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30,006,616 | OWR-14299911-018 | Problem 7. Travelling polytopes, Genevois Given a graph X, two vertices x, y \in V (X), and a finite set of vertices F \subset V (X), define Median Geometry and Applications 531… | Problem 7. Travelling polytopes, Genevois Given a graph X, two vertices x, y \in V (X), and a finite set of vertices F \subset V (X), define Median Geometry and Applications 531 Travelling salesman: TS(x, F, y) as the shortest length of a path connect- ing x to y and passing through all the vertices in F ; Travelling pol... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,617 | OWR-14299911-019 | A natural question is: TP(X) := sup\{\alpha | \existsC > 0, \forallx, y, \forallF, TP(x, F, y) + |F | \geq C(TS(x, F, y) + |F |)\alpha \}. | A natural question is: TP(X) := sup\{\alpha | \existsC > 0, \forallx, y, \forallF, TP(x, F, y) + |F | \geq C(TS(x, F, y) + |F |)\alpha \}. Question. Which values can take TP(\cdot) on median graphs? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,618 | OWR-14299911-020 | Question. Which values can take TP(\cdot) on median graphs? | Question. Which values can take TP(\cdot) on median graphs? For instance, it would be interesting to compute the travelling polytope constant of a product of (regular) trees. Problem 8. Metric actions on median graphs, Genevois An action G y X on a graph is proper if vertex-stabilisers are finite and metrically proper i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,619 | OWR-14299911-021 | Problem 8. Metric actions on median graphs, Genevois An action G y X on a graph is proper if vertex-stabilisers are finite and metrically proper if \{g \in G | d(o, go) \leq… | Problem 8. Metric actions on median graphs, Genevois An action G y X on a graph is proper if vertex-stabilisers are finite and metrically proper if \{g \in G | d(o, go) \leq R\} is finite for every R \geq 0 (given an arbitrary basepoint o \in V (X)). An interesting problem is to understand the difference between acting pr... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,620 | OWR-14299911-022 | Does it satisfy Kazhdan’s property (T)? | Does it satisfy Kazhdan’s property (T)? Question ii) Does the Grigorchuk group act metrically properly on a median graph? A construction of Schneeberger shows that a proper action does exist, but this specific action is not metrically proper. Problem 10. Covers of cube complexes, Shepherd The following question has been... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,621 | OWR-14299911-023 | Question ii) Is there an algorithm that takes as input a pair of finite non- positively curved cube complexes and determines whether they have isomorphic universal covers? | Question ii) Is there an algorithm that takes as input a pair of finite non- positively curved cube complexes and determines whether they have isomorphic universal covers? Problem 9. Fixed-point properties, Genevois Inspired by Thompson’s group V as a group of homeomorphisms of the Cantor set C, Brin defined a higher-dim... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,622 | OWR-14299911-024 | Is G cocompactly cubulable? | Is G cocompactly cubulable? Is G necessarily residually finite? Can one remove the word “uniform” from this statement, i.e., instead just suppose that every point has a neighbourhood in which every triple has a unique median? Problem 10. Covers of cube complexes, Shepherd The following question has been posed a while ag... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,623 | OWR-14299911-025 | Is G cocompactly cubulable? | Is G cocompactly cubulable? Is G necessarily residually finite? Problem 12. Cartan-Hadamard theorem for median spaces, Bowditch One can show that any complete simply connected path-metric space which is uniformly locally median is in fact median. Here, “uniformly locally median” means that there is some ǫ > 0 such that ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,624 | OWR-14299911-026 | Can one remove the word “uniform” from this statement, i.e., instead just suppose that every point has a neighbourhood in which every triple has a unique median? | Can one remove the word “uniform” from this statement, i.e., instead just suppose that every point has a neighbourhood in which every triple has a unique median? (1) Suppose that for all infinite-order g \in G, there exists a cobounded (not necessarily proper) action of G on a CAT(0) cube complex Xg such that the hyperp... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,625 | OWR-14299911-027 | Can we characterise groups quasi-isometric to an HHS within the class of coarse median groups in terms of their asymptotic cones? | Can we characterise groups quasi-isometric to an HHS within the class of coarse median groups in terms of their asymptotic cones? Problem 14. Graphical apiculate algebras, Chepoi \& Bandelt Every connected graph G = (V, E) can be turned into a ternary algebra, called an apex algebra of G: an apex operation (. . .) : V ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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30,006,626 | OWR-14299911-028 | Problem 14. Graphical apiculate algebras, Chepoi \& Bandelt Every connected graph G = (V, E) can be turned into a ternary algebra, called an apex algebra of G: an apex operation (. | Problem 14. Graphical apiculate algebras, Chepoi \& Bandelt Every connected graph G = (V, E) can be turned into a ternary algebra, called an apex algebra of G: an apex operation (. . .) : V 3 \to V maps any triplets u, v, w and Problem 13. Universal real cubings, Casals-Ruiz (from discussions with M. Hagen and I. Kazac... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/8 | [
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30,006,627 | OWR-14299911-029 | Problem 15. Corners in subcomplexes of Z3 , V. | Problem 15. Corners in subcomplexes of Z3 , V. Chepoi (from discussions with J. Chalopin and M. Kokkou) Let G be a finite connected (partial) subgraph of Z3 . Let X(G) be the cube complex of G, i.e., a square (respectively, a 3-cube) of Z3 belongs to X(G) if and only if all 4 vertices and 4 edges of this square belong t... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/8 | [
