomposition of $N_{\lambda_{i+1}}$ in terms of the $N_{\mu_i}$ positive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-002",
"literature-status:partially-solved",
"owr-year:2022"
] | The affine type A pre-canonical-basis positivity conjecture remains open beyond verified ranges, while Elias and Williamson proved positivity of Kazhdan--Lusztig polynomials in full generality. | [
{
"url": "https://doi.org/10.1016/j.aim.2022.108255",
"label": "Patimo--Plaza--Williamson, pre-canonical bases"
},
{
"url": "https://doi.org/10.4007/annals.2014.180.3.6",
"label": "Elias--Williamson, Soergel Hodge theory"
},
{
"url": "https://doi.org/10.4171/owr/2022/39",
"label": "o... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | In affine type $A$, is the decomposition of $N_{\lambda_{i+1}}$ in terms of the $N_{\mu_i}$ positive? | In affine type A we conjecture that the decomposition of N\lambdai+1 in terms of Nµi is positive. (2) The second problem is that of proving positivity properties for Kazhdan– Lusztig polynomials. Some aspects of Kazhdan–Lusztig polynomials Nicolas Libedinsky (joint work with Leonardo Patimo, David Plaza and Geordie Wil... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,219 | OWR-11101920-003 | Fields of Values of Irreducible Characters | What restrictions hold on the field of values $\mathbb{Q}(\chi)$ for $\chi\in\operatorname{Irr}(G)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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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-11101920-003",
"literature-status:open",
"owr-year:2022"
] | The question is intentionally broad; recent papers classify important degree- and prime-restricted cases but retain conjectures and do not give a general structural characterization of Q of chi. | [
{
"url": "https://arxiv.org/abs/2601.15987",
"label": "Hung--Navarro--Tiep, fields of character values"
},
{
"url": "https://doi.org/10.1016/j.aim.2024.109589",
"label": "Navarro--Ruhstorfer--Tiep--Vallejo, height-zero fields"
},
{
"url": "https://doi.org/10.4171/owr/2022/39",
"label... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | What restrictions hold on the field of values $\mathbb{Q}(\chi)$ for $\chi\in\operatorname{Irr}(G)$? | Is there anything special about the field of values Q(χ) whenever χ \in Irr(G)? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,220 | OWR-11101920-004 | Sylow Restrictions and Character Fields of Values | Let $P$ be a Sylow $p$-subgroup of a finite group $G$, and let $\chi\in\operatorname{Irr}(G)$ have $p'$-degree and conductor $p^am$ with $p\nmid m$. Is $[\mathbb Q_{p^a}:\mathbb Q(\chi_P)]$ always not divisible by $p$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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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-11101920-004",
"literature-status:open",
"owr-year:2022"
] | The cited character-theoretic context gives motivations and partial results, but no general theorem resolving the relation between restrictions of characters and fields of values was found. | [
{
"url": "https://doi.org/10.1112/jlms.12852",
"label": "Fayers--Kleshchev--Morotti, spin RoCK blocks"
},
{
"url": "https://ems.press/content/serial-article-files/46974",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | Let $P$ be a Sylow $p$-subgroup of a finite group $G$, and let $\chi\in\operatorname{Irr}(G)$ have $p'$-degree and conductor $p^am$ with $p\nmid m$. Is $[\mathbb Q_{p^a}:\mathbb Q(\chi_P)]$ always not divisible by $p$? | What all this has to do with restrictions of characters? We know that Q(χ)/Q is an abelian extension, but the converse is also true: If Q \subseteq F \subseteq Qn , then the semidirect product of Cn : Gal(Qn /F ) has irreducible characters with field of values F . As you have seen, my interest (surely by the McKay conj... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,221 | OWR-11101920-005 | Extending Character-Field Bounds Beyond p-Solvable Groups | Let $P$ be a Sylow $p$-subgroup of a finite group $G$, and let $\chi\in\operatorname{Irr}(G)$ have conductor $p^am$ with $p\nmid m$. Is
$$[\mathbb Q_{p^a}:\mathbb Q_p(\chi_P)]\leq\chi(1)_p$$
for arbitrary finite $G$, without a $p$-solvability assumption? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-005",
"literature-status:partially-solved",
"owr-year:2022"
] | The Isaacs--Navarro theorem settles the stated p-solvable case and establishes substantial arithmetic restrictions, but the non-p-solvable extension and the proposed general degree inequality remain unresolved. | [
{
"url": "https://doi.org/10.1112/jlms.12852",
"label": "Fayers--Kleshchev--Morotti, spin RoCK blocks"
},
{
"url": "https://ems.press/content/serial-article-files/46974",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | Let $P$ be a Sylow $p$-subgroup of a finite group $G$, and let $\chi\in\operatorname{Irr}(G)$ have conductor $p^am$ with $p\nmid m$. Is
$$[\mathbb Q_{p^a}:\mathbb Q_p(\chi_P)]\leq\chi(1)_p$$
for arbitrary finite $G$, without a $p$-solvability assumption? | Is the theorem above true for non p-solvable groups? Is it true that |Qpa : Qp (χP )| \leq χ(1)p ? the non-linear part. Hence L(\psi) has degree not divisible by p. Let’s order them according to their order: L(\psi) = p0 (\psi) + p1 (\psi) + . . . + pt (\psi) . That is, X pi (\psi) = [\psi, \lambda]\lambda . \lambda\in... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,222 | OWR-11101920-008 | Probability of Vanishing Character Values | For a finite group $G$, what is the probability that a randomly chosen character value $\chi(g)$ equals $0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
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"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-008",
"literature-status:open",
"owr-year:2022"
] | Known results describe substantial zero sets for character values, but no general probability law answering the question of when a character value is zero was found. | [
{
"url": "https://ems.press/content/serial-article-files/46974",
"label": "Oberwolfach Report 39/2022"
},
{
"url": "https://doi.org/10.1016/j.crma.2019.10.006",
"label": "Miller, Dense proportions of zeros"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | For a finite group $G$, what is the probability that a randomly chosen character value $\chi(g)$ equals $0$? | In particular, we ask the following [3]. What is the chance that a character value χ(g) equals 0? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,223 | OWR-11101920-009 | Limiting Vanishing Probability for Symmetric Group Characters | What is the limiting behavior of $\Pr(\chi_\lambda(\mu)=0)$ for random irreducible characters and conjugacy classes of symmetric groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-009",
"literature-status:open",
"owr-year:2022"
] | The joint character-and-element probability of a zero tends to one in several settings, but the limiting behavior under uniform partitions and conjugacy classes for symmetric groups is explicitly left open. | [
{
"url": "https://doi.org/10.1016/j.crma.2019.10.006",
"label": "Miller, Dense proportions of zeros"
},
{
"url": "https://ems.press/content/serial-article-files/46974",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | What is the limiting behavior of $\Pr(\chi_\lambda(\mu)=0)$ for random irreducible characters and conjugacy classes of symmetric groups? | What can be said about the limiting behavior of Prob(χ\lambda (µ) = 0)? Example 2. If G = S4 , then 28 4 Prob(χ(g) = 0) = \approx 0.194 and Prob(χ(K) = 0) = = 0.16. 120 25 §1. It turns out that many characters have many zeros. The first result in this direction is for symmetric groups [3, Theorem 1]. Theorem 3. If χ \i... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,224 | OWR-11101920-011 | Optimal Lower Bounds for Character Proportions | What are the greatest lower bounds $\inf_G\theta(G)$ and $\inf_G\theta'(G)$ in the Thompson and Gallagher character-proportion bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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-11101920-011",
"literature-status:open",
"owr-year:2022"
] | The known universal lower bounds for the two character proportions are one third, with evidence toward one half, but the optimal lower bounds are not proved in general. | [
{
"url": "https://ems.press/content/serial-article-files/46974",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | What are the greatest lower bounds $\inf_G\theta(G)$ and $\inf_G\theta'(G)$ in the Thompson and Gallagher character-proportion bounds? | We ask in [6] if the Thompson and Gallagher lower bounds are the best possible. More specifically, we ask the following [6, Questions 1 and 2]. What are the greatest lower bounds inf G \theta(G) and inf G \theta′ (G)? The main conjecture of [6] is the following answer. The report passage is retained verbatim as the rel... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,225 | OWR-11101920-013 | Combinatorial Description of Plethysm Coefficients | Find a combinatorial description of the plethysm coefficients $a^\nu_{\lambda,\mu}$ in general. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-013",
"literature-status:open",
"owr-year:2022"
] | Plethysm has important formulas and special-case stability theorems, but the requested general combinatorial description remains an open problem. | [
{
"url": "https://arxiv.org/abs/2505.06104",
"label": "Paget--Wildon, two stability theorems"
},
{
"url": "https://arxiv.org/abs/2311.02721",
"label": "Bowman--Paget--Wildon, plethysm"
},
{
"url": "https://ems.press/content/serial-article-files/46975",
"label": "Oberwolfach Report 39... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | Find a combinatorial description of the plethysm coefficients $a^\nu_{\lambda,\mu}$ in general. | Plethysm is one of the most important operations on symmetric functions that is still not fully understood combinatorially: indeed, the question of finding a combi- natorial description of aν\lambda,µ in general is Problem 9 from Stanley’s 1999 survey of positivity problems in algebraic combinatorics [13]. A recursive ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,226 | OWR-11101920-014 | Stable Limits of Plethysm Multiplicities | What is the limit of $A_{\ell,m}(\nu,\lambda)$, and can the known stability results for plethysm multiplicities be generalized from $(m-1,1)$ to arbitrary partitions of $m$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,022 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-014",
"literature-status:partially-solved",
"owr-year:2022"
] | Eventual constancy of the displayed plethysm multiplicities is proved, but determining the limit, strict positivity, and the proposed generalization to arbitrary maximal tableaux remain open. | [
{
"url": "https://doi.org/10.1090/proc/16556",
"label": "Law--Okitani, Some stable plethysms"
},
{
"url": "https://arxiv.org/abs/2505.06104",
"label": "Paget--Wildon, two stability theorems"
},
{
"url": "https://ems.press/content/serial-article-files/46975",
"label": "Oberwolfach Rep... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | What is the limit of $A_{\ell,m}(\nu,\lambda)$, and can the known stability results for plethysm multiplicities be generalized from $(m-1,1)$ to arbitrary partitions of $m$? | What is the limit of Al,m (ν, \lambda)? Indeed, Wildon’s conjecture of the form of ν m−1,m \{j\} appears related to cer- j tain plethystic semistandard tableaux, as defined in [5], of shape (m − 1, 1)(1 ) of maximal weight. A question of Wildon from this workshop asks, could such sta- bility results be generalised furt... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,227 | OWR-11101920-015 | Weight Conjectures for Spetsial Reflection Groups | For a spetsial $\mathbb Z_\ell$-reflection group $W$, prove analogues of the Alperin weight conjecture and Robinson's ordinary weight conjecture that relate the unipotent principal-block invariants of $W$ to the fusion-system invariants of $\ell$-compact groups with Weyl group $W$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333](https://doi.org/10.4171/owr/2022/39)
## Literature review (checked 2026-08-22)
... | 3 | partially_solved | null | 2,022 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101920-015",
"literature-status:partially-solved",
"owr-year:2022"
] | The weight conjectures for l-compact groups and spetses are formulated and proved in significant special cases, but the general conjectures are not settled. | [
{
"url": "https://doi.org/10.24033/ASENS.2583",
"label": "Kessar--Malle--Semeraro, weight conjectures"
},
{
"url": "https://arxiv.org/abs/2008.07213",
"label": "Kessar--Malle--Semeraro, preprint"
},
{
"url": "https://ems.press/content/serial-article-files/46975",
"label": "Oberwolfac... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/39 | null | null | null | For a spetsial $\mathbb Z_\ell$-reflection group $W$, prove analogues of the Alperin weight conjecture and Robinson's ordinary weight conjecture that relate the unipotent principal-block invariants of $W$ to the fusion-system invariants of $\ell$-compact groups with Weyl group $W$. | Attached to a finite group G and a prime ℓ are various representation theoretic objects related to one another by deep and longstanding conjectures, like for ex- ample the Alperin weight conjecture. In our talk we described how to construct similarly looking objects starting out from a spetsial Zℓ -reflection group W b... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Character Theory and Categorification (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/39, pp. 2267--2333 |
30,005,228 | OWR-11101921-002 | Hermitian Volume Invariants for Plurisigned Metrics | For a plurisigned Hermitian metric $\omega$, is $v_+(\omega)$ always finite and is $v_-(\omega)$ always positive? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Complex Geometry and Dynamical Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/40, pp. 2335--2397](https://doi.org/10.4171/owr/2022/40)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101921-002",
"literature-status:open",
"owr-year:2022"
] | The finiteness of the positive volume invariant and positivity of the negative one are still identified as open outside restrictive hypotheses; later envelope results do not give the requested general resolution. | [
{
"url": "https://www.math.univ-toulouse.fr/~guedj/fichierspdf/TAMS22.pdf",
"label": "Angella--Guedj--Lu, Plurisigned Hermitian metrics"
},
{
"url": "https://arxiv.org/abs/2106.04272",
"label": "Darvas--Di Nezza--Lu, Monge--Ampere volumes"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/40 | null | null | null | For a plurisigned Hermitian metric $\omega$, is $v_+(\omega)$ always finite and is $v_-(\omega)$ always positive? | The latter conditions are however rather restrictive and it is an important open problem to decide whether v+ (\omega) (resp. v− (\omega)) is always finite (resp. positive). Plurisigned hermitian metrics Vincent Guedj (joint work with Daniele Angella, Hoang Chinh Lu) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Complex Geometry and Dynamical Systems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/40, pp. 2335--2397 |
30,005,229 | OWR-11101922-001 | High-Density Aperiodic Lorentz Gases | What is the behavior of an aperiodic Lorentz gas in the high-density regime? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-001",
"literature-status:open",
"owr-year:2022"
] | Results for periodic and finite-horizon Lorentz gases do not resolve the high-density aperiodic Lorentz gas problem; the requested general limiting behavior remains open. | [
{
"url": "https://www.aimsciences.org/article/doi/10.3934/dcds.2023057",
"label": "Treviño--Zelerowicz, aperiodic Lorentz gas"
},
{
"url": "https://ems.press/content/serial-article-files/46978",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | What is the behavior of an aperiodic Lorentz gas in the high-density regime? | On the contrary, understanding the aperiodic Lorentz gas, in the high density regime, is almost completely an open problem. Random Lorentz gas Carlangelo Liverani (joint work with Mark Demers) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,230 | OWR-11101922-002 | Planar Coexistence in Hostile-Environment First-Passage Percolation | Does coexistence occur for hostile-environment first-passage percolation in dimension $d=2$, and can one obtain a coexistence regime in any dimension when $p<p_c^{\mathrm{site}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-002",
"literature-status:open",
"owr-year:2022"
] | Coexistence in hostile-environment first-passage percolation is proved in dimensions at least three, while the planar case and the full low-density coexistence regime asked for here remain unresolved. | [
{
"url": "https://ems.press/journals/jems/articles/8736482",
"label": "Finn--Stauffer, hostile-environment first-passage percolation"
},
{
"url": "https://content.ems.press/assets/public/full-texts/serials/jems/no-issue/8736482/online-first/10.4171-jems-1309-online-first.pdf",
"label": "Finn--St... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | Does coexistence occur for hostile-environment first-passage percolation in dimension $d=2$, and can one obtain a coexistence regime in any dimension when $p<p_c^{\mathrm{site}}$? | It is an interesting open problem to establish whether coexistence occurs in d = 2, and to obtain a coexistence regime (in any dimension) for p < psitec . FPPHE has also been studied in hyperbolic and non-amenable graphs, where the results are shown to change drastically [3]. For example, in such graphs type 2 survives... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,231 | OWR-11101922-003 | Removing Monotonicity Assumptions in Interacting Particle Systems | Can the monotonicity assumptions used for the Ising and random-cluster interacting-particle-system results be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-003",
"literature-status:open",
"owr-year:2022"
] | The record is an unresolved open-questions fragment about essential monotonicity assumptions; subsequent work still treats the relevant hostile-environment models as non-monotone rather than supplying a general resolution. | [
{
"url": "https://kclpure.kcl.ac.uk/portal/en/publications/first-passage-percolation-in-hostile-environment-is-not-monotone-2",
"label": "Candellero--Stauffer, non-monotonicity"
},
{
