Top Open Problems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-4551 p-Adic Gross–Kudla–Zagier Formula for Diagonal Cycles
- Math-4552 Algebraicity of Rigid Cocycle Values at Real Multiplication Points
- Math-4553 Elliptic Curve Values of Rigid Cocycles
- Math-4554 Cuspidal Spectral-Multiplier Theorem
- Math-4555 Basis Numbers and Torsion Units in Skew Group Algebras
- Math-4556 Uniform Freeness Bounds for Bicyclic Units
- Math-4557 Derived Subgroups, Automorphisms, and Solvable Group-Algebra Units
- Math-4558 Exact Dimensions of Secant Cones
- Math-4559 Euclidean Red–Blue Ramsey Sets
- Math-4560 Unbounded Girth Minus Diameter at Minimum Degree Three
- Math-4561 Symmetric Intersecting Families in Discrete Product Spaces
- Math-4562 Maximum Independent Sets in Regular Uniform Hypergraphs
- Math-4563 Elementary-Theory Classification of Virtually Free Groups
- Math-4564 Braid-Group Extensions of Zamolodchikov Actions
- Math-4565 Jordan-Recoverable Quiver Subcategories
- Math-4566 Completion of Presilting Complexes
- Math-4567 Jacobi Algebras as Contraction Algebras
- Math-4568 Periodicity of Symmetric Tame Algebras
- Math-4569 Sharp Singularity Asymptotics for Sparse Bernoulli Matrices
- Math-4570 Positive Scalar Curvature Through Odd-Order Finite Covers
- Math-4571 Lipschitz Growth of Puncture Classes and Formality
- Math-4572 Vanishing Normalized Homology Under Local Manifold Convergence
- Math-4573 Duplicate Integral-Approximation Question
- Math-4574 CAT(0) Geometry and Retraction of the Bestvina Complex
- Math-4575 Homological Stability for Stabilized Four-Manifold Diffeomorphisms
- Math-4576 Universal Additive Vassiliev Invariants from Embedding Calculus
- Math-4577 Minimal Exotic Smooth Structures on Closed Four-Manifolds
- Math-4578 Smooth Embeddings of Knot Traces in Homology Four-Spheres
- Math-4579 Slice Candidates and Shared Trace Boundaries of Knots
- Math-4580 Kernels of Nonfaithful Type-Preserving Punctured-Torus Representations
- Math-4581 Detecting Abelian Sylow Subgroups from Character Tables
- Math-4582 Character Fields of Odd-Degree Representations
- Math-4583 Combinatorics of Sylow Branching Coefficients
- Math-4584 Maximality of Normalizers of Quasisimple Subgroups
- Math-4585 Wrapped Fukaya Categories as Crepant Resolutions
- Math-4586 Triangle Condition in Long-Range Percolation
- Math-4587 Codegree Thresholds for Tight Hypergraph Hamilton Cycles
- Math-4588 Critical Biases in Positional Graph Games
- Math-4589 Real-Rooted Barycentric h-Polynomials and g-Theorem Conditions
- Math-4590 Almost-Disjointness Numbers at Singular Cardinals
- Math-4591 Jónsson Cardinals, Trace Filters, and Indecomposable Ultrafilters
- Math-4592 Forcing-Invariant Elementary Equivalence Models
- Math-4593 Consistency Strength of Forcing-Invariant Elementary Equivalence
- Math-4594 Universality of Quasi-Isometry among Marked Groups
- Math-4595 Nonemptiness of Affine Deligne–Lusztig Varieties
- Math-4596 Linear Divergence of Higher-Rank Lattices
- Math-4597 Hyperbolic Rank of Affine Buildings
- Math-4598 Lattices and Covolumes in Davis-Complex Automorphism Groups
- Math-4599 Closed Contraction Groups of Totally Disconnected Groups
- Math-4600 Harder Congruences and Yoshida-Type Siegel Modular Liftings