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30,006,628 | OWR-14299911-031 | Does this remain true for a random quotient of a free product of at least 3 factors in the free product density model at density d > 1/3? | Does this remain true for a random quotient of a free product of at least 3 factors in the free product density model at density d > 1/3? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Median Geometry and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/8, pp. 487--540](https://doi.org/10.4171/owr/2026/8)
## Literature review (checked 2026-08-22)
**Status:... | 3 | open | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/8 | [
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30,006,629 | OWR-14299912-001 | conjecture. (2) Probabilistic methods. | conjecture. (2) Probabilistic methods. For example, Björn Bringmann presented recent re- sults on the the global well-posedness of singular stochastic PDEs of para- bolic type and explained how the methods connect to dispersive problems. In a different direction, Nikolay Tzvetkov’s lecture on probabilistic well- posedn... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/10, pp. 611--682](https://doi.org/10.4171/owr/2026/10)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/10 | [
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30,006,630 | OWR-14299912-002 | Below, we list some interesting open questions regarding the blowup phenome- non for the mass critical gKdV equation. | Below, we list some interesting open questions regarding the blowup phenome- non for the mass critical gKdV equation. (i) Does there exist a blowup residue r\alpha in H 1 for any solution of (1) blowing up in finite time at a finite point (thus, ν \in ( 13 , 21 ))? This question is open even for the solution constructed ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/10, pp. 611--682](https://doi.org/10.4171/owr/2026/10)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"description": "Problems whose source classification does not fit the main mathematical categories.",
"slug": "miscellaneous",
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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 | null | null | null | null | null | https://doi.org/10.4171/owr/2026/10 | [
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{
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"url": "https://arxiv.org/abs/2601.20801",
"label": "Martel--Pilod preprint"
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30,006,631 | OWR-14299912-003 | Note that Gr1 (C2 ) \sim = S2. | Note that Gr1 (C2 ) \sim = S2. • In [5] we prove global well-posedness for (HWM) posed on the real line R and all initial data in Ḣ 1/2 (R; S 2 ) along with the soliton resolution. • It is an interesting open question to understand the behavior of higher Sobolev norms H s with s > 1/2 for non-rational data. Is blowup ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Nonlinear Waves and Dispersive Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/10, pp. 611--682](https://doi.org/10.4171/owr/2026/10)
## Literature review (checked 2026-08-22)
... | 3 | open | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/10 | [
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] | Nonlinear Waves and Dispersive Equations (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/10, pp. 611--682 | For half-wave maps, the cited work proves global well-posedness at critical H^{1/2}, while the behavior of higher H^{s} norms for non-rational data is explicitly left open. | [
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"url": "https://publications.mfo.de/bitstream/handle/mfo/4444/OWR_2026_10.pdf?sequence=1",
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"url": "https://arxiv.org/abs/2602.20985",
"label": "Gérard--Lenzmann preprint"
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30,006,632 | OWR-14299913-001 | This conjecture is logically related to, but not implied by, the cobordism hypoth- esis, as I will indicate. | This conjecture is logically related to, but not implied by, the cobordism hypoth- esis, as I will indicate. Generally, this conjecture is expected to be true based on heuristics of topological defects/operators in a quantum field theory on Rn . Orthogonal symmetries of higher categories David Ayala (joint work with Joh... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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"url": "https://arxiv.org/abs/2205.04954",
"label": "Ayala--Francis, Symmetries of a rigid braided category"
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] | 2026-08-22T00:00:00 |
30,006,633 | OWR-14299913-002 | However, finding a precise technique for reformulating various standard examples of symmetries (continuous symmetries, spacetime symmetries) in terms of such data has largely… | However, finding a precise technique for reformulating various standard examples of symmetries (continuous symmetries, spacetime symmetries) in terms of such data has largely remained an open question. Symmetry Theories from the Universal Bulk Ilka Brunner (joint work with Severin König, Ingmar Saberi) Higher Structure... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/12 | [
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{
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"url": "https://doi.org/10.1002/prop.202200143",
"label": "Bhardwaj et al., Universal Non-Invertible Symmetries"
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30,006,634 | OWR-14299913-003 | By direct calculation we also found an example in a 2d quantum lattice model, but here the connection with categories remains an open problem. | By direct calculation we also found an example in a 2d quantum lattice model, but here the connection with categories remains an open problem. Could a 2-category be involved? Higher Structures from Symmetries in Quantum Field Theory 755 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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{
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{
"url": "https://doi.org/10.1007/s00220-025-05363-w",
"label": "Bols et al., Classification of the Anyon Sectors of Kitaev's Quantum Double Model"
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30,006,635 | OWR-14299913-004 | We conjecture that, when applied to the Virasoro conformal net, our construc- tion produces Liouville theory. | We conjecture that, when applied to the Virasoro conformal net, our construc- tion produces Liouville theory. Construction of fully extended 2d CFTs via conformal net methods André Henriques (joint work with James Tener) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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{