"url": "https://doi.org/10.1002/rsa.21191",
"label": "Gheissari, random-cluster dynamics"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | Can the monotonicity assumptions used for the Ising and random-cluster interacting-particle-system results be removed? | Open questions In the above, we relied on the monotonicity of the Ising and random-cluster models quite strongly. 3. Critical random-cluster dynamics The random-cluster model is a model of dependent edge-percolation parametrized by (p, q), that at integer q is coupled to the Ising (q = 2) and more generally q-state Pot... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,232 | OWR-11101922-004 | Confining Potentials for Generalized Gibbs Ensembles | What is the precise class of confining potentials for which the generalized Gibbs ensemble has the desired infinite-volume behavior? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-004",
"literature-status:open",
"owr-year:2022"
] | Existing hydrodynamic treatments describe stationary states and special integrable regimes, but no precise general class of confining potentials for the Calogero-type generalized Gibbs ensemble was found. | [
{
"url": "https://doi.org/10.1088/1742-5468/ad3ccd",
"label": "Revised Enskog equation for hard rods"
},
{
"url": "https://ems.press/content/serial-article-files/46978",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | What is the precise class of confining potentials for which the generalized Gibbs ensemble has the desired infinite-volume behavior? | To under- stand the precise class of confining potentials is still an open problem. In the sense of hamiltonian systems the constant function is a trivial conservation law. But it must be included in a hydrodynamic context, since the particle density is a central physical observable. Having obtained the conserved field... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,233 | OWR-11101922-005 | Continuous-Time Extensions of Attractive Percolation Models | For finite-range continuous-time attractive spin systems, establish a critical-parameter dichotomy with positive survival probability above criticality and exponential decay below criticality, extending the corresponding discrete-time result and including the contact process. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-005",
"literature-status:open",
"owr-year:2022"
] | Partial bootstrap-percolation and attractive-PCA results are known, but the requested continuous-time extension and the full exponential tail bound remain open in the stated generality. | [
{
"url": "https://arxiv.org/abs/1806.11405",
"label": "Hartarsky, bootstrap percolation and attractive PCA"
},
{
"url": "https://ems.press/content/serial-article-files/46978",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | For finite-range continuous-time attractive spin systems, establish a critical-parameter dichotomy with positive survival probability above criticality and exponential decay below criticality, extending the corresponding discrete-time result and including the contact process. | Our setting of interest is slightly different, as we will work in discrete time, but it is an interesting open problem to extend our results to the continuous time setting, so as to include Theorem 1. 1. A classical example Let us start by recalling a classical result on the contact process. The latter is d a continuou... | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,234 | OWR-11101922-006 | Critical Tails and Cooperative Survival in Attractive Systems | Does the infection-time tail above criticality decay exponentially for bootstrap percolation in full generality, and what happens for attractive probabilistic cellular automata in the intermediate regime of cooperative survival but individual death? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-006",
"literature-status:open",
"owr-year:2022"
] | Exponential decay of the infection-time tail above criticality is not established for bootstrap percolation in full generality, and the intermediate cooperative-survival regime for attractive PCA remains open. | [
{
"url": "https://arxiv.org/abs/1806.11405",
"label": "Hartarsky, bootstrap percolation and attractive PCA"
},
{
"url": "https://ems.press/content/serial-article-files/46978",
"label": "Oberwolfach Report 39/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | Does the infection-time tail above criticality decay exponentially for bootstrap percolation in full generality, and what happens for attractive probabilistic cellular automata in the intermediate regime of cooperative survival but individual death? | It remains open to show the exponential decay of the tail of the infection time above criticality for bootstrap percolation in full generality. It is a wide open problem to study the behaviour of attractive PCA in the intermediate regime of cooperative survival, but individual death. where \leq holds pointwise. Let υ b... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,235 | OWR-11101922-007 | Bounded-Degree Sensitivity of Mixing Times | Can one construct uniformly quasi-isometric sequences of finite Cayley graphs $G_n,H_n$, both of uniformly bounded degree, such that
$$t_{\mathrm{mix}}(G_n)\geq\log\log\log|G_n|\,t_{\mathrm{mix}}(H_n)?$$
Can the factor $\log\log\log|G_n|$ be improved? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466](https://doi.org/10.4171/owr/2022/41)
## Literature review (checked 2026-08-22)
**Stat... | 3 | open | null | 2,022 | 3 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101922-007",
"literature-status:open",
"owr-year:2022"
] | The known Cayley-graph constructions produce sensitivity of mixing times, but the requested uniformly bounded-degree example and improvement of the iterated-logarithm factor are not resolved by the published result. | [
{
"url": "https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/sensitivity-of-mixing-times-of-cayley-graphs/0FDBD1D1ED671C875FB2DBB0DC7E905C",
"label": "Hermon--Kozma, sensitivity of mixing times"
},
{
"url": "https://www.cambridge.org/core/services/aop-cambridge-core/cont... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/41 | null | null | null | Can one construct uniformly quasi-isometric sequences of finite Cayley graphs $G_n,H_n$, both of uniformly bounded degree, such that
$$t_{\mathrm{mix}}(G_n)\geq\log\log\log|G_n|\,t_{\mathrm{mix}}(H_n)?$$
Can the factor $\log\log\log|G_n|$ be improved? | We concluded with two open problems. Is it possible to give such an example which, in addition, satisfies that the graphs Gn and Hn have uniformly bounded degrees? The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Large Scale Stochastic Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/41, pp. 2399--2466 |
30,005,236 | OWR-11101923-001 | Wave-Driven Surface Ocean Currents | How does wave-field evolution drive surface ocean currents? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/42, pp. 2467--2510](https://doi.org/10.4171/owr/2022/42)
## Literature rev... | 3 | open | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101923-001",
"literature-status:open",
"owr-year:2022"
] | Radiation stress, Stokes drift, Langmuir circulation, and phase-averaged models address important mechanisms, but a general two-way theory explaining how wave evolution drives surface currents remains open. | [
{
"url": "https://arxiv.org/abs/2602.21976",
"label": "A consistent phase-averaged model"
},
{
"url": "https://doi.org/10.1002/2016JC011768",
"label": "Mellor, wave-current interaction"
},
{
"url": "https://ems.press/content/serial-article-files/46979",
"label": "Oberwolfach Report 4... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/42 | null | null | null | How does wave-field evolution drive surface ocean currents? | How does wave field evolution drive surface ocean currents? In the context of atmosphere–ocean interaction the role played by wind waves is one of the key outstanding problems of obvious huge significance. It has been long known that wind waves and surface currents are intricately linked in many different ways. Histori... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/42, pp. 2467--2510 |
30,005,237 | OWR-11101923-002 | Land Heterogeneity and Monin–Obukhov Similarity Uncertainty | How much uncertainty in Monin–Obukhov similarity theory can be systematically attributed to local heterogeneity of the land surface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/42, pp. 2467--2510](https://doi.org/10.4171/owr/2022/42)
## Literature rev... | 3 | open | null | 2,022 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101923-002",
"literature-status:open",
"owr-year:2022"
] | The report poses the relation between MOST uncertainty and local land-surface heterogeneity as an important question; no general quantified resolution of that relation was identified. | [
{
"url": "https://doi.org/10.4171/owr/2022/42",
"label": "Oberwolfach Report 42/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/42 | null | null | null | How much uncertainty in Monin–Obukhov similarity theory can be systematically attributed to local heterogeneity of the land surface? | How much of the un- certainty of MOST, here attributed to the impact of sub-mesoscale motions and intermittency of turbulence, could actually be systematically related to local het- erogeneity of the land surface? Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean 2499 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/42, pp. 2467--2510 |
30,005,238 | OWR-11101924-001 | High-Frequency Helmholtz Green-Function Separability | Why is high frequency Helmholtz equation difficult to solve? Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems 2529 The minimum number of terms needed in a separable approximation for a Green’s function reveals the intrinsic complexity of the solution space of the underlying differential equatio... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | partially_solved | null | 2,022 | 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"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report presents separability bounds answering this rhetorical title and does not isolate an unresolved mathematical claim.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101924-001",
"literature-status:partially-solved",
"owr-year:2022"
] | High-frequency oscillation, pollution, indefiniteness, and Green-function separability explain the difficulty, with sharp bounds in important settings; a complete uniformly sharp theory for general heterogeneous problems is not established. | [
{
"url": "https://doi.org/10.4171/owr/2022/43",
"label": "Oberwolfach Report 43/2022"
},
{
"url": "https://doi.org/10.1002/cpa.21755",
"label": "Engquist--Zhao, CPAM 2018"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | null | Why is high frequency Helmholtz equation difficult to solve? Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems 2529 The minimum number of terms needed in a separable approximation for a Green’s function reveals the intrinsic complexity of the solution space of the underlying differential equatio... | unrecoverable | The official report presents separability bounds answering this rhetorical title and does not isolate an unresolved mathematical claim. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,239 | OWR-11101924-002 | Phase-Space Quantization for Variable-Coefficient PDEs | What about non-constant coefficient PDE? Can we then quantise any of the phase space maps to work on the level of operators? When working with constant coefficient PDE the Fourier transform has a num- ber of natural advantages. For example consider (1) P (D)u = 0 or P (D)u = small where P is a differential operator wit... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | partially_solved | null | 2,022 | 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",
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"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report immediately answers this question by a semiclassical Fourier-integral-operator construction, so it is not an open proble) | null | null | null | [
"owr",
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"OWR-11101924-002",
"literature-status:partially-solved",
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] | Semiclassical Fourier integral operators quantize the relevant maps locally when the characteristic set is a graph, but the fragment does not establish a construction for arbitrary variable-coefficient PDEs or global gluing. | [
{
"url": "https://doi.org/10.4171/owr/2022/43",
"label": "Oberwolfach Report 43/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | null | What about non-constant coefficient PDE? Can we then quantise any of the phase space maps to work on the level of operators? When working with constant coefficient PDE the Fourier transform has a num- ber of natural advantages. For example consider (1) P (D)u = 0 or P (D)u = small where P is a differential operator wit... | unrecoverable | The official report immediately answers this question by a semiclassical Fourier-integral-operator construction, so it is not an open problem. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,240 | OWR-11101924-003 | Rigorous Boundary-Layer Density Asymptotics | Prove that the asymptotic rate-of-convergence formulas derived for the slow densities $\eta_m$ along periodic multiple-scattering orbits describe the actual densities. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11101924-003",
"literature-status:open",
"owr-year:2022"
] | The source explicitly states that a completely rigorous proof connecting the asymptotic formulas to the actual densities eta_m remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/43",
"label": "Oberwolfach Report 43/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | Prove that the asymptotic rate-of-convergence formulas derived for the slow densities $\eta_m$ along periodic multiple-scattering orbits describe the actual densities. | Yet, a completely rigorous proof re- lating to the actual densities ηm remains as an open problem. for the Dirichlet boundary condition, and X slow ηm (x, k) \sim ap,q,r,ℓ,m (x, k) p,q,r\geq0 ℓ\leq−1 X 1+2p+3q+r+ℓ 1 = k− 3 +(ℓ+1)− bp,q,r,ℓ,m (x) (Ψr,ℓ )(p) (k 3 Zm (x)) p,q,r\geq0 ℓ\leq−1 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,241 | OWR-11101924-004 | Infinite Tails of Multiple-Scattering Series | Develop a collective method for computing exponentially many single-scattering returns and control the infinite tail of the multiple-scattering series even when that series diverges. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 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-11101924-004",
"literature-status:open",
"owr-year:2022"
] | The source leaves the collective computation of exponentially many scattering returns and the infinite tail unresolved, noting that the multiple-scattering series may diverge. | [
{
"url": "https://doi.org/10.4171/owr/2022/43",
"label": "Oberwolfach Report 43/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | Develop a collective method for computing exponentially many single-scattering returns and control the infinite tail of the multiple-scattering series even when that series diverges. | problem. While, perhaps, this issue can be resolved using the stabilization of mul- tiple scattering ray paths, computation of the remaining infinite tail in the multiple series scattering poses an additional difficulty since the series may actually diverge. The report passage is retained verbatim as the relevant conte... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,242 | OWR-11101924-005 | Resolved Helmholtz Degrees-of-Freedom Question | Is it enough ? Decompositions of high-frequency Helmholtz solutions and application to the finite element method David Lafontaine (joint work with Jeffrey Galkowski, Euan A. Spence, Jared Wunsch) Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems 2551 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | partially_solved | null | 2,022 | 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"
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"name": "L3: Advanced",
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"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 answers the degrees-of-freedom question and develops its extension; the extraction does not retain an open problem.) | null | null | null | [
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] | The degrees-of-freedom threshold is sufficient for hp-FEM under analytic-obstacle assumptions, while the cited results leave broader variable-coefficient and general-scattering settings conditional or incomplete. | [
{
"url": "https://doi.org/10.4171/owr/2022/43",
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{
"url": "https://doi.org/10.1090/S0025-5718-10-02362-8",
"label": "Melenk--Sauter, Mathematics of Computation"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | null | Is it enough ? Decompositions of high-frequency Helmholtz solutions and application to the finite element method David Lafontaine (joint work with Jeffrey Galkowski, Euan A. Spence, Jared Wunsch) Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems 2551 | unrecoverable | The official report answers the degrees-of-freedom question and develops its extension; the extraction does not retain an open problem. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,243 | OWR-11101924-007 | Diffractive High-Frequency Wave Propagation | What about the diffractive effects ? • (part of) a circular front of directly propagated singularities • a curved front of singularities re- flected off the obstacle in accordance with Snell’s law. An incoming (incident) ray that is tangent to the boundary splits into two branches: one branch goes along the shadow boun... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | partially_solved | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report treats this heading through sharp results and counterexamples rather than stating an unresolved mathematical problem.) | null | null | null | [
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{
"url": "https://doi.org/10.1016/j.crma.2017.05.011",
