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-4501 Convex Geometry of General Polytope Face Vectors
- Math-4502 Limit Rays and Fatness of Polytope Face Vector Cones
- Math-4503 Cubical Facet Counts and Nonintersecting Spatial Triangles
- Math-4504 Equivariant Log-Concavity of Orlik–Solomon Algebras
- Math-4505 Extending Combinatorial Spheres on the Same Vertex Set
- Math-4506 Boltzmann Limits for Long-Range Lorentz Gases
- Math-4507 KdV Evolution from General Ergodic Random Fields
- Math-4508 Kinetic Relaxation and Bootstrap Percolation Infection Times
- Math-4509 Combinatorial Deformations of Toric Fano Varieties
- Math-4510 Deformations of Non-Gorenstein Toric Fano Varieties
- Math-4511 Unified Constructions of Supercuspidal Representations
- Math-4512 Derived Equivalence for Spherical Hamiltonian Duality
- Math-4513 Stratified Equivalence for Bernstein Components
- Math-4514 Depth-Controlled Relative Local Character Expansions
- Math-4515 Index Bundles for General Foliations
- Math-4516 Novikov–Shubin Positivity and Foliated Index Characters
- Math-4517 Rho Invariants for Foliated Dirac Operators
- Math-4518 Kasparov’s Baum–Connes Method in Higher Rank
- Math-4519 Realization of Oriented Dimension Functions by Equivariant Spheres
- Math-4520 Hopkins Conjecture for Morava-Stabilizer Subgroups
- Math-4521 Reduced $C^*$-Algebras of Free Orthogonal Quantum Groups
- Math-4522 Finite-Dimensional Uniform Embeddings of Compact Metric Spaces
- Math-4523 Orbit Closures in Degenerate Flag Varieties
- Math-4524 Essential Self-Adjointness on Almost-Riemannian Regular Regions
- Math-4525 Self-Adjointness and Extensions of Infinite Metric-Graph Laplacians
- Math-4526 Universal Grading of Hyperfinite Factor Bimodules
- Math-4527 Optimal Exponent for Counting Monogenic Number Fields
- Math-4528 Typical Size of the Erdős–Hooley Function
- Math-4529 Coefficient Normalization of Positive Definite Homogeneous Forms
- Math-4530 Involutivity and Cancellativity of Yang–Baxter Solutions
- Math-4531 Semiprime Yang–Baxter Structure Algebras
- Math-4532 Prime Quotients of Yang–Baxter Structure Algebras
- Math-4533 Abelian Derived Racks and Their Structure Groups
- Math-4534 Solvability and Realizability of Finite Skew Braces
- Math-4535 Groups Arising as Quandle Structure Groups
- Math-4536 Descent of Rational Points from Laurent Series Fields
- Math-4537 Characterizing Projective Space by Tangent Bundle Seshadri Constants
- Math-4538 Rationality of Seshadri Constants on Plane Blowups
- Math-4539 Rationality of Seshadri Constants from Plane-Curve Singularities
- Math-4540 Waldschmidt Constants of Plane Curve Singular Sets
- Math-4541 Harbourne Constants, Symbolic Powers, and Resurgence of Line Arrangements
- Math-4542 Uniform Doubling for Compact Connected Lie Groups
- Math-4543 Pointwise Equidistribution Under Toral Endomorphisms with Fewer Hypotheses
- Math-4544 Galois Actions on Moduli of General-Type Surfaces
- Math-4545 Boundary-Intersection Vanishing on Abelian-Variety Moduli
- Math-4546 Reid’s Fundamental-Group Conjecture for General-Type Surfaces
- Math-4547 Uniruledness and Generic Nefness of Tangent Bundles
- Math-4548 Deformations of Complex Nilmanifolds and Torus Bundles
- Math-4549 S-Unit Differences of Singular Moduli
- Math-4550 Harder Congruences for Holomorphic Jacobi Forms