"url": "https://doi.org/10.4171/owr/2026/12",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2507.20735",
"label": "Henriques--Tener, Every conformal net has an associated unitary VOA"
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{
"url": "https://arxiv.org/abs/2204.02745",
"label": "Vargas, T... | 2026-08-22T00:00:00 |
30,006,636 | OWR-14299913-005 | Open Questions • It is unknown to us, if our trisection invariants of 4-manifolds can be extended to a 4d TQFT. | Open Questions • It is unknown to us, if our trisection invariants of 4-manifolds can be extended to a 4d TQFT. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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{
"url": "https://doi.org/10.4171/owr/2026/12",
"label": "originating Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2511.19384",
"label": "Meusburger--Mulevicius--Torzewska, Categorical 4-manifold invariants from trisection diagrams"
}
] | 2026-08-22T00:00:00 |
30,006,637 | OWR-14299913-006 | These anyons, if the braiding is non-trivial, can work as an index in the classification of mixed state topological order, where we ask if there is a finite-depth quantum… | These anyons, if the braiding is non-trivial, can work as an index in the classification of mixed state topological order, where we ask if there is a finite-depth quantum channel to map one state to the other[2]. Topological Order: The Operator-Algebraic Approach Yoshiko Ogata | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | partially_solved | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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] | Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794 | Recent work gives a partial classification of mixed-state topological order under quasilocal quantum channels and proves obstruction results for nontrivial braiding, but a complete finite-depth-channel criterion remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2026/12",
"label": "originating Oberwolfach report"
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"url": "https://doi.org/10.1103/PRXQuantum.6.010315",
"label": "Lee et al., Toward a Classification of Mixed-State Topological Orders"
},
{
"url": "https://arxiv.org/abs/2501.02398",
"label... | 2026-08-22T00:00:00 |
30,006,638 | OWR-14299913-008 | A natural question is whether there are anything else interesting in the quo- tient other than lattice translation in higher dimensions. | A natural question is whether there are anything else interesting in the quo- tient other than lattice translation in higher dimensions. [3] constructed the first example of a QCA in 3 spatial dimensions. Quantum Cellular Automata from TQFT Nathanan Tantivasadakarn (joint work with Meng Sun, Bowen Yang, Zongyuan Wang an... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | partially_solved | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | null | https://doi.org/10.4171/owr/2026/12 | [
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] | Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794 | Explicit higher-dimensional QCAs beyond lattice translation are now constructed, including dimension-periodic Clifford and non-Clifford families; a complete classification of all interesting quotient elements is not established. | [
{
"url": "https://doi.org/10.4171/owr/2026/12",
"label": "originating Oberwolfach report"
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{
"url": "https://doi.org/10.1103/4519-v15s",
"label": "Sun et al., Clifford quantum cellular automata from TQFTs"
},
{
"url": "https://arxiv.org/abs/2607.21697",
"label": "Sun et al., Non-Cl... | 2026-08-22T00:00:00 |
30,006,639 | OWR-14299913-009 | A remaining open question is to show that these QCAs cannot be realized as constant depth circuits. | A remaining open question is to show that these QCAs cannot be realized as constant depth circuits. More generally, it remains open whether there are QCAs corresponding to the Witt group of non-degenerated braided fusion categories [9], to which what was covered here is only the pointed part. The report passage is reta... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794](https://doi.org/10.4171/owr/2026/12)
## Literature review (che... | 3 | open | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
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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 | null | https://doi.org/10.4171/owr/2026/12 | [
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] | Higher Structures from Symmetries in Quantum Field Theory (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/12, pp. 737--794 | The non-constant-depth nature of the constructed QCAs and the realization of the full Witt group remain unresolved in general; existing papers provide constructions and conditional or partial classification results only. | [
{
"url": "https://doi.org/10.4171/owr/2026/12",
"label": "originating Oberwolfach report"
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{
"url": "https://doi.org/10.1103/PRXQuantum.3.030326",
"label": "Shirley et al., Three-dimensional quantum cellular automata"
},
{
"url": "https://doi.org/10.1103/4519-v15s",
"label": "Sun e... | 2026-08-22T00:00:00 |
30,006,640 | OWR-14299914-001 | What are geometric quantities, including Riemannian and sectional curvatures, in probability manifolds? | What are geometric quantities, including Riemannian and sectional curvatures, in probability manifolds? Can we use these computations to design algorithms in sampling distributions supported on simplex sets? Geometric calculations on probability manifolds from reciprocal relations in Master equations Wuchen Li | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884](https://doi.org/10.4171/owr/2026/13)
## Literature review (... | 3 | partially_solved | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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"
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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 | null | https://doi.org/10.4171/owr/2026/13 | [
"owr",
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] | Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884 | Riemannian, sectional, Ricci, and scalar curvature calculations on several probability manifolds are available, but a general algorithmic theory for sampling on simplex-supported distributions is not established. | [
{
"url": "https://doi.org/10.4171/owr/2026/13",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2504.19368",