"label": "Ivanovici--Lebeau, Comptes Rendus Mathématique"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | null | What about the diffractive effects ? • (part of) a circular front of directly propagated singularities • a curved front of singularities re- flected off the obstacle in accordance with Snell’s law. An incoming (incident) ray that is tangent to the boundary splits into two branches: one branch goes along the shadow boun... | unrecoverable | The official report treats this heading through sharp results and counterexamples rather than stating an unresolved mathematical problem. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,244 | OWR-11101924-008 | Spectral Approximation of Discrete-Dipole Operators | For discrete-dipole matrices $T_{\kappa h}$, characterize and prove the observed convergence as $h\to0$ of isolated nonreal eigenvalues outside the real accumulation interval $[\Lambda_-,\Lambda_+]$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587](https://doi.org/10.4... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://doi.org/10.4171/owr/2022/43",
"label": "Oberwolfach Report 43/2022"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/43 | null | null | null | For discrete-dipole matrices $T_{\kappa h}$, characterize and prove the observed convergence as $h\to0$ of isolated nonreal eigenvalues outside the real accumulation interval $[\Lambda_-,\Lambda_+]$. | Open question From numerical computations of the eigenvalues of the matrices Tκh , one sees that apart from accumulation of eigenvalues around the real interval [Λ− , Λ+ ], there is a discrete set of non-real eigenvalues of the volume integral equation that seem to be well approximated as h \to 0, so that whereas DDA d... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/43, pp. 2511--2587 |
30,005,245 | OWR-11695854-001 | Workshop Contents Listing for Quantum Geometry and Character Varieties | Murad Alim (joint with L. Hollands, A. Saha, J. Teschner, I. Tulli) Non-perturbative quantum geometry, resurgence and BPS structures . . . 2635 Jennifer Brown (joint with David Jordan) Skein Theory and Quantizing Character Varieties . . . . . . . . . . . . . . . . . . . 2638 John Alexander Cruz Morales (joint with Maur... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658](https://doi.org/10.4171/owr/2022/45)
## Literature review ... | 3 | open | null | 2,022 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is) | null | null | null | [
"owr",
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"OWR-11695854-001",
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] | The extracted record is only a table-of-contents fragment and contains no identifiable mathematical claim whose truth or resolution can be checked. | [
{
"url": "https://doi.org/10.4171/owr/2022/45",
"label": "Oberwolfach Report 45/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/45 | null | null | null | null | Murad Alim (joint with L. Hollands, A. Saha, J. Teschner, I. Tulli) Non-perturbative quantum geometry, resurgence and BPS structures . . . 2635 Jennifer Brown (joint with David Jordan) Skein Theory and Quantizing Character Varieties . . . . . . . . . . . . . . . . . . . 2638 John Alexander Cruz Morales (joint with Maur... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a mathematical problem. No separate clean statement is promoted; the original record remains publicly visible and retained for provenance. | null | null | null | null | null | Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658 |
30,005,246 | OWR-11695854-002 | Mathematical Construction of the Negative-Phase Coulomb Category | For the $U(1)$ gauged linear sigma model with target $\mathbb P^n$ and stability parameter $\zeta<0$, construct mathematically the Coulomb-branch category $\mathcal C$ predicted by physics and prove the predicted equivalence $D^b(\mathbb P^n)\simeq\mathcal C$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658](https://doi.org/10.4171/owr/2022/45)
## Literature review ... | 3 | open | null | 2,022 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
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"slug": "physics",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695854-002",
"literature-status:open",
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] | For zeta less than zero the report describes a physical Coulomb-branch construction but explicitly says that the category C has no mathematical description, so the extracted question remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/45",
"label": "Oberwolfach Report 45/2022"
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{
"url": "https://arxiv.org/abs/1811.09235",
"label": "Cotti--Dubrovin--Guzzetti"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/45 | null | null | null | For the $U(1)$ gauged linear sigma model with target $\mathbb P^n$ and stability parameter $\zeta<0$, construct mathematically the Coulomb-branch category $\mathcal C$ predicted by physics and prove the predicted equivalence $D^b(\mathbb P^n)\simeq\mathcal C$. | What about ζ < 0?. 1There is a third part of the conjecture that relates the connection matrix of the quantum differential equation of X with some data coming from E, but we are not interested in this part of the conjecture for the moment | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658 |
30,005,247 | OWR-11695854-003 | Knots–Quivers Correspondence for All Knots | Does the knots–quivers correspondence hold for every knot, relating its colored HOMFLY–PT generating series $P(x,a,q)$ to the motivic generating series $P_C(x,q)$ of a corresponding quiver? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658](https://doi.org/10.4171/owr/2022/45)
## Literature review ... | 3 | partially_solved | null | 2,022 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695854-003",
"literature-status:partially-solved",
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] | The knots--quivers identity is proved for many families and examples, but current literature still describes the all-knots assertion as conjectural, especially beyond the exponential-growth setting. | [
{
"url": "https://doi.org/10.4171/owr/2022/45",
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"url": "https://arxiv.org/abs/1707.04017",
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"url": "https://doi.org/10.1007/s11005-025-02038-4",
"label": "Unlinking symmetric quivers, 2025... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/45 | null | null | null | Does the knots–quivers correspondence hold for every knot, relating its colored HOMFLY–PT generating series $P(x,a,q)$ to the motivic generating series $P_C(x,q)$ of a corresponding quiver? | The knots-quivers correspondence is the statement that for a given knot there exists a corresponding quiver, such that various invariants of the knot are expressed in terms of invariants of this quiver. In particular, the generating series of colored HOMFLY-PT polynomials P (x, a, q) is related to the motivic generatin... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Mini-Workshop: Quantization of Complex Symplectic Varieties (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/45, pp. 2629--2658 |
30,005,248 | OWR-11695855-001 | Local Complexity of Functional Estimation | For which functionals $\rho$ and distribution classes does the local minimax rate for estimating $\rho(P,P_0)$ depend strongly on $P_0$, and how do fuzzy-testing rates transition to functional-estimation rates as the null radius grows? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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] | The source explicitly says it is unknown whether the local dependence on P_0 seen in testing rates also occurs in functional estimation. | [
{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | For which functionals $\rho$ and distribution classes does the local minimax rate for estimating $\rho(P,P_0)$ depend strongly on $P_0$, and how do fuzzy-testing rates transition to functional-estimation rates as the null radius grows? | On the other hand, it is completely unknown if such effects arise in functional estimation (i.e. does the rate for estimating ρ(P, P0 ) depend strongly on P0 or not?). Breaking the sample complexity barrier in reinforcement learning Yuxin Chen | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,249 | OWR-11695855-002 | Neural Network Robustness under Adversarial and Distribution Shifts | Characterize the robustness of neural-network signal reconstruction under worst-case perturbations and distribution shifts. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | Characterize the robustness of neural-network signal reconstruction under worst-case perturbations and distribution shifts. | However, it is still an open problem to characterize the robustness of neural networks for signal reconstruction for worst-case and for distribution shifts. In this note, we describe open problems on the worst-case robustness and on charac- terizing the robustness with regard to distribution shifts. where expectation i... | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,250 | OWR-11695855-003 | Optimal Worst-Case Estimators for Signal Reconstruction | Characterize minimax-optimal estimators for broad signal and worst-case noise models. When are robust-optimization formulations equivalent to regularized estimation, and when is in-distribution risk $R_P(f)$ monotonically related to shifted-distribution risk $R_Q(f)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
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{
"url": "https://doi.org/10.4171/owr/2022/46",
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{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC12721873/",
"label": "Provably robust estimators for inverse problems"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | Characterize minimax-optimal estimators for broad signal and worst-case noise models. When are robust-optimization formulations equivalent to regularized estimation, and when is in-distribution risk $R_P(f)$ monotonically related to shifted-distribution risk $R_Q(f)$? | An important open problem is to characterize optimal worst-case estimators for different signal models and for different worst-case noise models. An interesting question is whether such relations between robust optimization and certain types of regularization also hold in more general setups. Mathematical Foundations o... | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,251 | OWR-11695855-004 | Sharp Universal Gaussian Mean-Estimation Constant | Determine the sharp constant in the universal deviation-minimax rate for Gaussian mean estimation over all pseudonorms. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"label": "Oberwolfach Report 46/2022"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | Determine the sharp constant in the universal deviation-minimax rate for Gaussian mean estimation over all pseudonorms. | 1In this work, we do not consider the important problem of getting sharp optimal constants. Universal property of the empirical mean. Let us first recall the universal estima- tion property satisfied by the empirical mean in the Gaussian model. Let S be a symetric set of Rd and denote by k\cdotkS : x \in Rd \to supv\in... | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,252 | OWR-11695855-005 | Universal Gaussian Mean Estimation under Adversarial Corruption | Are there estimators other than the empirical mean with the intended universal estimation property? Is the empirical mean's property explained by its being a sufficient statistic? Can universal estimation be extended beyond Gaussian samples, including to the $\varepsilon$-adversarial corruption model, and what is the l... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695855-005",
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] | The report states a Gaussian adversarial-corruption Tukey-median bound and proposes median-of-means extensions, but the broader universality questions beyond Gaussian data and across corruption levels remain open. | [
{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | Are there estimators other than the empirical mean with the intended universal estimation property? Is the empirical mean's property explained by its being a sufficient statistic? Can universal estimation be extended beyond Gaussian samples, including to the $\varepsilon$-adversarial corruption model, and what is the l... | a) is there any other estimator enjoying this univsersal estimation property? b) is this property satisfied by the empirical mean is due to the fact that the empirical mean is a sufficient statistics (and that it is somehow better than any other estimator)? c) is it possible to extend this result beyond the Gaussian ca... | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,253 | OWR-11695855-006 | Optimality of Monotonized Asymptotic Risk | For an estimator with deterministic asymptotic risk $R_{\mathrm{det}}(\gamma)$, characterize an optimality property of the monotonized risk $\gamma\mapsto\inf_{\zeta\geq\gamma}R_{\mathrm{det}}(\zeta)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "oberwolfach_reports_open_problems",
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695855-006",
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] | The source explicitly presents establishing any optimality principle for the monotonized risk as an open problem. | [
{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | For an estimator with deterministic asymptotic risk $R_{\mathrm{det}}(\gamma)$, characterize an optimality property of the monotonized risk $\gamma\mapsto\inf_{\zeta\geq\gamma}R_{\mathrm{det}}(\zeta)$. | An interesting open problem is that of establishing some form of optimality for the monotonized risk. The above function is a monotonically non-decreasing function of \gamma, regardless of whether \gamma 7\to Rdet (\gamma; fˆ) is non-monotonic. Furthermore, since min Rdet (ζ; fˆ) \leq Rdet (\gamma; fˆ), for all \gamma ... | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,254 | OWR-11695855-007 | Global Margin Maximization beyond the Neural Tangent Regime | Under what conditions does gradient descent globally optimize a maximum-margin objective for deep homogeneous networks, and when does it move beyond the neural-tangent regime to learn stronger representations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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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",
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{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | Under what conditions does gradient descent globally optimize a maximum-margin objective for deep homogeneous networks, and when does it move beyond the neural-tangent regime to learn stronger representations? | This family of open problems is concerned with low-norm deep networks in clas- sification settings where moreover the model is powerful enough to perfectly label the data. Margin maximization with shallow ReLU networks Matus Telgarsky (joint work with Ziwei Ji) | 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,255 | OWR-11695855-008 | Cancellation-Sensitive Norms for Two-Layer Networks | For a two-layer network with weights $(a,V)$, when can the squared parameter norm be replaced by the tighter product $\lVert a\rVert\lVert V\rVert$, and is there a still tighter cancellation-sensitive expression usable in gradient-descent and test-error bounds? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686](https://doi.org/10.4171/owr/2022/46)
## L... | 3 | open | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
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"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695855-008",
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] | The source labels the tighter norm and cancellation-aware NTK or near-initialization bounds as an open technical question; existing gradient-flow results do not settle it. | [
{
"url": "https://doi.org/10.4171/owr/2022/46",
"label": "Oberwolfach Report 46/2022"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/46 | null | null | null | For a two-layer network with weights $(a,V)$, when can the squared parameter norm be replaced by the tighter product $\lVert a\rVert\lVert V\rVert$, and is there a still tighter cancellation-sensitive expression usable in gradient-descent and test-error bounds? | To build towards a much more modest open problem, then, consider the Neu- ral Tangent Kernel or near initialization regime, where network weights are only allowed to move a constant distance from initialization as measured by Frobenius norm. The final question is a purely technical curiosity relating to the choice of 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 | Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/46, pp. 2659--2686 |
30,005,256 | OWR-11695856-001 | Mapping-Class-Invariant Parametrization of Hitchin Components | Construct a mapping-class-group-invariant parametrization of higher-rank Hitchin and maximal components that remains valid after nonuniqueness of equivariant conformal maps invalidates Labourie's parametrization. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Higher Rank Teichmüller Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/47, pp. 2687--2740](https://doi.org/10.4171/owr/2022/47)
## Literature review (checked... | 3 | partially_solved | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695856-001",
"literature-status:partially-solved",
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] | The construction is surjective and uniqueness holds in rank two, while later primary work gives non-uniqueness in rank at least three; the fragment therefore does not yield a general invariant parametrization. | [
{
"url": "https://doi.org/10.4171/owr/2022/47",
"label": "Oberwolfach Report 47/2022"
},
{
"url": "https://doi.org/10.4007/annals.2017.185.1.1",
"label": "Labourie, Annals of Mathematics"
},
{
"url": "https://annals.math.princeton.edu/articles/22504",
"label": "Sagman--Smillie, Annal... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/47 | null | null | null | Construct a mapping-class-group-invariant parametrization of higher-rank Hitchin and maximal components that remains valid after nonuniqueness of equivariant conformal maps invalidates Labourie's parametrization. | In order to understand how this conjecture is related to the problem of the Mod(S)-invariant parametrization of Hit(S), let us denote with E the holomorphic vector bundle on Teichmüller space whose fiber over a point J is L EJ = li=2 H 0 (Σ, K mi +1 ), where l is the rank of G 0 and (1, m2 , . . . , ml ) are its expon... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arbeitsgemeinschaft: Higher Rank Teichmüller Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/47, pp. 2687--2740 |
