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-4951 Pfaffian Conditions for Graphs on Orientable Surfaces
- Math-4952 Derived Equivalence of Maximal Orthogonal Subcategories
- Math-4953 Carrell Minimality Conjecture
- Math-4954 Metrics and Coordinate Rings on Voronoi Compactifications
- Math-4955 Semiampleness and Ampleness on Abelian Moduli Spaces
- Math-4956 Local Recognition of Graphs and Geometries
- Math-4957 Splitting Bundles for Hilbert-Scheme Equivalences
- Math-4958 Homology-Sphere Factors in Simplicial Decompositions
- Math-4959 Reachable States of Time-Dependent Schrödinger Systems
- Math-4960 Effective Factorization in Monoid Rings
- Math-4961 Affine Pseudocoverings and Their Endomorphisms
- Math-4962 Injective Ext Systems for Cofinal Ideal Chains
- Math-4963 Uniqueness and Signature Ranges of Rough Paths
- Math-4964 Decay Rates for Nonlinear Waves on Black-Hole Backgrounds
- Math-4965 Modular Forms from Generalized Cohomology Theories
- Math-4966 Stable Superpolynomials for Khovanov–Rozansky Homology
- Math-4967 Smooth Extensions of Multiplicative Cohomology Transformations
- Math-4968 Lifting Cohomology Operations to Smooth Extensions
- Math-4969 Consistent Conical Bicombings in Metric Spaces
- Math-4970 Finite Euclidean Models of Compact Nonpositively Curved Surfaces
- Math-4971 Critical-Exponent Geometry of Negatively Pinched Hadamard Quotients
- Math-4972 Ruelle Zeta Vanishing for Generic Negatively Curved Metrics
- Math-4973 Absence of Absolutely Periodic Euclidean Billiard Orbits
- Math-4974 Displacement-Energy Bounds for Poisson Brackets of Open Covers
- Math-4975 $\gamma$-Topology Limits of Hamiltonians with Singular Sets
- Math-4976 Integral Points over Almost All Primitive Number Fields
- Math-4977 Degree-$d$ Points on Algebraic Curves
- Math-4978 Unified Selmer and Cohen-Lenstra-Martinet Heuristics
- Math-4979 Bogomolov–Miyaoka–Yau Inequality for Smooth Four-Manifolds
- Math-4980 Geometry of Singular Monge–Ampère Solution Loci
- Math-4981 Regularity of Varifolds for Anisotropic Energies
- Math-4982 Extending Generator Maps to Finite Group Homomorphisms
- Math-4983 Formal Degrees for Symplectic and Even Orthogonal Groups
- Math-4984 Spectral Expansion of Twisted Orbital Integrals
- Math-4985 The Twisted Fourier–Jacobi Gan–Gross–Prasad Conjecture
- Math-4986 Direct Poisson Summation for Split Classical Groups
- Math-4987 Hiraga–Ichino–Ikeda Degrees for Essentially Discrete Series
- Math-4988 Root Numbers and Central Characters of Langlands Parameters
- Math-4989 The Refined Formal-Degree Conjecture
- Math-4990 Plancherel Densities on Yu-Induced Tempered Components
- Math-4991 Equality of Discrete and Automorphic Multiplicities
- Math-4992 Endoscopic Identities and Archimedean Independence of Local Packets
- Math-4993 Knot Complements and Prime Decomposition in General Three-Manifolds
- Math-4994 The Weak Gordon–Luecke Conjecture
- Math-4995 The Q-Form Classification Conjecture
- Math-4996 Concordance Rigidity of Positive Braid Knots
- Math-4997 Regularity of Equivariant Monomial-Ideal Filtrations
- Math-4998 Eventual Linearity of Equivariant Projective Dimensions
- Math-4999 Spectrahedrality Under the Eigenvalue-Set Transformation
- Math-5000 Polynomial Specht Multiplicities in Symmetric-Variety Cohomology