"label": "Li, Geometric calculations on probability manifolds"
},
{
"url": "https://arxiv.org/abs/1803.06360",
"label": "Li, Transport information... | 2026-08-22T00:00:00 |
30,006,641 | OWR-14299914-002 | For a distinguished site i∗ = ⌊\sigma0 N ⌋, with \sigma0 \in (0, 1), we ask whether the last token \thetaN (t) at time t decodes to the initial token at position i∗ . | For a distinguished site i∗ = ⌊\sigma0 N ⌋, with \sigma0 \in (0, 1), we ask whether the last token \thetaN (t) at time t decodes to the initial token at position i∗ . Large language models based on causal transformers are routinely deployed in regimes where the available context is much longer than the part of the prom... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884](https://doi.org/10.4171/owr/2026/13)
## Literature review (... | 3 | partially_solved | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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 | null | https://doi.org/10.4171/owr/2026/13 | [
"owr",
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] | Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884 | The causal-attention model now has rigorous mean-field and next-order correlation results and a U-shaped retrieval theorem under explicit assumptions, but this does not settle exact decoding for the full transformer setting or all parameters. | [
{
"url": "https://doi.org/10.4171/owr/2026/13",
"label": "originating Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2605.09213",
"label": "Duerinckx--Geshkovski--Rossi, Kinetic theory for Transformers"
},
{
"url": "https://doi.org/10.1162/tacl_a_00638",
"label": "Liu et al.,... | 2026-08-22T00:00:00 |
30,006,642 | OWR-14299914-003 | Furthermore, the rigor- ous justification of the limit to the massive Arratia flow [6] in the scaling regime N \to \infty, \gamma \to \infty, ℓ \to 0 : \gammaℓ/ log N \to \infty… | Furthermore, the rigor- ous justification of the limit to the massive Arratia flow [6] in the scaling regime N \to \infty, \gamma \to \infty, ℓ \to 0 : \gammaℓ/ log N \to \infty is a challenging open question. (E2) Coalescence of clusters (tcoalesce \sim N ). After initial clustering, K \approx kmax (k) clusters have for... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884](https://doi.org/10.4171/owr/2026/13)
## Literature review (... | 3 | open | null | 2,026 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/13 | [
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] | Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884 | The originating work explicitly identifies rigorous convergence to the massive Arratia flow in the stated joint scaling regime as an open question; existing Arratia-flow papers study the limit model rather than this particle-system justification. | [
{
"url": "https://doi.org/10.4171/owr/2026/13",
"label": "originating Oberwolfach report"
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{
"url": "https://arxiv.org/abs/1504.00559",
"label": "Konarovskyi--von Renesse, Modified massive Arratia flow"
}
] | 2026-08-22T00:00:00 |
30,006,643 | OWR-14299914-004 | We conjecture that the convergence result above is far from optimal, since, unlike when \pi is Gaussian, it depends on the parameter \lambda > 0. | We conjecture that the convergence result above is far from optimal, since, unlike when \pi is Gaussian, it depends on the parameter \lambda > 0. A better decay estimate remains open, as does a good (provably convergent) numerical scheme for non-Gaussian targets. and one still has a projected gradient structure on G. T... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884](https://doi.org/10.4171/owr/2026/13)
## Literature review (... | 3 | open | null | 2,026 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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"
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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 | null | https://doi.org/10.4171/owr/2026/13 | [
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{
"url": "https://doi.org/10.4171/owr/2026/13",
"label": "originating Oberwolfach report"
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{
"url": "https://arxiv.org/abs/2505.24384",
"label": "Provably convergent stochastic fixed-point algorithm for Wasserstein barycenters"
}
] | 2026-08-22T00:00:00 |
30,006,644 | OWR-14299914-005 | To sidestep this problem, we propose to consider a more regular subset of measures or tangent vectors. | To sidestep this problem, we propose to consider a more regular subset of measures or tangent vectors. The theoretical proof of convergence, however, remains an open question. Accelerated Fixed-point Iteration over Spaces of Probability Measures Vitalii Aksenov (joint work with M. Eigel and M. Oster) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Flows on Measure Spaces and Applications in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/13, pp. 795--884](https://doi.org/10.4171/owr/2026/13)
## Literature review (... | 3 | partially_solved | null | 2,026 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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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"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/13 | [
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{
"url": "https://doi.org/10.4171/owr/2026/13",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2601.22038",
"label": "Aksenov--Eigel--Oster, Anderson Mixing in Bures--Wasserstein Space"
},
{
"url": "https://doi.org/10.1007/s10915-025-03027-4",
"label": "... | 2026-08-22T00:00:00 |
30,006,645 | OWR-14299915-001 | The talk focused on recent results and stating open questions related to the finite generation of the co- homology of finite group schemes over Verlinde categories. | The talk focused on recent results and stating open questions related to the finite generation of the co- homology of finite group schemes over Verlinde categories. Cohomology of Finite Groups: Interactions and Applications 543 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | open | null | 2,026 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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{
"url": "https://doi.org/10.4171/owr/2026/9",
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{
"url": "https://arxiv.org/abs/2510.02908",
"label": "Notes on Cohomological Finite Generation for Finite Group Schemes"
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] | 2026-08-22T00:00:00 |