30,005,257 | OWR-11695858-001 | Invariance Principle for Reversible Random Conductance Walks | Can we still derive an invariance principle for the RWRE ? Let (e1 , . . . , ed ) be the canonical basis of Rd and E = \{e1 , . . . , ed , −e1 , \cdot \cdot \cdot − ed \}. On the grid Zd , we put random conductances: at each site x \in Zd , the conductance in direction e \in E is given by ae (x) with ae (x) in [b1 , b2... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantitative Stochastic Homogenization (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/48, pp. 2741--2809](https://doi.org/10.4171/owr/2022/48)
## Literature review ... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 19,
"name": "probability",
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"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
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"created_at": "2026-07-31T15:26:25.671Z"
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report answers the extracted question with an invariance-principle theorem and does not leave it as an open problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695858-001",
"literature-status:partially-solved",
"owr-year:2022"
] | An invariance principle is proved for the stated reversible, stationary, ergodic conductance environment using additive-functional limit theorems, but this is conditional on those hypotheses and is not a general theorem for unrestricted RWRE. | [
{
"url": "https://doi.org/10.4171/owr/2022/48",
"label": "Oberwolfach Report 48/2022"
},
{
"url": "https://doi.org/10.1007/BF01210789",
"label": "Kipnis--Varadhan"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/48 | null | null | null | null | Can we still derive an invariance principle for the RWRE ? Let (e1 , . . . , ed ) be the canonical basis of Rd and E = \{e1 , . . . , ed , −e1 , \cdot \cdot \cdot − ed \}. On the grid Zd , we put random conductances: at each site x \in Zd , the conductance in direction e \in E is given by ae (x) with ae (x) in [b1 , b2... | unrecoverable | The official report answers the extracted question with an invariance-principle theorem and does not leave it as an open problem. | null | null | null | null | null | Arbeitsgemeinschaft: Quantitative Stochastic Homogenization (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/48, pp. 2741--2809 |
30,005,258 | OWR-11695858-003 | Bourgain–Spencer Regularity Conjecture | If a stationary random conductivity field $A$ satisfies sufficiently strong mixing, prove that the symbol $\overline A$ of the averaged operator is almost $C^{2d}$ near the origin. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Quantitative Stochastic Homogenization (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/48, pp. 2741--2809](https://doi.org/10.4171/owr/2022/48)
## Literature review ... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
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"description": "Problems involving probability theory, stochastic processes, and random structures.",
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695858-003",
"literature-status:partially-solved",
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] | Perturbative results prove nearly C^{2d} regularity and non-perturbative work gives an intermediate nearly C^d result, but the general strong-mixing C^{2d} Bourgain--Spencer conjecture remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/48",
"label": "Oberwolfach Report 48/2022"
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{
"url": "https://doi.org/10.1016/j.matpur.2023.06.005",
"label": "Duerinckx, Journal de Mathematiques Pures et Appliquees"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/48 | null | null | null | If a stationary random conductivity field $A$ satisfies sufficiently strong mixing, prove that the symbol $\overline A$ of the averaged operator is almost $C^{2d}$ near the origin. | conjecture. Conjecture (Bourgain–Spencer). If A satisfies strong enough mixing conditions, then the symbol Ā is of class (almost) C 2d in a neighborhood of 0. The rest of this note is devoted to a brief description of Bourgain’s perturbative argument. As in [1, 5], we focus on the discrete iid setting for simplicity (... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Arbeitsgemeinschaft: Quantitative Stochastic Homogenization (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/48, pp. 2741--2809 |
30,005,259 | OWR-11695859-002 | Limit Theorems for Object Data on Metric Spaces | For object-valued data in a metric measure space, define an appropriate notion of mean and determine conditions under which its empirical version satisfies a law of large numbers and a central limit theorem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893](https://doi.org/10.4171/owr/2022/49)
## Literature revi... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
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"created_at": "2026-07-31T15:26:25.671Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695859-002",
"literature-status:partially-solved",
"owr-year:2022"
] | The Oberwolfach source reports partial answers to the law of large numbers and central limit questions, but no general theorem settling the extracted problem. | [
{
"url": "https://ems.press/content/serial-article-files/46987",
"label": "Oberwolfach Report 49"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/49 | null | null | null | For object-valued data in a metric measure space, define an appropriate notion of mean and determine conditions under which its empirical version satisfies a law of large numbers and a central limit theorem. | Does it fulfill a law of large number? What about the central limit theorem? Object data analysis – statistics on metric spaces Thomas Hotz Gromov-Wasserstein Distances, Distance Distributions and Inverse Problems for Metric Measure Spaces Tom Needham (joint work with Facundo Mémoli) | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893 |
30,005,260 | OWR-11695859-003 | Removing Curvature Restrictions from Metric Measure Reconstruction | Can the curvature restrictions in the metric-measure reconstruction theorem be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893](https://doi.org/10.4171/owr/2022/49)
## Literature revi... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"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-11695859-003",
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{
"url": "https://ems.press/content/serial-article-files/46987",
"label": "Oberwolfach Report 49"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/49 | null | null | null | Can the curvature restrictions in the metric-measure reconstruction theorem be removed? | A natural question is whether these pseudometrics are true metrics on some subclass of isomorphism classes of mm-spaces. We now describe a few of these results, coming from [6], and pose some related open questions. Can the curvature restrictions in Theorem 2 be removed? Heat Kernels, Stochastic Processes and Functiona... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893 |
30,005,261 | OWR-11695859-004 | Removing Contractibility from Metric Measure Reconstruction | Can the contractibility assumption in the metric-measure reconstruction theorem be removed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893](https://doi.org/10.4171/owr/2022/49)
## Literature revi... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695859-004",
"literature-status:open",
"owr-year:2022"
] | Removing contractibility from Theorem 3 is presented as a conjectural extension, and the source gives no proof or counterexample. | [
{
"url": "https://ems.press/content/serial-article-files/46987",
"label": "Oberwolfach Report 49"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/49 | null | null | null | Can the contractibility assumption in the metric-measure reconstruction theorem be removed? | Can the contractibility assumption be removed from Theorem 3? We end with one more open question. We conjecture that the answer is “yes”, based on numerical and heuristic argu- ments. The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893 |
30,005,262 | OWR-11695859-005 | Classifying Globally Lipschitz Transport Settings | In which additional settings is the transport map globally Lipschitz? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893](https://doi.org/10.4171/owr/2022/49)
## Literature revi... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695859-005",
"literature-status:open",
"owr-year:2022"
] | The source poses the search for further settings with globally Lipschitz maps as a natural question and does not give a general classification. | [
{
"url": "https://ems.press/content/serial-article-files/46987",
"label": "Oberwolfach Report 49"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/49 | null | null | null | In which additional settings is the transport map globally Lipschitz? | A natural question is to find other settings where the map is globally Lipschitz, and some further results have been obtained, for example [2]. Globally Lipschitz transport maps Max Fathi (joint work with Dan Mikulincer, Yair Shenfeld) Heat Kernels, Stochastic Processes and Functional Inequalities 2845 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893 |
30,005,263 | OWR-11695859-006 | Dimension-Free Lipschitz Optimal Transport Maps | Is the quadratic optimal-transport map from $\gamma$ onto $\mu$ globally Lipschitz, with Lipschitz norm depending only on $\|f\|_{\mathrm{Lip}}$ and not on the dimension $n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893](https://doi.org/10.4171/owr/2022/49)
## Literature revi... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695859-006",
"literature-status:open",
"owr-year:2022"
] | The dimension-free Lipschitz conjecture for the quadratic optimal transport map remains unproved; only a dimension-free nonoptimal transport map is established. | [
{
"url": "https://ems.press/content/serial-article-files/46987",
"label": "Oberwolfach Report 49"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/49 | null | null | null | Is the quadratic optimal-transport map from $\gamma$ onto $\mu$ globally Lipschitz, with Lipschitz norm depending only on $\|f\|_{\mathrm{Lip}}$ and not on the dimension $n$? | Is the quadratic optimal transport map from \gamma onto µ globally Lipschitz, with a Lipschitz norm that depends only on ||f ||lip , and not on n? Heat Kernels, Stochastic Processes and Functional Inequalities 2845 This conjecture is motivated by the fact that if we linearize around small pertur- bations of \gamma the ... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/49, pp. 2811--2893 |
30,005,264 | OWR-11695860-001 | Gaussian-Prime Paths with Bounded Steps | Does there exist an infinite path through the Gaussian primes whose successive Euclidean step lengths are bounded by an absolute constant? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-001",
"literature-status:open",
"owr-year:2022"
] | The primitive-set conjecture component is proved, but the Gaussian moat bounded-step question in the same extracted record remains unresolved despite partial progress. | [
{
"url": "https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/proof-of-the-erdos-primitive-set-conjecture/7D838547DEF207B0442E6DCB8BBAA657",
"label": "Lichtman"
},
{
"url": "https://doi.org/10.1080/00029890.2007.11920399",
"label": "Loh"
},
{
"url": "https://ems.press... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Does there exist an infinite path through the Gaussian primes whose successive Euclidean step lengths are bounded by an absolute constant? | In a sensational piece of work, Lichtman presented a proof of a famous open conjecture of Erdős on primitive sets. Merikoski showcased joint work with Maynard on a well known open question of Gordon from 1962 which asks if it is possible to walk to infinity in the complex plane with bounded steps by using Gaussian prim... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,265 | OWR-11695860-002 | Vinogradov-Type Bounds for Large-Order Dirichlet Characters | For primitive characters $\chi$ modulo primes $q$ whose orders tend to infinity, find general conditions ensuring that the least $n$ with $\chi(n)\notin\{0,1\}$ is $O_\epsilon(q^\epsilon)$ and that $\chi$ takes varied values below $q^\epsilon$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-002",
"literature-status:open",
"owr-year:2022"
] | The cited work proves substantial large-order character estimates, but the extracted analogue of Vinogradov's conjectural problem is not settled in general. | [
{
"url": "https://doi.org/10.1112/jlms.12841",
"label": "Mangerel"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For primitive characters $\chi$ modulo primes $q$ whose orders tend to infinity, find general conditions ensuring that the least $n$ with $\chi(n)\notin\{0,1\}$ is $O_\epsilon(q^\epsilon)$ and that $\chi$ takes varied values below $q^\epsilon$. | Mangerel Large order Dirichlet characters and an analogue of a conjecture of Vinogradov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The report passage is retained verbatim as the relevant context for this extracted problem. | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,266 | OWR-11695860-003 | Bateman–Horn Asymptotics for Prime Polynomial Values | For an irreducible integer polynomial $f$ of degree at least two, establish the Bateman–Horn asymptotic for $\sum_{n\leq x}\Lambda(f(n))$, including fixed polynomials such as $f(t)=t^2+1$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-003",
"literature-status:open",
"owr-year:2022"
] | Prime values of even the fixed polynomial t squared plus one remain out of reach, so the broader polynomial-prime question is open. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For an irreducible integer polynomial $f$ of degree at least two, establish the Bateman–Horn asymptotic for $\sum_{n\leq x}\Lambda(f(n))$, including fixed polynomials such as $f(t)=t^2+1$. | For the von Mangoldt function Λ, this encodes the fundamental question of when polynomials capture their primes. Bateman-Horn, Chowla and the integral Hasse principle for random polynomials Tim Browning (joint work with Efthymios Sofos, Joni Teräväinen) parameterising polynomials fc (t) = c0 td + \cdot \cdot \cdot + ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,267 | OWR-11695860-004 | Infinitely Many Prime Values of Integer Polynomials | Let $P\in\mathbb Z[X]$ be irreducible of degree at least two with no fixed prime divisor. Prove that $P(n)$ is prime for infinitely many integers $n$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-004",
"literature-status:open",
"owr-year:2022"
] | For irreducible polynomials of degree at least two with no fixed prime divisor, infinitude of prime values is still not known in general. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Let $P\in\mathbb Z[X]$ be irreducible of degree at least two with no fixed prime divisor. Prove that $P(n)$ is prime for infinitely many integers $n$. | Are there infin- itely many integers n such that P (n) is a prime number? On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases Cécile Dartyge (joint work with James Maynard) The best general result was obtained by Tenenbaum [6] who proved that if f (X) \in Z[X] is irreducible with deg... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,268 | OWR-11695860-005 | Optimal Gaps Between Binary Quadratic-Form Values | Determine the optimal order of the largest gaps between consecutive positive integers represented by a fixed primitive positive-definite binary quadratic form. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-005",
"literature-status:partially-solved",
"owr-year:2022"
] | Published work gives strong lower bounds for long gaps between represented integers, but the full gap behavior, especially short gaps, remains open. | [
{
"url": "https://doi.org/10.1093/imrn/rnac130",
"label": "Dietmann, Elsholtz, and Shparlinski"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Determine the optimal order of the largest gaps between consecutive positive integers represented by a fixed primitive positive-definite binary quadratic form. | A natural question is the behaviour of the gaps sn+1 − sn , in particular regarding short and longs gaps. Longer gaps between values of binary quadratic forms Rainer Dietmann (joint work with Christian Elsholtz, Alexander Kalmynin, Sergei Konyagin and James Maynard) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,269 | OWR-11695860-006 | Gonek’s Conjecture on Shifted Negative Zeta Moments | For fixed $k>0$, determine the uniform asymptotic order of $I_{-k}(\alpha,T)=T^{-1}\int_T^{2T}|\zeta(\tfrac12+\alpha+it)|^{-2k}\,dt$ throughout $0<\alpha\leq1$, including every transition regime near $\alpha=1/\log T$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-006",
"literature-status:partially-solved",
"owr-year:2022"
] | The negative-moment problem for the zeta function has been settled in restricted ranges, but the full Gonek conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2302.07226",
"label": "Bui and Florea"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For fixed $k>0$, determine the uniform asymptotic order of $I_{-k}(\alpha,T)=T^{-1}\int_T^{2T}|\zeta(\tfrac12+\alpha+it)|^{-2k}\,dt$ throughout $0<\alpha\leq1$, including every transition regime near $\alpha=1/\log T$. | A conjecture of Gonek [3] predicts the size of the negative moments in different ranges. Negative moments of the Riemann zeta-function Alexandra Florea (joint work with Hung Bui) | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,270 | OWR-11695860-007 | Fractional Moments of Möbius Character and Archimedean Twists | For $0\leq q\leq1$ and fixed $A>0$, prove $\frac1{r-1}\sum_{\chi\bmod r}|\sum_{n\leq x}\mu(n)\chi(n)|^{2q}\ll(\frac{x}{1+(1-q)\sqrt{\log\log x}})^q$ for $x\leq r^A$, and $\frac1{2T}\int_{-T}^T|\sum_{n\leq x}\mu(n)n^{it}|^{2q}\,dt\ll(\frac{x}{1+(1-q)\sqrt{\log\log x}})^q$ for $x\leq T^A$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-007",
"literature-status:partially-solved",
"owr-year:2022"
