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-4601 Asymptotic Stability of Orbitally Stable NLS Ground States
- Math-4602 Denominators of Cluster Variables from Nonacyclic Seeds
- Math-4603 Admissibility and Kinetic Relations for Undercompressive Shocks
- Math-4604 Soundararajan Conjecture on Zeta Zero Spacing
- Math-4605 Hausdorff Dimension of Critical Almost Mathieu Spectra
- Math-4606 Perfect Images of Prosoluble Groups
- Math-4607 Detection and Classification of Virtual Knots by Biquandles
- Math-4608 Quantum Invariants and Boundary Character Varieties
- Math-4609 Quantum Knot Invariants and Boundary Character Varieties
- Math-4610 Recursive Ideals and Knot Character Varieties
- Math-4611 Uniqueness of Dirichlet Forms on the Sierpinski Carpet
- Math-4612 Bigness of Very Moving Algebraic Cycles
- Math-4613 Existence Criteria for Good Moduli Spaces
- Math-4614 Eisenbud's Fiber-Regularity Conjecture
- Math-4615 Modular Compactifications from Curve Singularities
- Math-4616 Algebraic Realizability of Tropical Varieties
- Math-4617 Ample and Extremal Classes on K3-Type Hyperkähler Manifolds
- Math-4618 Perelman Functionals for Coupled Geometric Flows
- Math-4619 Global Existence and Singularities for the Euler–Nordström System
- Math-4620 Uniform Representation Zeta Functions of Congruence Groups
- Math-4621 Infinite-Index Maximal Subgroups of Just-Infinite Groups
- Math-4622 Natural Boundaries of Polynomial Euler Products
- Math-4623 Regularity of Minimal Surfaces in the Heisenberg Group
- Math-4624 Prime-Entry Matrices of Fixed Determinant
- Math-4625 Mean-Curvature Flow from Isolated Conical Singularities
- Math-4626 Dominance of Pure-Cycle Hurwitz-Space Components
- Math-4627 Vector-Bundle Invariants of Cuntz–Pimsner Fields
- Math-4628 Rational Algebraic Realizations of Compact Manifolds
- Math-4629 General Type of Orthogonal Modular Varieties
- Math-4630 Intersection Numbers on First Voronoi Compactifications
- Math-4631 Global Generation of Relative Pluricanonical Pushforwards
- Math-4632 Geodesic Expansions of Off-Diagonal Spectral Functions
- Math-4633 Integrable Convex Hamiltonians on Exotic Tori
- Math-4634 Borel Structure and Generic Triviality of Flow Self-Similarities
- Math-4635 Realization of Rapidly Growing Følner Functions
- Math-4636 Følner Growth and Trivial Poisson Boundary
- Math-4637 Nontrivial Floyd Boundaries Beyond Relative Hyperbolicity
- Math-4638 Subgroup Structure of Interval Exchange Transformations
- Math-4639 Free and Orthogonal Subgroups of Interval Exchange Groups
- Math-4640 Detection and Uniqueness of Lie Quasi States
- Math-4641 Torus Realizations of Adding Machines and Bernoulli Shifts
- Math-4642 Bilipschitz Group Equivalences and 3-Manifold Hyperbolicity
- Math-4643 Unique Integrability of Center Bundles
- Math-4644 Hyperbolic Minimal Geodesics and Measurable Rotation Models
- Math-4645 Simon’s Epimorphism Conjecture for Knot Groups
- Math-4646 Simplicial Volume and Rational Rank of Locally Symmetric Spaces
- Math-4647 Sharp Bounds for Exceptional Dehn-Filling Slopes
- Math-4648 Functorial Maps Between p-Local Finite-Group Classifying Spaces
- Math-4649 Hanani–Tutte Theorems on Surfaces
- Math-4650 Density Thresholds for Finite-Field Configurations