30,006,646 | OWR-14299915-002 | Conjecture 1.2 (Etingof-Ostrik’04). | Conjecture 1.2 (Etingof-Ostrik’04). Let C be a finite tensor category. (1) H ∗ (C) = Ext∗C (1, 1) is Noetherian; (2) For any M, N \in C, Ext∗C (M, N ) is a finite module over Ext∗C (1, 1). When conjecture holds, we say that C satisfies CFG (Cohomological Finite Generation). This is an essential property to be able to stud... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 6 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
"owr",
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | The Etingof--Ostrik CFG conjecture remains open for arbitrary finite tensor categories, although it is proved in important classes including braided categories and several Hopf-algebraic cases. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
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{
"url": "https://doi.org/10.1112/blms.13048",
"label": "Bergh, Support varieties without the tensor product property"
},
{
"url": "https://doi.org/10.1007/s00209-023-03309-3",
"label": "Separ... | 2026-08-22T00:00:00 |
30,006,647 | OWR-14299915-003 | Conjecture 1.3 (Nakano-Vashaw-Yakimov, 2021). | Conjecture 1.3 (Nakano-Vashaw-Yakimov, 2021). Let C be a finite tensor cate- gory. Then the Balmer spectrum of the stable category of C can be identified with a certain subring Zc (H ∗ (C)) of H ∗ (C), called the “categorical center”. When conjecture holds, we say that C satisfies CFG (Cohomological Finite Generation). Th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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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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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | Comparison maps to the categorical center and partial support/spectrum results are established under finite-generation hypotheses and in several classes, but the stated identification for every finite tensor category remains conjectural. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2112.11170",
"label": "Nakano--Vashaw--Yakimov, On the spectrum and support theory"
},
{
"url": "https://arxiv.org/abs/2506.19946",
"label": "Nakano--Vashaw--Ya... | 2026-08-22T00:00:00 |
30,006,648 | OWR-14299915-004 | In the study of modular representations of Lie algebras arising from algebraic groups, a fundamental problem is determining when such representations lift to the ambient… | In the study of modular representations of Lie algebras arising from algebraic groups, a fundamental problem is determining when such representations lift to the ambient algebraic group. Cohomology for Algebraic Groups and Donkin’s Conjectures Daniel K. Nakano (joint work with Christopher P. Bendel, Cornelius Pillen, P... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | open | null | 2,026 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | The extracted statement is a broad lifting problem rather than a theorem; Donkin-related lifting conjectures have substantial case-by-case progress and counterexamples to nearby formulations, but no general resolution. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2103.14164",
"label": "Bendel--Nakano--Pillen--Sobaje, Donkin's Tilting Module Conjecture I"
},
{
"url": "https://arxiv.org/abs/2107.11615",
"label": "Bendel--N... | 2026-08-22T00:00:00 |
30,006,649 | OWR-14299915-005 | Is this 0 for n > 0, as it is for Hncts ? | Is this 0 for n > 0, as it is for Hncts ? Cohomology of Finite Groups: Interactions and Applications 551 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | open | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 20,
"name": "miscellaneous",
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"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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"level": 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 | null | https://doi.org/10.4171/owr/2026/9 | [
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | The question concerns abstract cohomology of pro-p groups with coefficients of characteristic different from p; the report records it as unresolved, and the cited discrete-cohomology work does not settle the general vanishing claim. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/1705.09131",
"label": "Ivanov--Mikhailov, On discrete homology of a free pro-p-group"
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] | 2026-08-22T00:00:00 |
30,006,650 | OWR-14299915-006 | Conjecture 9. Let G be a finite p-group. | Conjecture 9. Let G be a finite p-group. Then H•• (G) is Noetherian. Independent of Noetherianity, we obtain that the above theorem holds at the trivial subgroup of G. As a result, we obtain a nice alternative characterization of the usual cohomology ring of a p-group. In particular, Spc(K(G)) is a Dirac scheme. (2) The... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | open | null | 2,026 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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,
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 | null | https://doi.org/10.4171/owr/2026/9 | [
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | Noetherianity of the twisted cohomology ring for every finite p-group is still posed as a conjecture; current work extends the construction and proves control results but not the required Noetherianity. | [
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"url": "https://doi.org/10.4171/owr/2026/9",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2509.00954",
"label": "Miller, Permutation twisted cohomology, remixed"
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"url": "https://arxiv.org/abs/2307.04398",
"label": "Balmer--Gallauer, The tt-geome... | 2026-08-22T00:00:00 |
30,006,651 | OWR-14299915-007 | Conjecture 7. Let G be a (pro-)finite group, H \leq G a (pro-)p-subgroup. | Conjecture 7. Let G be a (pro-)finite group, H \leq G a (pro-)p-subgroup. Then P(H, p) is periodic iff p is. In other words, the periodic locus of Spec(DPerm(G; k)\omega ) is precisely the com- plement of the closed points. Remark 8 (Twisted group cohomology). The natural proof strategy would follow the one of Example 2 ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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"
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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 | null | https://doi.org/10.4171/owr/2026/9 | [