] | Harper proves related upper bounds for shorter character and multiplicative sums, but the conjectured bounds in the full extracted ranges remain unproved. | [
{
"url": "https://arxiv.org/abs/2301.04390",
"label": "Harper"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For $0\leq q\leq1$ and fixed $A>0$, prove $\frac1{r-1}\sum_{\chi\bmod r}|\sum_{n\leq x}\mu(n)\chi(n)|^{2q}\ll(\frac{x}{1+(1-q)\sqrt{\log\log x}})^q$ for $x\leq r^A$, and $\frac1{2T}\int_{-T}^T|\sum_{n\leq x}\mu(n)n^{it}|^{2q}\,dt\ll(\frac{x}{1+(1-q)\sqrt{\log\log x}})^q$ for $x\leq T^A$. | In particular, I conjecture that for any 0 \leq q \leq 1 and any fixed A > 0, we should have 1 X X x | µ(n)χ(n)|2q ≪ ( \sqrt{ } )q \forall x \leq rA , r−1 1 + (1 − q) log log x χ mod r n\leqx and Z T X 1 x (1) | µ(n)nit |2q dt ≪ ( \sqrt{ } )q \forall x \leq T A . 2T −T 1 + (1 − q) log log x n\leqx | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,271 | OWR-11695860-008 | Square-Root-Scale Cancellation in Short Möbius Sums | Prove cancellation in $\sum_{x<n\leq x+y}\mu(n)$ for intervals of length $y$ at the square-root scale or below. A concrete range arising from the proposed fractional-moment bound is $\sqrt{x}/(\log\log x)^{1/4}\ll y\leq x^{1-\epsilon}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-008",
"literature-status:partially-solved",
"owr-year:2022"
] | Guth and Maynard improve the relevant prime-interval exponent to 17 over 30 up to lower-order terms, but the square-root interval barrier is not reached. | [
{
"url": "https://doi.org/10.4007/annals.2026.203.2.6",
"label": "Guth and Maynard"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Prove cancellation in $\sum_{x<n\leq x+y}\mu(n)$ for intervals of length $y$ at the square-root scale or below. A concrete range arising from the proposed fractional-moment bound is $\sqrt{x}/(\log\log x)^{1/4}\ll y\leq x^{1-\epsilon}$. | It is a major open problem to go below, or even to reach, the squareroot interval barrier in problems of this kind. Whilst I do not know how to prove this conjecture, it seems plausibly attackable (at least assuming standard conjectures like the Riemann Hypothesis), and if true it would have significant arithmetic conse... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,272 | OWR-11695860-011 | Cancellation in Twisted-Multiplicative Exponential Sums | For $W_f(a;q)=q^{-1/2}\sum_{x\bmod q}e(af(x)/q)$, develop methods for estimating $\sum_{q\leq x}W_f(a;q)$ without replacing each summand by its absolute value. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-011",
"literature-status:open",
"owr-year:2022"
] | The cited theory supplies upper bounds for twisted-multiplicative sums, but a general modulus-free method and the requested lower bounds are not known. | [
{
"url": "https://doi.org/10.1007/978-3-031-05331-3_13",
"label": "Kowalski and Soundararajan"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For $W_f(a;q)=q^{-1/2}\sum_{x\bmod q}e(af(x)/q)$, develop methods for estimating $\sum_{q\leq x}W_f(a;q)$ without replacing each summand by its absolute value. | Problem 1. Find other methods to estimate sums of twisted-multiplicative func- tions, without modulus. Problem 2. Obtain lower-bounds for the same quantities (with modulus). Remark. Estimates for sums of this kind were obtained by Hooley [1964] for Kloosterman sums (f = X + X −1 ) and generalized by Fouvry and Michel [... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,273 | OWR-11695860-012 | Lower Bounds for Twisted-Multiplicative Exponential Sums | For $W_f(a;q)=q^{-1/2}\sum_{x\bmod q}e(af(x)/q)$, obtain lower bounds of the same order as the best available upper estimates for $\sum_{q\leq x}|W_f(a;q)|$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-012",
"literature-status:open",
"owr-year:2022"
] | No general lower bounds matching the extracted twisted-multiplicative upper-bound problem are established in the cited primary literature. | [
{
"url": "https://doi.org/10.1007/978-3-031-05331-3_13",
"label": "Kowalski and Soundararajan"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For $W_f(a;q)=q^{-1/2}\sum_{x\bmod q}e(af(x)/q)$, obtain lower bounds of the same order as the best available upper estimates for $\sum_{q\leq x}|W_f(a;q)|$. | Problem 2. Obtain lower-bounds for the same quantities (with modulus). Remark. Estimates for sums of this kind were obtained by Hooley [1964] for Kloosterman sums (f = X + X −1 ) and generalized by Fouvry and Michel [2003] for “generic” rational functions. However, for the bound (2), they obtained an upper bound of siz... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,274 | OWR-11695860-013 | Elementary Fourth-Moment Bounds for Cubic Exponential Sums | For $f(X)=X^3+X$, prove by methods no deeper than Chebotarev density that the normalized fourth moment of $W_f(a;p)$ either tends to $2$ or is at least $3+O(p^{-1/2})$ on a positive-density set of primes. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-013",
"literature-status:open",
"owr-year:2022"
] | The source asks for elementary proofs of special cases of its fourth-moment theorem, and no such proof settling the extracted problem was identified. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | For $f(X)=X^3+X$, prove by methods no deeper than Chebotarev density that the normalized fourth moment of $W_f(a;p)$ either tends to $2$ or is at least $3+O(p^{-1/2})$ on a positive-density set of primes. | Can one prove special cases of Theorem 2 (say for f = X 3 +X) using more elementary means? (E.g., not beyond the Chebotarev Density Theorem.) Remark. or there exists \delta > 0 depending only on d and a set of primes of natural density \geq \delta such that for such primes, we have 1 X |Wf (a; p)|4 \geq 3 + O(p−1/2 ). ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,275 | OWR-11695860-014 | Recovering Polynomials from Fourier-Magnitude Data | Let $f$ and $g$ be polynomials satisfying $|W_f(a;p)|=|W_g(a;p)|$ for every $a$ coprime to one large prime $p$, or for all sufficiently large primes. Determine the algebraic relationship between $f$ and $g$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-014",
"literature-status:partially-solved",
"owr-year:2022"
] | A relation theorem is proved under restrictive Sidon and Morse hypotheses, while the extracted general question remains unresolved. | [
{
"url": "https://doi.org/10.1007/978-3-031-05331-3_13",
"label": "Kowalski and Soundararajan"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Let $f$ and $g$ be polynomials satisfying $|W_f(a;p)|=|W_g(a;p)|$ for every $a$ coprime to one large prime $p$, or for all sufficiently large primes. Determine the algebraic relationship between $f$ and $g$. | What are the relations, if any, between f and g? are probability measures on Fp , and this condition is equivalent to Wf (a; p) = Wg (a; p) for all a. Davenport’s question asks about relations between f and g if only the support of the measures is remembered, while Problem 4 asks for relations if the phase of the discr... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,276 | OWR-11695860-016 | Density Hypothesis for Riemann-Zeta Zeros | Let $N(\sigma,T)$ count zeros $\rho$ of $\zeta$ with $\operatorname{Re}\rho\geq\sigma$ and $0\leq\operatorname{Im}\rho\leq T$. Prove $N(\sigma,T)<T^{2-2\sigma+o(1)}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** par... | 3 | partially_solved | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695860-016",
"literature-status:partially-solved",
"owr-year:2022"
] | The density estimate has been substantially improved by Guth and Maynard, but their exponent does not prove the full Density Hypothesis. | [
{
"url": "https://doi.org/10.4007/annals.2026.203.2.6",
"label": "Guth and Maynard"
},
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Let $N(\sigma,T)$ count zeros $\rho$ of $\zeta$ with $\operatorname{Re}\rho\geq\sigma$ and $0\leq\operatorname{Im}\rho\leq T$. Prove $N(\sigma,T)<T^{2-2\sigma+o(1)}$. | conjecture. Conjecture 1 (Density Hypothesis). For any \sigma, T > 0 we have N (\sigma, T ) < T 2−2\sigma+o(1) . For many applications, the Density Hypothesis would give results which are comparably strong to the Riemann Hypothesis. Unconditionally Huxley [1] showed that N (\sigma, T ) \leq T (12−12\sigma)/5+o(1) , whi... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,277 | OWR-11695860-017 | Zero–One Laws in Simultaneous Diophantine Approximation | Let $f:\mathbb R^d\to\mathbb R^m$, put $n=d+m$ and $\alpha_{d+j}=f_j(\alpha_1,\ldots,\alpha_d)$, and let $A(h)$ consist of points admitting denominators $q_j\leq h$ with $\|q_j\alpha_j\|\leq\psi(h)$. Under suitable nondegeneracy assumptions on $f$, prove that the limsup $A^*$ has measure zero or full measure according ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-017",
"literature-status:open",
"owr-year:2022"
] | The proposed zero-one law for simultaneous approximation with separate denominators is stated as an open problem, with no later resolution identified. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Let $f:\mathbb R^d\to\mathbb R^m$, put $n=d+m$ and $\alpha_{d+j}=f_j(\alpha_1,\ldots,\alpha_d)$, and let $A(h)$ consist of points admitting denominators $q_j\leq h$ with $\|q_j\alpha_j\|\leq\psi(h)$. Under suitable nondegeneracy assumptions on $f$, prove that the limsup $A^*$ has measure zero or full measure according ... | Is it true that, with suitable “non-degeneracy” conditions on the f that there is a 0 - 1 law, namely A∗ contains almost no, or almost all (\alpha1 , . . . , \alphad ) in Rd according as \infty X hn−1 \psi(h) h=1 achieved the above by appealing to Plancherel’s identity to show that Z \infty X 2 Z \infty sin \pi\deltat ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,278 | OWR-11695860-018 | Degree-Five Two-Superirreducible Polynomials | Does there exist $f\in\mathbb Z[x]$ of degree five such that $f(g(x))$ is irreducible for every $g\in\mathbb Z[x]$ of degree at most two? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695860-018",
"literature-status:open",
"owr-year:2022"
] | The integral degree-five two-superirreducibility question remains unresolved; recent work addresses finite-field analogues rather than this integer-polynomial problem. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
},
{
"url": "https://doi.org/10.1016/j.indag.2024.08.005",
"label": "Bober, Du, Fretwell, Kopp, and Wooley"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Does there exist $f\in\mathbb Z[x]$ of degree five such that $f(g(x))$ is irreducible for every $g\in\mathbb Z[x]$ of degree at most two? | Question: Does there exist a polynomial of degree 5 that is 2-superirreducible? (This is a question of J. for almost all \alpha2 , for some \tau > 0. 8. \sqrt{ } (proposed by Trevor Wooley) Apéry showed that ζ(3) \in / Q. Show ζ(3) \in \sqrt{ } that / Q 2 . Alternatively find a nonsquare d > 0 such that ζ(3) \in / Q d ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,279 | OWR-11695860-019 | Six Problems from an Analytic Number Theory Session | Resolve the following six problems: (1) construct a degree-five $2$-superirreducible polynomial; (2) for each finite abelian group $G$, optimize $n$ and $d$ in a representation $G\cong\{z^d:z\in(\mathbb Z/n\mathbb Z)^\times\}$; (3) find homogeneous forms $f$ and $g$ of degrees $3$ and $2$ in five variables with $f^2+g^... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960](https://doi.org/10.4171/owr/2022/50)
## Literature review (checked 2026-08-22)
**Status:** ope... | 3 | open | null | 2,022 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 literature review, 2026-09-29] . Sub-question 11 (J. Merikoski) asks whether f² + g³ can be an incomplete sextic norm form in five variables. | [
"owr",
"oberwolfach-reports",
"OWR-11695860-019",
"literature-status:open",
"owr-year:2022"
] | This extracted fragment contains several separate research questions, including unresolved covering, prime-pattern, and quaternionic Weyl-sum problems; the combined record is therefore open. | [
{
"url": "https://ems.press/content/serial-article-files/46986",
"label": "Oberwolfach Report 50"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/50 | null | null | null | Resolve the following six problems: (1) construct a degree-five $2$-superirreducible polynomial; (2) for each finite abelian group $G$, optimize $n$ and $d$ in a representation $G\cong\{z^d:z\in(\mathbb Z/n\mathbb Z)^\times\}$; (3) find homogeneous forms $f$ and $g$ of degrees $3$ and $2$ in five variables with $f^2+g^... | 12. (proposed by Ben Green) Cover the integers \{1, 2, . . . , N \} by residue classes ap (mod p), one residue class per prime. (1) Can you cover each number twice (meaning at least 2 times each), using only primes p \leq N ? (This Pwas asked by Erdős.) (2) Can you do it with p 1/p \leq K ? (This has been considered b... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Analytic Number Theory (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/50, pp. 2895--2960 |
30,005,280 | OWR-11695861-001 | Onsager Thresholds for Hydrostatic Euler Energy Conservation | Determine the critical anisotropic regularity thresholds above which weak solutions of the hydrostatic Euler equations conserve horizontal kinetic energy and below which anomalous dissipation can occur. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mathematical Advances in Geophysical Fluid Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/51, pp. 2961--3003](https://doi.org/10.4171/owr/2022/51)
## Literature review (checked... | 3 | open | null | 2,022 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"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-11695861-001",
"literature-status:open",
"owr-year:2022"
] | The extracted record is only a report table-of-contents fragment and does not identify a definite conjecture or proposition; its mathematical claim is therefore unclear and is classified as open. | [
{
"url": "https://doi.org/10.4171/owr/2022/51",
"label": "EMS Press, OWR 2022/51"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/51 | null | null | null | Determine the critical anisotropic regularity thresholds above which weak solutions of the hydrostatic Euler equations conserve horizontal kinetic energy and below which anomalous dissipation can occur. | conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2983 Felix Brandt (joint with T. Binz, K. Disser, R. Haller and M. Hieber) Hibler’s viscous-plastic sea ice model: rigorous analysis, time periodic solutions and interaction with a rigid body . . . . . . . . . . . . . . . .... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Mathematical Advances in Geophysical Fluid Dynamics (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/51, pp. 2961--3003 |
30,005,281 | OWR-11695862-001 | O-Minimality Workshop Table-of-Contents Fragment | problem . . . . . . . . . . . . . . . . . . . . . 3014 Françoise Point Definable groups in tame theories of differential topological fields . . . . . . 3017 Antongiulio Fornasiero Generic derivations on topological fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3020 Alexander Berenstein (joint with C... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 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"
} | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report confirms that the extraction is a table-of-contents fragment, not a standalone open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695862-001",
"literature-status:open",
"owr-year:2022"
] | The extracted text is a table-of-contents fragment listing talks rather than a complete problem statement, so no definite claim can be assessed; under the queue rule it remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | null | problem . . . . . . . . . . . . . . . . . . . . . 3014 Françoise Point Definable groups in tame theories of differential topological fields . . . . . . 3017 Antongiulio Fornasiero Generic derivations on topological fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3020 Alexander Berenstein (joint with C... | unrecoverable | The official report confirms that the extraction is a table-of-contents fragment, not a standalone open mathematical problem. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,282 | OWR-11695862-003 | Noiseless Open Cores and Tame Real-Field Expansions | Prove that every expansion of the real field that does not define $\mathbb Z$ has a noiseless open core, and classify such expansions under a common notion of tameness. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-003",
"literature-status:open",
"owr-year:2022"
] | The record combines a set-theoretic measurability fact with broad research questions about noiseless open cores and classification of expansions; the main classification conjectures remain unresolved. | [
{
"url": "https://www.sciencedirect.com/science/article/pii/S0168007217301197",
"label": "Hieronymi--Walsberg, Wild theories with o-minimal open core"
},
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Prove that every expansion of the real field that does not define $\mathbb Z$ has a noiseless open core, and classify such expansions under a common notion of tameness. | The question whether every set definable in (R, Z) is Lebesgue measurable, is independent of ZFC. The most ambitions conjecture is that the open core4 of such a structure is noiseless. Can we classify expansions of R that do not define Z, up to some common notion of tameness? Topological and Differential Expansions of ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,283 | OWR-11695862-004 | Borovik–Cherlin Generic-Transitivity Conjecture | Let a group $G$ of finite Morley rank act definably and generically $k$-transitively on $X$. Prove $k\leq\operatorname{RM}(X)+2$, with equality only when the action is definably isomorphic to $\operatorname{PGL}_n$ acting on $\mathbb P^{n-1}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | partially_solved | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-004",
"literature-status:partially-solved",
"owr-year:2022"
] | The Borovik--Cherlin generic-transitivity bound and rigidity conjectures are proved in important special cases, including algebraic-group settings, while the general finite-Morley-rank statement continues to have active partial results. | [
{
"url": "https://arxiv.org/abs/2407.09636",
"label": "Borovik--Nesin--Wagner, Bounding generic sharp transitivity"
},
{
"url": "https://doi.org/10.1112/jlms/jdm088",
"label": "Borovik--Burdges, J. London Math. Soc."
},
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Pr... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Let a group $G$ of finite Morley rank act definably and generically $k$-transitively on $X$. Prove $k\leq\operatorname{RM}(X)+2$, with equality only when the action is definably isomorphic to $\operatorname{PGL}_n$ acting on $\mathbb P^{n-1}$. | conjecture. Additionally, the existence of some bound depending only on the rank of the type p, rather than the type itself was shown to follow from work of Borovik and Cherlin [1]. The Borovik-Cherlin conjecture was verified for algebraic groups of characteristic zero, and the case was shown to be sufficient to obtain... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,284 | OWR-11695862-005 | Forking Degree and Generic Transitivity | Control $\alpha$-forking degree for arbitrary ordinals via Borovik–Cherlin-type bounds; find model-theoretic applications of generalized generic transitivity; extend Borovik–Cherlin theory to supersimple groups and Kolchin polynomials; and relate definable primitivity of binding groups to geometric stability, different... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695862-005",
"literature-status:open",
"owr-year:2022"
] | The listed generalizations of forking degree, generic transitivity, definable primitivity, and Kolchin-polynomial versions are posed as future problems; no complete solution of these questions was found. | [
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Control $\alpha$-forking degree for arbitrary ordinals via Borovik–Cherlin-type bounds; find model-theoretic applications of generalized generic transitivity; extend Borovik–Cherlin theory to supersimple groups and Kolchin polynomials; and relate definable primitivity of binding groups to geometric stability, different... | Problems and questions We hope the following questions and problems give significant interesting direc- tions for future work around forking degree and variants of the Borovik-Cherlin conjecture. (1) Can one control \alpha-forking degree for arbitrary (perhaps infinite) ordinals using an appropriate version of the Boro... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,285 | OWR-11695862-006 | Transfer Principles for NSOP and NTP Theories | Establish transfer principles for NSOP, NTP, and elimination of imaginaries from a model-complete theory of large fields of characteristic zero to its theory of differentially large fields. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-006",
"literature-status:open",
"owr-year:2022"
] | The extracted question asks for a transfer principle for NSOP or NTP properties and elimination of imaginaries without specifying a precise theory or hypotheses; the claim is incomplete and unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Establish transfer principles for NSOP, NTP, and elimination of imaginaries from a model-complete theory of large fields of characteristic zero to its theory of differentially large fields. | Here are some interesting questions: (1) Is there a transfer principle for NSOP or NTP? How about elimination of imaginaries? Topological and Differential Expansions of o-minimal Structures 3031 | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,286 | OWR-11695862-008 | Model Theory and Zilber Dichotomies for SDCF | Determine further model-theoretic properties of separably differentially closed fields, describe types of $\operatorname{SDCF}_{\ell,p,\epsilon}$ using separable ideals in differential polynomial rings, and establish an appropriate Zilber dichotomy. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-008",
"literature-status:open",
"owr-year:2022"
] | The model-theoretic properties, type descriptions, and a Zilber-dichotomy analogue for SDCF and its variants are posed as open directions; existing work gives completeness and quantifier-elimination results but not the requested full classification. | [
{
"url": "https://arxiv.org/abs/2302.11319",
"label": "Ino--Sánchez, Separably differentially closed fields"
},
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Determine further model-theoretic properties of separably differentially closed fields, describe types of $\operatorname{SDCF}_{\ell,p,\epsilon}$ using separable ideals in differential polynomial rings, and establish an appropriate Zilber dichotomy. | For instance, (1) What other model theoretic properties does SDCF have? (taking the cue from SCF)? (2) Can we describe types of SDCFℓp,ǫ in terms of separable ideals in some differential polynomial ring? Is there a form of Zilber’s dichotomy in this context? Topological and Differential Expansions of o-minimal Structur... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,287 | OWR-11695862-009 | Zilber’s Quasiminimality Conjecture for Complex Exponentiation | Prove that the complex exponential field $\langle\mathbb C;+ ,\cdot,\exp\rangle$ is quasiminimal: every definable subset is countable or cocountable. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-009",
"literature-status:open",
"owr-year:2022"
] | The quasiminimality conjecture for the complex exponential field remains open; quasiminimality of the richer complex-powers structure is proved, but that result is only evidence toward the exponential-field conjecture. | [
{
"url": "https://arxiv.org/abs/2304.06450",
"label": "Gallinaro--Kirby, Quasiminimality of complex powers"
},
{
"url": "https://arxiv.org/abs/2306.05811",
"label": "Kirby, Around Zilber's quasiminimality conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Prove that the complex exponential field $\langle\mathbb C;+ ,\cdot,\exp\rangle$ is quasiminimal: every definable subset is countable or cocountable. | Around Zilber’s quasiminimality conjecture Jonathan Kirby This is an extended abstract for a survey talk given in Oberwolfach on 1st Decem- ber 2022. About 25 years ago, Zilber stated: Conjecture 1. [Zil97] The complex field with the exponential function, ⟨C;+,⋅, exp⟩, is quasiminimal (QM): every definable subset is co... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,288 | OWR-11695862-010 | Quasiminimal Excellence Above Aleph-Two | If a quasiminimal structure $M$ has cardinality at least $\aleph_2$, must $M$ be quasiminimally excellent? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-010",
"literature-status:open",
"owr-year:2022"
] | Kirby records the implication QME to QM and an aleph-one counterexample, but the question whether every QM structure of cardinality at least aleph-two is QME remains unresolved. | [
{
"url": "https://arxiv.org/abs/2306.05811",
"label": "Kirby, Around Zilber's quasiminimality conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2022/52",
"label": "EMS Press, OWR 2022/52"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | If a quasiminimal structure $M$ has cardinality at least $\aleph_2$, must $M$ be quasiminimally excellent? | Question 5. Suppose ∣M∣ ⩾ ℵ2 and M is QM. Must it be QME? A counterexample for ∣M∣ = ℵ1 is given by the dense linear order \omega1 \timeslex Q< , which is QMAut but not QME. This structure is approximated by countable sub- structures in a fundamentally different way, via the linear order \omega1 , whereas in the excell... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,289 | OWR-11695862-011 | Categoricity of the Complex Exponential Field | Prove that the complex exponential field $\mathbb C_{\exp}$ is isomorphic to Zilber's pseudo-exponential field $\mathbb B_{\exp}$; equivalently, prove Schanuel's conjecture and strong exponential-algebraic closedness for $\mathbb C_{\exp}$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open 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-11695862-012"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695862-011",
"literature-status:open",
"owr-year:2022"
] | The proposed identification of the actual complex exponential field with Zilber's pseudo-exponential model would imply Schanuel's conjecture and strong exponential-algebraic closedness; neither is known for Cexp. | [
{
"url": "https://arxiv.org/abs/2306.05811",
"label": "Kirby, Around Zilber's quasiminimality conjecture"
},
{
"url": "https://link.springer.com/article/10.1007/s00029-023-00853-y",
"label": "Gallinaro, Exponential sums equations and tropical geometry"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Prove that the complex exponential field $\mathbb C_{\exp}$ is isomorphic to Zilber's pseudo-exponential field $\mathbb B_{\exp}$; equivalently, prove Schanuel's conjecture and strong exponential-algebraic closedness for $\mathbb C_{\exp}$. | (1) Algebraic properties of Cexp : ACF0 , exp is a surjective homomorphism from the additive to the multiplicative group of the field, and the kernel is \tau Z for a transcendental \tau . (2) Schanuel’s conjecture: for any tuple z̄ we have td(z̄, exp(z̄)) ⩾ ldimQ (z̄). (3) Strong Exponential-Algebraic Closedness (SEAC)... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,290 | OWR-11695862-012 | Duplicate Complex-Exponential Categoricity Formulation | Equivalently, Schanuel’s conjecture is true in Cexp and Cexp is Strongly Exponentially-Algebraically Closed. (1) Algebraic properties of Cexp : ACF0 , exp is a surjective homomorphism from the additive to the multiplicative group of the field, and the kernel is \tau Z for a transcendental \tau . (2) Schanuel’s conjectu... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | open | null | 2,022 | 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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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 Oberwolfach report confirms that this extraction repeats the equivalent Schanuel and strong exponential-algebraic-closedness fo) | [
"OWR-11695862-011"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695862-012",
"literature-status:open",
"owr-year:2022"
] | Schanuel's conjecture and strong exponential-algebraic closedness for Cexp are still open in general; only substantial special cases of exponential-algebraic closedness are proved. | [
{
"url": "https://link.springer.com/article/10.1007/s00029-023-00853-y",
"label": "Gallinaro, Exponential sums equations and tropical geometry"
},
{
"url": "https://arxiv.org/abs/2409.12860",
"label": "Aslanyan--Gallinaro, Exponential Closedness conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | null | Equivalently, Schanuel’s conjecture is true in Cexp and Cexp is Strongly Exponentially-Algebraically Closed. (1) Algebraic properties of Cexp : ACF0 , exp is a surjective homomorphism from the additive to the multiplicative group of the field, and the kernel is \tau Z for a transcendental \tau . (2) Schanuel’s conjectu... | unrecoverable | The official Oberwolfach report confirms that this extraction repeats the equivalent Schanuel and strong exponential-algebraic-closedness formulation already preserved in OWR-11695862-011. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,291 | OWR-11695862-013 | Exponential-Algebraic Closedness | Let $V\subseteq\mathbb C^n\times(\mathbb C^\times)^n$ be a free rotund algebraic subvariety. Prove that $V$ contains a point $(z,\exp z)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | partially_solved | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-013",
"literature-status:partially-solved",
"owr-year:2022"
] | Gallinaro proves the split linear-subspace times multiplicative-variety case of Zilber's exponential-algebraic closedness conjecture, while the full conjecture remains open. | [
{
"url": "https://arxiv.org/abs/2203.13767",
"label": "Gallinaro, Exponential sums equations and tropical geometry"
},
{
"url": "https://arxiv.org/abs/2409.12860",
"label": "Aslanyan--Gallinaro, Exponential Closedness conjecture"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Let $V\subseteq\mathbb C^n\times(\mathbb C^\times)^n$ be a free rotund algebraic subvariety. Prove that $V$ contains a point $(z,\exp z)$. | This talk focuses on a case of the Exponential-Algebraic Closedness Conjecture. This conjecture, due to Boris Zilber, predicts sufficient conditions for systems of exponential sums equations to have solutions in the complex numbers. Exponential-Algebraic Closedness Francesco Paolo Gallinaro Definition 1. Let V \subsete... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,292 | OWR-11695862-014 | Residue-Field Domination in Henselian Valued Fields | Extend residue-field domination to broad classes of equicharacteristic-zero henselian valued fields, with the goal of lifting tameness properties of the residue field to the entire valued field. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050](https://doi.org/10.4171/owr/2022/52)
##... | 3 | partially_solved | null | 2,022 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"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"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "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-11695862-014",
"literature-status:partially-solved",
"owr-year:2022"
] | Residue-field domination has been extended from the original setting to several classes of henselian equicharacteristic-zero fields, including bounded-Galois-group and maximal-model cases, but the broad extension suggested in the record is not complete. | [
{
"url": "https://arxiv.org/abs/2109.08243",
"label": "Vicaria, Residue field domination"
},
{
"url": "https://arxiv.org/abs/2212.05188",
"label": "Ealy--Haskell--Simon, Residue field domination"
},
{
"url": "https://arxiv.org/abs/2410.22712",
"label": "Cubides Kovacsics--Rideau-Kiku... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/52 | null | null | null | Extend residue-field domination to broad classes of equicharacteristic-zero henselian valued fields, with the goal of lifting tameness properties of the residue field to the entire valued field. | Our main motivation arises from the natural question of how much further a notion of residue field domination could be extended to henselian valued fields of equicharacteristic zero. Topological and Differential Expansions of o-minimal Structures 3047 Theorem 4 (Vicaria). Let C \subseteq L be substructures of C with C ... | corrected_verified | The statement was reconstructed and checked against the official Oberwolfach report. | null | null | null | null | null | Mini-Workshop: Topological and Differential Expansions of o-minimal Structures (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/52, pp. 3005--3050 |
30,005,293 | OWR-11695863-001 | Dirac Rayleigh–Faber–Krahn Inequality | For every smooth bounded domain $\Omega\subset\mathbb R^2$, is $E_1(\Omega)\geq\sqrt{\pi/|\Omega|}\,E_1(\mathbb D)$, with equality only for disks? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092](https://doi.org/10.4171/owr/2022/53)
## Li... | 3 | open | null | 2,022 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695863-001",
"literature-status:open",
"owr-year:2022"
] | The Dirac--Rayleigh--Faber--Krahn inequality for the first infinite-mass Dirac eigenvalue is supported by numerical evidence and partial bounds, but the conjectured sharp inequality remains open. | [
{
"url": "https://arxiv.org/abs/2003.04061",
"label": "Antunes--Benguria--Lotoreichik--Ourmieres-Bonafos, Dirac operators"
},
{
"url": "https://doi.org/10.4171/owr/2022/53",
"label": "EMS Press, OWR 2022/53"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/53 | null | null | null | For every smooth bounded domain $\Omega\subset\mathbb R^2$, is $E_1(\Omega)\geq\sqrt{\pi/|\Omega|}\,E_1(\mathbb D)$, with equality only for disks? | Nevertheless this conjecture is still open. A variational formulation for Dirac Operators in bounded domains and applications to spectral geometric inequalities Rafael D. Benguria (joint work with Pedro S. Antunes, Vladimir Lotoreichik, Thomas Ourmières-Bonafos) | 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 | Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092 |
30,005,294 | OWR-11695863-002 | Sharp Fractional Inradius Constants with Fixed Connectivity | For $0<s<1$ and $k\geq2$, determine the sharp constant
$$
T_{s,k}=\inf\{\lambda_1^s(\Omega)r_\Omega^{2s}:\Omega\subset\mathbb R^2\text{ has connectivity }k\}.