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | The periodic-locus conjecture is proved when the ambient group is a pro-p group and in important elementary-abelian cases, but the general profinite-group statement remains open because the needed ampleness is not known. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
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"label": "Miller, Permutation twisted cohomology, remixed"
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"url": "https://arxiv.org/abs/2307.04398",
"label": "Balmer--Gallauer, The tt-geome... | 2026-08-22T00:00:00 |
30,006,652 | OWR-14299915-008 | So a natural question is the following: Question 8. | So a natural question is the following: Question 8. How much of the E\infty ring structure is determined by the Frobenius lifts ϕp : \pi0 (A) \to \pi0 (A)∧ p? \pi0 map(X ⊗n , X)hΣn , which satisfy composition relations only up to homotopy. The following observation goes back to Nikolaus-Scholze [2], and is an important... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
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"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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{
"url": "https://doi.org/10.4171/owr/2026/9",
"label": "originating Oberwolfach report"
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"url": "https://arxiv.org/abs/2405.06448",
"label": "Carmeli--Nikolaus--Yuan, Maps between spherical group rings"
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{
"url": "https://doi.org/10.4310/ACTA.2018.v221.n2.a1",
"label": "Nikola... | 2026-08-22T00:00:00 |
30,006,653 | OWR-14299915-009 | The rank conjecture is still open in its full generality. | The rank conjecture is still open in its full generality. For free actions of G = (Z/p)r on X ≃ (S n )k , the conjecture is completely settled except for the cases p = 2 and n = 3, 7. Cohomology of Finite Groups: Interactions and Applications 567 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"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"
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"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
"owr",
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{
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"url": "https://eudml.org/doc/142960",
"label": "Carlsson, On the Rank of Abelian Groups Acting Freely on Products of Spheres"
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"url": "https://doi.org/10.1016/0040-9383(88)90024-9",
"la... | 2026-08-22T00:00:00 |
30,006,654 | OWR-14299915-015 | What do they look like? | What do they look like? How many of them are there? What are the minimal synthetic buildings? Cohomology of Finite Groups: Interactions and Applications 583 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"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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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
"owr",
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | Synthetic buildings now have a general definition, many constructions, and partial classification results, but the questions of their full form and number remain open; current work still states classification conjectures. | [
{
"url": "https://arxiv.org/abs/2608.13414",
"label": "Gullerud--Webb, Synthetic Buildings for Finite Groups"
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"url": "https://doi.org/10.4171/owr/2026/9",
"label": "Oberwolfach Report 9/2026"
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30,006,655 | OWR-14299915-016 | Conjecture 5. For each finite group and prime p, the p-subgroups complex ∆(Sp (G)) always has the equivariant homotopy type of a minimal synthetic build- ing. | Conjecture 5. For each finite group and prime p, the p-subgroups complex ∆(Sp (G)) always has the equivariant homotopy type of a minimal synthetic build- ing. Conjecture 6. Minimal synthetic buildings are all equivariantly homotopy equiv- alent to homomorphic images of ∆(Sp (G)). Conjecture 7. For groups of Lie type in ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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"label": "Gullerud--Webb, Synthetic Buildings for Finite Groups"
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"label": "Oberwolfach Report 9/2026"
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30,006,656 | OWR-14299915-017 | Can we say whether X G , the fixed point set, is non-empty? | Can we say whether X G , the fixed point set, is non-empty? Group actions on compact contractible complexes Kevin Ivan Piterman (joint work with Ivan Sadofschi Costa) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
## Literature review (chec... | 3 | partially_solved | null | 2,026 | 20 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 20,
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"order_index": 20,
"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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"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
"owr",
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"OWR-14299915-017",
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] | Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610 | The unrestricted fixed-point question has negative examples, including finite fixed-point-free actions on compact contractible complexes, while the compact contractible 2-complex case is settled positively and broader cases remain open. | [
{
"url": "https://doi.org/10.4171/owr/2026/9",
"label": "Piterman--Sadofschi Costa, Oberwolfach Report 9/2026"
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{
"url": "https://arxiv.org/abs/2102.11458",
"label": "Sadofschi Costa, Group actions on contractible 2-complexes I"
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"url": "https://arxiv.org/abs/2102.11459",
"labe... | 2026-08-22T00:00:00 |
30,006,657 | OWR-14299915-018 | How much of the homological information about X Z/p can be re- covered from that of X? | How much of the homological information about X Z/p can be re- covered from that of X? The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/9 | [