$$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092](https://doi.org/10.4171/owr/2022/53)
## Li... | 3 | open | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695863-002",
"literature-status:open",
"owr-year:2022"
] | Bianchi and Brasco obtain explicit lower bounds with sharp parameter ranges and important asymptotics, but the sharp constant for the multiply connected fractional shape-optimization problem remains open. | [
{
"url": "https://arxiv.org/abs/2301.08017",
"label": "Bianchi--Brasco, Optimal lower bound with topological constraints"
},
{
"url": "https://arxiv.org/abs/2110.11748",
"label": "Bianchi--Brasco, Fractional Makai--Hayman inequality"
},
{
"url": "https://doi.org/10.4171/owr/2022/53",
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/53 | null | null | null | For $0<s<1$ and $k\geq2$, determine the sharp constant
$$
T_{s,k}=\inf\{\lambda_1^s(\Omega)r_\Omega^{2s}:\Omega\subset\mathbb R^2\text{ has connectivity }k\}.
$$. | We conjecture that this should be the optimal behaviour of ϑs for k \geq 2, as well. Thus, the previous result naturally leads to the following Open problem. Find the sharp constant Ts,k in (1), i.e. determine the value of the following shape optimization problem Ω \subset R2 open multiply connected set Ts,k = inf \lam... | 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 | Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092 |
30,005,295 | OWR-11695863-003 | Geometric Spectral Bounds for Infinite Quantum Graphs | A natural question is to find spectral estimates, that is, estimates for the infimum of the spectrum \lambda0 (H) = inf\{\lambda| \lambda \in \sigma(H)\} in terms of geometric data of the metric graph G. Spectral Estimates for Infinite Quantum Graphs Noema Nicolussi (joint work with A. Kostenko) A Geometric Fairytale ful... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092](https://doi.org/10.4171/owr/2022/53)
## Li... | 3 | partially_solved | null | 2,022 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
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} | {
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official report poses a motivating question about geometric spectral estimates and then supplies the relevant theorem and corollary in t) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695863-003",
"literature-status:partially-solved",
"owr-year:2022"
] | Kostenko and Nicolussi prove Cheeger-type and related spectral estimates for infinite quantum graphs and derive positivity and discreteness criteria, but the broad request for spectral estimates is not exhausted by those results. | [
{
"url": "https://arxiv.org/abs/1711.02428",
"label": "Kostenko--Nicolussi, Spectral estimates for infinite quantum graphs"
},
{
"url": "https://doi.org/10.4171/owr/2022/53",
"label": "EMS Press, OWR 2022/53"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/53 | null | null | null | null | A natural question is to find spectral estimates, that is, estimates for the infimum of the spectrum \lambda0 (H) = inf\{\lambda| \lambda \in \sigma(H)\} in terms of geometric data of the metric graph G. Spectral Estimates for Infinite Quantum Graphs Noema Nicolussi (joint work with A. Kostenko) A Geometric Fairytale ful... | unrecoverable | The official report poses a motivating question about geometric spectral estimates and then supplies the relevant theorem and corollary in the same contribution. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/53, pp. 3051--3092 |
30,005,296 | OWR-11695864-001 | Classification and Grid Structure of Geproci Sets | Classify nontrivial geproci point sets in projective three-space. Must every geproci set of at least five points contain three collinear points, and can a general finite subset of a smooth plane curve ever be geproci? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-11695864-006"
] | {
"source_url": "https://arxiv.org/abs/2308.00761",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] keep **partially_solved**, but **correct the statement and the literature note**. Problem A in the organizers' introduction to OWR 54/2022 (T. Bauer, G. Favacchio, J. Migliore and J. Szpond; p. 3094) asks to show that every geproci set of at least 5 points in P³ contains 3 ... | [
"owr",
"oberwolfach-reports",
"OWR-11695864-001",
"literature-status:partially-solved",
"owr-year:2022"
] | Classification has advanced through systematic constructions and classifications of several families, including the 16-point four-skew-line case, but no classification of all geproci sets is known. | [
{
"url": "https://arxiv.org/abs/2303.16263",
"label": "Chiantini et al., Classification of certain geproci sets"
},
{
"url": "https://arxiv.org/abs/2308.00761",
"label": "Chiantini et al., Geproci sets and skew-line combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"l... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | Classify nontrivial geproci point sets in projective three-space. Must every geproci set of at least five points contain three collinear points, and can a general finite subset of a smooth plane curve ever be geproci? | A natural problem is to characterize subschemes of PN with the geproci prop- erty. A. Geproci sets and grids. Try to classify geproci sets. The study needs to begin with (4, 4) geproci. Show that every geproci set of n \geq 5 points in P3 contains at least 3 collinear points. If this succeeds, the immediate consequence... | 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 | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,297 | OWR-11695864-002 | Matroid Invariance and Reflection Constructions for Geproci Sets | Can irreducible complex reflection groups be used to classify nontrivial geproci sets? Which matroid properties are invariant under the resulting reflection constructions? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-002",
"literature-status:open",
"owr-year:2022"
] | The reflection-group, uniform-matroid, and same-matroid questions are still posed as open combinatorial-geometric problems; known same-matroid examples need not be projectively equivalent, which does not settle geproci invariance. | [
{
"url": "https://arxiv.org/abs/2308.00761",
"label": "Chiantini et al., Geproci sets and skew-line combinatorics"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"label": "EMS Press, OWR 2022/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | Can irreducible complex reflection groups be used to classify nontrivial geproci sets? Which matroid properties are invariant under the resulting reflection constructions? | Can the classification of irreducible complex reflection groups give some ideas towards a possible classification of nontrivial geproci sets? It also seems natural to ask to what extent the combinatorics (specifically, the underlying matroid) of a collection of points determines the geproci property. • Are there necessary ... | 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 | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,298 | OWR-11695864-003 | Dimensions of General Weddle Loci | What is the dimension of the $d$-Weddle locus of a general set of $r$ points in $\mathbb P^n$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-003",
"literature-status:partially-solved",
"owr-year:2022"
] | The 2026 Weddle-schemes paper determines the hypersurface case and its degree for general sets of binomially many points and analyzes nearby cardinalities, but the dimension for arbitrary r remains open, including the cited unresolved P3 case. | [
{
"url": "https://arxiv.org/abs/2606.25060",
"label": "Chiantini et al., Weddle schemes"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"label": "EMS Press, OWR 2022/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | What is the dimension of the $d$-Weddle locus of a general set of $r$ points in $\mathbb P^n$? | What is the dimension of the d-Weddle locus of a general set Z of r points in Pn ? Even in P3 the question about d+2 2 − 1 general points is still open. Subvarieties in Projective Spaces and Their Projections 3103 While the Weddle surface determined by 6 points is quite special (e.g. it contains the 15 lines joining pa... | 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 | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,299 | OWR-11695864-004 | Determinantal Quartics as Weddle Surfaces | Which quartic surfaces arise as the Weddle surface of a three-dimensional linear system of quadrics in $\mathbb P^3$? In particular, is a general determinantal quartic such a Weddle surface? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-004",
"literature-status:open",
"owr-year:2022"
] | The question whether a general determinantal quartic is a Weddle surface of a net of quadrics remains unresolved; recent work studies related Weddle loci and tensor singularities without proving the proposed characterization. | [
{
"url": "https://arxiv.org/abs/2510.16571",
"label": "Chiantini--Fagioli, Weddle loci of nets of quadrics"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"label": "EMS Press, OWR 2022/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | Which quartic surfaces arise as the Weddle surface of a three-dimensional linear system of quadrics in $\mathbb P^3$? In particular, is a general determinantal quartic such a Weddle surface? | Question 2. Which quartic surfaces is the Weddle surface of a linear system S of dimension 3 of quadrics in P3 ? More specifically, is a general determinantal quartic surface the Weddle surface of a suitable linear system of quadrics? The interpolation matrix arising from general linear systems of quadrics is not necess... | 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 | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,300 | OWR-11695864-005 | Complete-Intersection Realizations of Matroids | Which matroids admit a realization by a point configuration that is a complete intersection? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | partially_solved | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-005",
"literature-status:partially-solved",
"owr-year:2022"
] | Terao's freeness conjecture remains open in general, although it is established for important classes and finite ranges and has substantial computational verification; the extracted motivating question is not settled. | [
{
"url": "https://arxiv.org/abs/1307.3750",
"label": "Abe, Combinatorial data of a free arrangement and Terao's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"label": "EMS Press, OWR 2022/54"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | Which matroids admit a realization by a point configuration that is a complete intersection? | Are there necessary combinatorial conditions, beyond the obvious ones? This leads to the more general question of which matroids admit a realization by points Z which (themselves) form a complete intersection. A motivating open question is whether or not the freeness of an arrangement is a combinatorial property: Terao... | 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 | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,301 | OWR-11695864-006 | Nonexistence of Geproci Sets in Linear General Position | Is it true that such point configurations are never geproci? Subvarieties in Projective Spaces and Their Projections 3107 The reciprocal plane. Another construction from a hyperplane arrangement that gives rise to some interesting commutative algebra is the reciprocal plane: this is the Zariski closure of the image of W... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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 narrower duplicate of the geproci classification questions retained in OWR-11695864-001. No sepa) | [
"OWR-11695864-001"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-006",
"literature-status:open",
"owr-year:2022"
] | For point configurations in linear general position, nontrivial geproci examples beyond four points remain an explicit open problem; existing classifications rule out several low-degree families but do not prove the universal nonexistence claim. | [
{
"url": "https://arxiv.org/abs/2209.04820",
"label": "Chiantini et al., Configurations of points and projections"
},
{
"url": "https://arxiv.org/abs/2407.01744",
"label": "Chiantini et al., Special projection properties in P4"
},
{
"url": "https://doi.org/10.4171/owr/2022/54",
"labe... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | null | Is it true that such point configurations are never geproci? Subvarieties in Projective Spaces and Their Projections 3107 The reciprocal plane. Another construction from a hyperplane arrangement that gives rise to some interesting commutative algebra is the reciprocal plane: this is the Zariski closure of the image of W... | unrecoverable | The official report confirms that this is a narrower duplicate of the geproci classification questions retained in OWR-11695864-001. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,302 | OWR-11695864-007 | Ten-Point Blowup Interpolation Consequences | conjecture. The effective divisors D satisfying this inequality can be classified by solving a Pell’s equation, and\sqrt{ }the solutions correspond to the convergents in the continued fraction expansion of 10. Homogeneous interpolation and moduli spaces of vector bundles Jack Huizenga (joint work with Izzet Coskun) 3112 ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119](https://doi.org/10.4171/owr/2022/54)
## Literat... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"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 extracted Pell-equation and vector-bundle passage reports established constructions and consequences but states no standalone open probl) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695864-007",
"literature-status:open",
"owr-year:2022"
] | The extracted record is truncated and does not state a complete mathematical claim; the related divisor classification for ten-point blowups is conditional on the Nagata conjecture, so the unresolved general problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2022/54",
"label": "original OWR report"
},
{
"url": "https://epiga.episciences.org/13666/pdf",
"label": "Coskun--Huizenga primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/54 | null | null | null | null | conjecture. The effective divisors D satisfying this inequality can be classified by solving a Pell’s equation, and\sqrt{ }the solutions correspond to the convergents in the continued fraction expansion of 10. Homogeneous interpolation and moduli spaces of vector bundles Jack Huizenga (joint work with Izzet Coskun) 3112 ... | unrecoverable | The extracted Pell-equation and vector-bundle passage reports established constructions and consequences but states no standalone open problem. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Mini-Workshop: Subvarieties in Projective Spaces and Their Projections (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/54, pp. 3093--3119 |
30,005,303 | OWR-11695865-001 | Total Positivity and Graphical Model Factorization | For a graph $G$, is $\mathcal{M}_I(G)\cap\mathcal{M}_2(G)$ closed under pointwise limits, and is every multivariate totally positive order-two Markov distribution in $\mathcal{M}_F(G)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": null,
"checked_at": "2026-10-11",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **partially solved (second question: no as stated; first question open)**. S. Lauritzen, the same abstract, p. 3125: Conjecture 1: M_I(G) ∩ M₂(G) is closed under pointwise limits; Conjecture 2: M₂(G) ⊆ M_F(G), i.e. every globally Markov distribution of binary variables that... | [
"owr",
"oberwolfach-reports",
"OWR-11695865-001",
"literature-status:open",
"owr-year:2022"
] | The two total-positivity conjectures are still posed in the source; later work gives special results for binary MTP2 models, but no general proof or counterexample was located. | [
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "Lauritzen OWR report"
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{
"url": "https://par.nsf.gov/servlets/purl/10339054",
"label": "Total positivity primary article"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | For a graph $G$, is $\mathcal{M}_I(G)\cap\mathcal{M}_2(G)$ closed under pointwise limits, and is every multivariate totally positive order-two Markov distribution in $\mathcal{M}_F(G)$? | The article [1] gives general conditions for P \in ME (G) to factorize, chiefly formulated in terms of a condition on the support of P . Now consider a distribution P that is multivariate totally positive of order two, i.e. its density p satisfies (1) p(x ∨ y)p(x ∧ y) \geq p(x)p(y) for all x, y \in X , where the maximu... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,304 | OWR-11695865-002 | Lattice Supports and Graphical Model Factorization | If the support of a Markov distribution $P\in\mathcal{M}(G)$ is a lattice, must $P$ factorize, that is, must $P\in\mathcal{M}_F(G)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"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": "2026-10-11",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **solved (as stated: no; for natural lattice supports: yes, by a preprint)**. S. Lauritzen, Oberwolfach Report 55/2022, p. 3126, Conjecture 3, for binary variables and the global Markov property: if the support of P ∈ M(G) is a lattice, then P factorizes over the complete s... | [
"owr",
"oberwolfach-reports",
"OWR-11695865-002",
"literature-status:open",
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] | The extracted passage states a strengthened factorization conjecture but then becomes a different optimization discussion; the factorization claim remains unresolved in the generality stated. | [
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "Lauritzen OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | If the support of a Markov distribution $P\in\mathcal{M}(G)$ is a lattice, must $P$ factorize, that is, must $P\in\mathcal{M}_F(G)$? | The results in [1] clearly indicate that conditions for factorization of P \in M (G) only relate to the support of P it is worth noting that (1) clearly implies that the support of a totally positive distribution is a lattice, it seems natural to strengthen the conjectures further to Conjecture 3. If the support of P i... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,305 | OWR-11695865-003 | Rank Preservation Under Singular Covariance Updates | In neighborhood coordinate descent for singular covariance matrices, if $\det\Sigma_{\setminus u,\setminus u}=0$, does the updated matrix still satisfy $\det\widetilde\Sigma=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"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-11695865-003",