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30,006,658 | OWR-14299915-021 | Question 2.2. If G is a compact Lie group of dimension d > 0 with \pi0 (G) not p-nilpotent, does it follow that the map \pi∗ (Γk C∗ (ΩBGp )) −\to \pi∗ (C∗ (ΩBGp )) is zero? | Question 2.2. If G is a compact Lie group of dimension d > 0 with \pi0 (G) not p-nilpotent, does it follow that the map \pi∗ (Γk C∗ (ΩBGp )) −\to \pi∗ (C∗ (ΩBGp )) is zero? 2.4. The singularity category as a bounded derived category. The main result is that the singularity category is the bounded derived category of th... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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30,006,659 | OWR-14299915-022 | A fundamental question in the theory of transformation groups is: Which finite groups can act freely on a given product of spheres? | A fundamental question in the theory of transformation groups is: Which finite groups can act freely on a given product of spheres? Free symmetries of products of spheres and Steenrod closed parameter ideals Marc Stephan (joint work with Henrik Rüping, Ergün Yalçın) | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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30,006,660 | OWR-14299915-023 | We conjecture that Theorem 5 extends to every prime p. | We conjecture that Theorem 5 extends to every prime p. The report passage is retained verbatim as the relevant context for this extracted problem. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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30,006,661 | OWR-14299915-024 | More generally, we ask: Question 2.2. | More generally, we ask: Question 2.2. 2. The quadratic bias invariant and Tate cohomology The quadratic bias invariant \betaQ : M 4 (G) \to BQ (G) is defined for a thickening M (X) by an invariant in the isometry group of the hyperbolic Tate form ebG : (( b L)∗ ⊕ b L) \times (( b L)∗ ⊕ b L) \to Z/|G| associated to the e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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30,006,662 | OWR-14299915-025 | In this case we have X ≃ Y , M (X) = S 4 , M (Y ) ≃ S 4 and so 2.2 is equivalent to the question of whether M (Y ) is an exotic 4-sphere. | In this case we have X ≃ Y , M (X) = S 4 , M (Y ) ≃ S 4 and so 2.2 is equivalent to the question of whether M (Y ) is an exotic 4-sphere. Cohomology of Finite Groups: Interactions and Applications 605 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Cohomology of Finite Groups: Interactions and Applications (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/9, pp. 541--610](https://doi.org/10.4171/owr/2026/9)
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30,006,663 | OWR-14299916-001 | What notions of complexity govern learning and generalization in highly overparameterized and moderately overparametrized models? | What notions of complexity govern learning and generalization in highly overparameterized and moderately overparametrized models? Why do gradient- based optimization methods consistently identify solutions that generalize well? How do useful representations emerge during training? What are the computa- tional limitatio... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
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30,006,664 | OWR-14299916-002 | Whether such a synthesis ultimately takes the form of a unified mathematical theory remains an open question. | Whether such a synthesis ultimately takes the form of a unified mathematical theory remains an open question. Modern and Emerging Phenomena in Machine Learning 689 Modern and Emerging Phenomena in Machine Learning 691 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
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30,006,665 | OWR-14299916-003 | Can one characterize, beyond the stylized settings studied so far, which curricula encourage algorithmic reasoning in Transformers? | Can one characterize, beyond the stylized settings studied so far, which curricula encourage algorithmic reasoning in Transformers? How should one identify potentially disruptive but clean examples for SSMs or hy- brid architectures? Modern and Emerging Phenomena in Machine Learning 695 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
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30,006,666 | OWR-14299916-004 | Three ques- tions drove the talk: (1) What do Wt and Ht converge to? | Three ques- tions drove the talk: (1) What do Wt and Ht converge to? (2) What does the trajectory look like – is convergence monotone in some metric? (3) How does the answer depend on initialization and on the number of classes k? Cross-entropy (CE) is the workhorse loss for training deep-net classifiers, yet our theore... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
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"url": "https://arxiv.org/abs/2512.04006",
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30,006,667 | OWR-14299916-005 | A key question is which probability distributions cannot be represented by LLMs due to this bottleneck, and how significant are they to performance? | A key question is which probability distributions cannot be represented by LLMs due to this bottleneck, and how significant are they to performance? How do the answers to these questions vary with m? The Softmax Bottleneck Does Not Limit the Probabilities of the Most Likely Tokens Ronen Basri Modern and Emerging Phenome... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
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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 | null | https://doi.org/10.4171/owr/2026/11 | [
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] | Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736 | The ICLR 2026 analysis gives bounds and experiments for top-m representability and shows that many likely-token distributions are attainable, but it does not characterize all excluded distributions or settle their performance significance. | [
{
"url": "https://openreview.net/forum?id=DgJqQk6y19",
"label": "Basri--Jacobs, The Softmax Bottleneck"
},
{
"url": "https://doi.org/10.4171/owr/2026/11",
"label": "Oberwolfach Report 11/2026"
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] | 2026-08-22T00:00:00 |
30,006,668 | OWR-14299916-006 | We conjecture, and support with empirical evidence, that at inference time, the probabilities of tokens beyond the top 1,000 will not significantly affect performance when… | We conjecture, and support with empirical evidence, that at inference time, the probabilities of tokens beyond the top 1,000 will not significantly affect performance when nucleus sampling is used. What is the largest m for which there exists an OPM such that, for any collection of m tokens, there exists an embedding tha... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | open | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"name": "computer_science",