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] | The record only says that the question is whether Conjecture 4, without reproducing the conjecture; the source context is insufficient to identify a solved claim, so it is normalized to open. | [
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | In neighborhood coordinate descent for singular covariance matrices, if $\det\Sigma_{\setminus u,\setminus u}=0$, does the updated matrix still satisfy $\det\widetilde\Sigma=0$? | The question is whether Conjecture 4. If det Σ\u,\u = 0, we will still have det Σ = 0 after the update. However, since rank Σ = rank Σ\u,\u + rank Σuu − Σu,\u (Σ\u,\u )− Σ\u,u Algebraic Structures in Statistical Methodology 3127 | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,306 | OWR-11695865-004 | Unique Genome Reconstruction from Seven Beads | In the noiseless genome-reconstruction model, do the locations of seven unambiguous beads uniquely determine the locations of all remaining beads? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"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": "2026-10-11",
"kind": "partial",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-11] **partially solved (proved for the exponent α = −2 and sufficiently general data)**. K. Kubjas (joint work with D. Cifuentes, J. Draisma, O. Henriksson, A. Korchmaros), Oberwolfach Report 55/2022, p. 3131: in the noiseless case, the locations of seven unambiguous beads dete... | [
"owr",
"oberwolfach-reports",
"OWR-11695865-004",
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] | The six-bead theorem gives finite identifiability, but the seven-bead unique-recovery assertion is explicitly still a conjecture in the primary genome-reconstruction paper. | [
{
"url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC10884149/",
"label": "3D genome reconstruction primary article"
},
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "original OWR report"
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] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | In the noiseless genome-reconstruction model, do the locations of seven unambiguous beads uniquely determine the locations of all remaining beads? | We conjecture that in the noiseless case, knowing locations of seven unambiguous beads one can uniquely recover the locations of the rest of the beads. Algebraic methods for 3D genome reconstruction Kaie Kubjas (joint work with Diego Cifuentes, Jan Draisma, Oskar Henriksson and Annachiara Korchmaros) | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,307 | OWR-11695865-006 | Generic Identifiability of Linear Compartment Models | For which linear compartment models is the coefficient-map Jacobian generically full rank, equivalently, when is the model generically locally identifiable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"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-11695865-006",
"literature-status:open",
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] | The record is descriptive rather than a complete conjecture; published work treats specific linear-compartment families, while the general parameter-identifiability problem remains unresolved. | [
{
"url": "https://doi.org/10.1016/j.aam.2021.102268",
"label": "Gross--Meshkat--Shiu primary article"
},
{
"url": "https://doi.org/10.1137/25M1728636",
"label": "recent compartment-model primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | For which linear compartment models is the coefficient-map Jacobian generically full rank, equivalently, when is the model generically locally identifiable? | The parameter identifiability problem concerns the question of which parameters can be deter- mined uniquely from data. For linear compartment models, using standard differential algebra techniques, the question of whether a given model is generically locally identifiable is equivalent to asking whether the Jacobian ma... | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,308 | OWR-11695865-007 | Singular Loci of Compartment Model Jacobians | For which parameter values does the Jacobian matrix of a linear compartment model drop rank? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | partially_solved | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | [Discussion #4 update, 2026-10-15] Source-adjacent result and scope clarification for OWR-11695865-007: | [
"owr",
"oberwolfach-reports",
"OWR-11695865-007",
"literature-status:partially-solved",
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] | Recent work characterizes generic identifiability and proves several hyperplanes in the singular locus, but explicitly does not compute the full rank-drop locus in all cases. | [
{
"url": "https://doi.org/10.1137/25M1728636",
"label": "Ahmed et al. primary article"
},
{
"url": "https://doi.org/10.1016/j.aam.2021.102268",
"label": "Gross--Meshkat--Shiu primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | For which parameter values does the Jacobian matrix of a linear compartment model drop rank? | can ask the same question that we asked for linear compartment models: for what parameter values does this Jacobian matrix drop in rank? Figure 1. The catenary (path) model with n compartments, in which compartment 1 has an input, output, and leak. | corrected_verified | Only clear formula delimiters, notation, grammar, and typography were repaired; the mathematical content and scope are preserved. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,309 | OWR-11695865-008 | Recursive Degree Formulas in Likelihood Geometry | Find recursive formulas for the SSL-degree, ML-degree, and dual-ML-degree sequences of the unrestricted $n\times n$ correlation model. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | open | null | 2,022 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695865-008",
"literature-status:open",
"owr-year:2022"
] | The degree table remains incomplete and the recursive formula is still posed as an open question; the cited likelihood-geometry work supplies small cases only. | [
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "original OWR report"
},
{
"url": "https://lematematiche.dmi.unict.it/index.php/lematematiche/article/download/2274/1147/6553",
"label": "Amendola--Zwiernik primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | Find recursive formulas for the SSL-degree, ML-degree, and dual-ML-degree sequences of the unrestricted $n\times n$ correlation model. | A natural open question is, can we find a (recursive) formula for these se- quences? n 1 2 3 4 5 6 7 8 9 SSL degree 1 4 28 292 ? ? ? ? ? ML degree 1 3 15 109 1077 13695 ? ? ? dual ML degree 1 2 5 14 43 144 522 2028 8357 | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,310 | OWR-11695865-009 | Exhaustiveness of Threshold Scenarios for Colored Gaussian Graphical Models | Let $G$ be a colored Gaussian graphical model with $I(G,n+1)=0$ and nonzero rank-$n$ elimination ideal $I(G,n)$. Must exactly one of the following mechanisms determine its thresholds: a nonvanishing signed sum of squares in $I(G,n)$, forcing $\operatorname{WMLT}(G)=\operatorname{MLT}(G)=n+1$; or a positive-definite cov... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170](https://doi.org/10.4171/owr/2022/55)
## Literature review (checked 202... | 3 | open | null | 2,022 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
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"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-11695865-009",
"literature-status:open",
"owr-year:2022"
] | The exact two-scenario claim remains stated as a conjecture; rigidity-based maximum-likelihood-threshold results give substantial structure but do not establish this exhaustive classification. | [
{
"url": "https://doi.org/10.4171/owr/2022/55",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/2108.02185",
"label": "Bernstein et al. primary article"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/55 | null | null | null | Let $G$ be a colored Gaussian graphical model with $I(G,n+1)=0$ and nonzero rank-$n$ elimination ideal $I(G,n)$. Must exactly one of the following mechanisms determine its thresholds: a nonvanishing signed sum of squares in $I(G,n)$, forcing $\operatorname{WMLT}(G)=\operatorname{MLT}(G)=n+1$; or a positive-definite cov... | Conjecture 4. The two cases in Proposition 3 are the only possible scenarios. 4(−l14 l23 + l13 l24 )2 + 4(−l14 l33 + l13 l34 )2 + 4(l13 l44 )2 + 4(l22 l33 )2 + 4(−l24 l33 + l23 l34 )2 + 4(l23 l44 )2 + 4(l33 l44 )2 , a non-vanishing SOS because l11 , l22 , l33 , l44 > 0. Therefore, WMLT(G9 ) = MLT(G9 ) = 2. | corrected_verified | The official Oberwolfach report was checked. The mathematical question was isolated from surrounding exposition and its notation was repaired for self-contained publication. | null | null | null | null | null | Algebraic Structures in Statistical Methodology (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/55, pp. 3121--3170 |
30,005,311 | OWR-11695866-001 | Handwriting and Chronology in Veblen’s Notebooks | Are there changes in pens and/or handwriting? – When was the manuscript written? 2. Focus on lecture notes Reading notes and lecture notes are a specific type of private manuscript which is of interest to us, since we are working on (at least one of) Veblen’s lecture notebooks on the foundations of geometry from 1901. ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214](https://doi.org/10.4171/owr/... | 3 | open | null | 2,022 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 | Unrecoverable OWR statement (The official report passage poses a historical and archival research inquiry about Veblen, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695866-001",
"literature-status:open",
"owr-year:2022"
] | The archive confirms that the relevant lecture notebooks exist, but the specific handwriting changes and dating question is not settled by the available archival description or scholarship. | [
{
"url": "https://findingaids.loc.gov/repositories/19/resources/4615",
"label": "Library of Congress primary finding aid"
},
{
"url": "https://doi.org/10.4171/owr/2022/56",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/56 | null | null | null | null | Are there changes in pens and/or handwriting? – When was the manuscript written? 2. Focus on lecture notes Reading notes and lecture notes are a specific type of private manuscript which is of interest to us, since we are working on (at least one of) Veblen’s lecture notebooks on the foundations of geometry from 1901. ... | unrecoverable | The official report passage poses a historical and archival research inquiry about Veblen, not an open mathematical problem. | null | null | null | null | null | History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214 |
30,005,312 | OWR-11695866-002 | Authorship and Composition of Private Mathematical Manuscripts | History of science has investigated the question of reading and lecture notes rather extensively (although history of mathematics is noticeably absent from most of these studies) and provides great methodological insights.6 The first, and maybe most important, aspect of such notes is what [18] calls “several enunciativ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214](https://doi.org/10.4171/owr/... | 3 | open | null | 2,022 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 passage concerns historical attribution and manuscript analysis, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695866-002",
"literature-status:open",
"owr-year:2022"
] | The record asks methodological questions about private manuscripts; archival sources describe the collection, but do not resolve the listed authorship, chronology, or writing-operation questions. | [
{
"url": "https://findingaids.loc.gov/repositories/19/resources/4615",
"label": "Library of Congress primary finding aid"
},
{
"url": "https://doi.org/10.4171/owr/2022/56",
"label": "original OWR report"
}
] | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/56 | null | null | null | null | History of science has investigated the question of reading and lecture notes rather extensively (although history of mathematics is noticeably absent from most of these studies) and provides great methodological insights.6 The first, and maybe most important, aspect of such notes is what [18] calls “several enunciativ... | unrecoverable | The official report passage concerns historical attribution and manuscript analysis, not an open mathematical problem. | null | null | null | null | null | History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214 |
30,005,313 | OWR-11695866-003 | Veblen’s Private Life and Archival Self-Presentation | What were his non-mathematical interests (if any)? What was his relationship with his wife and his extended family? How, if at all, did Veblen curate his own narrative by selecting what to leave to his archives? How much did he rely on others to do administrative tasks? 5. Deliverables We discussed what types of delive... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214](https://doi.org/10.4171/owr/... | 3 | open | null | 2,022 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 passage concerns biographical and archival history, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695866-003",
"literature-status:open",
"owr-year:2022"
] | Biographical and archival sources document Veblen's family and papers, but the private relationships, self-curation of archives, and administrative questions remain open historical research. | [
{
"url": "https://www.ias.edu/sites/default/files/library/page/FAC.VEBLEN.html",
"label": "Institute for Advanced Study primary finding aid"
},
{
"url": "https://findingaids.loc.gov/repositories/19/resources/4615",
"label": "Library of Congress primary finding aid"
},
{
"url": "https://d... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/56 | null | null | null | null | What were his non-mathematical interests (if any)? What was his relationship with his wife and his extended family? How, if at all, did Veblen curate his own narrative by selecting what to leave to his archives? How much did he rely on others to do administrative tasks? 5. Deliverables We discussed what types of delive... | unrecoverable | The official report passage concerns biographical and archival history, not an open mathematical problem. | null | null | null | null | null | History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214 |
30,005,314 | OWR-11695866-004 | Veblen’s Role in Princeton’s Institutional Rise | Within the greater story of competition between Chicago, Harvard and Princeton as to which university would become the greatest place for studying mathematics, we propose to investigate Veblen’s role in and contribution to the creation of an American institution mathematicians from Europe would never want to miss on th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214](https://doi.org/10.4171/owr/... | 3 | open | null | 2,022 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 passage concerns institutional history, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695866-004",
"literature-status:open",
"owr-year:2022"
] | Institutional sources document Veblen's role in Princeton and the Institute for Advanced Study, but the detailed proposed reconstruction of the center's intended contribution remains unresolved. | [
{
"url": "https://www.ias.edu/sites/default/files/library/page/FAC.VEBLEN.html",
"label": "Institute for Advanced Study primary finding aid"
},
{
"url": "https://www.ams.org/journals/notices/200705/200705FullIssue.pdf",
"label": "American Mathematical Society historical study"
},
{
"url"... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/56 | null | null | null | null | Within the greater story of competition between Chicago, Harvard and Princeton as to which university would become the greatest place for studying mathematics, we propose to investigate Veblen’s role in and contribution to the creation of an American institution mathematicians from Europe would never want to miss on th... | unrecoverable | The official report passage concerns institutional history, not an open mathematical problem. | null | null | null | null | null | History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214 |
30,005,315 | OWR-11695866-005 | Moore’s Laboratory Method in Veblen’s Geometry | Veblen, MSS 44016, Library of Con- gress, 6 RHS), Veblen remarks that “[t]he idea of the proof of the existence of a science is probably due to Hilbert, (Paris congress)” and raises the question of studying “whether the axioms are independent what is the simplest set of axioms.” Those themes are picked up in later publ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214](https://doi.org/10.4171/owr/... | 3 | partially_solved | null | 2,022 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 20,
"name": "miscellaneous",
"display_name": "Miscellaneous",
"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
"order_index": 20,
"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 passage concerns the history of mathematical practice and pedagogy, not an open mathematical problem.) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-11695866-005",
"literature-status:partially-solved",
"owr-year:2022"
] | Primary papers and later historical analysis document Moore's seminar influence on Veblen's geometry, but the exact relation to Moore's Laboratory Method is only partially reconstructed. | [
{
"url": "https://www.jstor.org/stable/1988666",
"label": "Moore primary paper"
},
{
"url": "https://www.ams.org/journals/notices/200705/200705FullIssue.pdf",
"label": "historical analysis of Veblen"
},
{
"url": "https://doi.org/10.4171/owr/2022/56",
"label": "original OWR report"
... | 2026-08-22T00:00:00 | null | https://doi.org/10.4171/owr/2022/56 | null | null | null | null | Veblen, MSS 44016, Library of Con- gress, 6 RHS), Veblen remarks that “[t]he idea of the proof of the existence of a science is probably due to Hilbert, (Paris congress)” and raises the question of studying “whether the axioms are independent what is the simplest set of axioms.” Those themes are picked up in later publ... | unrecoverable | The official report passage concerns the history of mathematical practice and pedagogy, not an open mathematical problem. | null | null | null | null | null | History of mathematics through collaboration: Toward a composite portrait of Oswald Veblen (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/56, pp. 3171--3214 |
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