"display_name": "Computer Science",
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/11 | [
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30,006,669 | OWR-14299916-007 | How can the behavior of AI systems be more closely aligned with that of human users? | How can the behavior of AI systems be more closely aligned with that of human users? Deep neural networks have achieved success across a wide range of applications, including as models of human behavior in vision tasks. However, neural network training and human learning differ in fundamental ways, and neural networks o... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | partially_solved | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/11 | [
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] | Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736 | Human-aligned visual representations have been constructed and shown to improve human-behavioral similarity, uncertainty, and robustness, but general alignment of AI behavior with human users remains unresolved. | [
{
"url": "https://arxiv.org/abs/2409.06509",
"label": "Muttenthaler et al., Aligning Machine and Human Visual Representations"
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{
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30,006,670 | OWR-14299916-008 | What is missing for modern learning systems to exhibit more human-like behavior? | What is missing for modern learning systems to exhibit more human-like behavior? How can the behavior of AI systems be more closely aligned with that of human users? Klaus-Robert Müller Modern and Emerging Phenomena in Machine Learning 713 | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | partially_solved | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
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30,006,671 | OWR-14299916-009 | The talk discussed results and open problems around three structural questions about ReLU neural networks: which functions they can represent exactly, how difficult it is to… | The talk discussed results and open problems around three structural questions about ReLU neural networks: which functions they can represent exactly, how difficult it is to verify properties of a trained network, and to what extent the parameters of a network are identifiable from the function it computes. However, the e... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | open | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | 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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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | null | https://doi.org/10.4171/owr/2026/11 | [
"owr",
"oberwolfach-reports",
"OWR-14299916-009",
"literature-status:open",
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] | Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736 | New constructions represent maximum functions through max10 with two hidden layers and improve general upper bounds, but whether any unrestricted CPWL function requires more than two hidden layers remains open. | [
{
"url": "https://arxiv.org/abs/2607.21651",
"label": "Ruess et al., Shallower ReLU Network Representations"
},
{
"url": "https://arxiv.org/abs/2505.14338",
"label": "Bakaev et al., Better Neural Network Expressivity"
},
{
"url": "https://doi.org/10.4171/owr/2026/11",
"label": "Oberw... | 2026-08-22T00:00:00 |
30,006,672 | OWR-14299916-010 | An important open question is whether the phenomena observed in contemporary foundation models require fundamentally new principles or can be understood through extensions of… | An important open question is whether the phenomena observed in contemporary foundation models require fundamentally new principles or can be understood through extensions of existing theories of approximation, optimization, and statistical learning. Direction 4: Understanding the Computational Limits of Learning. Clas... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | open | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
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"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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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 | null | https://doi.org/10.4171/owr/2026/11 | [
"owr",
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"OWR-14299916-010",
"literature-status:open",
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] | Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736 | Whether foundation-model phenomena require new principles or extensions of existing approximation, optimization, and learning theories is explicitly posed as an open direction with no settled answer. | [
{
"url": "https://doi.org/10.4171/owr/2026/11",
"label": "Oberwolfach Report 11/2026"
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] | 2026-08-22T00:00:00 |
30,006,673 | OWR-14299916-011 | The workshop demonstrated both the remarkable progress that has been achieved in understanding modern learning systems and the sub- stantial challenges that remain open. | The workshop demonstrated both the remarkable progress that has been achieved in understanding modern learning systems and the sub- stantial challenges that remain open. Whether machine learning will ultimately admit such a unified mathematical description remains an open question. Modern and Emerging Phenomena in Machi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736](https://doi.org/10.4171/owr/2026/11)
## Literature review (checked 202... | 3 | open | null | 2,026 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-08-25T00:00:00 | true | {
"id": 15,
"name": "computer_science",
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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 | null | https://doi.org/10.4171/owr/2026/11 | [
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] | Modern and Emerging Phenomena in Machine Learning (2026), Oberwolfach Reports, DOI 10.4171/owr/2026/11, pp. 683--736 | The report explicitly identifies the existence of a unified mathematical description of machine learning as open, and current literature does not establish one. | [
{
"url": "https://doi.org/10.4171/owr/2026/11",
"label": "Oberwolfach Report 11/2026"
}
] | 2026-08-22T00:00:00 |
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