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-4001 Duplicate Free-Group Word-Measure Conjecture
- Math-4002 Profinite Rigidity of Coxeter Groups
- Math-4003 Generalized Fried Conjecture for Anosov Flows
- Math-4004 Mean-Curvature Blowup at Intermediate-Dimensional Singularities
- Math-4005 Isoperimetric Inequalities Between Total Q-Curvatures
- Math-4006 Uniqueness and Fundamental Solutions for Fractional Diffusion
- Math-4007 Constant-Dimension Framings of Simple Locally Finite Localities
- Math-4008 Cameron Greedy Base-Size Conjecture
- Math-4009 Transitive Binary Actions of Almost Simple Groups
- Math-4010 Realizability and Tameness of Fusion Systems
- Math-4011 Optimal Character Bounds for Almost Quasisimple Groups
- Math-4012 Smooth Projective Realization of Connected Algebraic Groups
- Math-4013 Simplicity of Special Automorphism Groups of Affine Space
- Math-4014 Open Problems on Ind-Groups of Automorphisms
- Math-4015 Alternating Signs in Equivariant Quantum K-Theory
- Math-4016 Centers of Small Quantum Groups
- Math-4017 Invariant Centers of Small Quantum Groups
- Math-4018 Modes and Maximum A Posteriori Estimators on Metric Spaces
- Math-4019 Lagrangian p-Supports of Holonomic Quantization Modules
- Math-4020 Cluster Monomials as Simple Shifted Quantum Affine Modules
- Math-4021 K-Theory Equivalence of Hall and Quasi-BPS Categories
- Math-4022 Higher-Genus Gromov–Witten Invariants of Elliptic Targets
- Math-4023 All-Genus Gromov–Witten Invariants of Hilbert Schemes
- Math-4024 Semiorthogonal Decompositions Along Extremal Contractions
- Math-4025 Quantum-Monodromy Computation of Mutation Braids
- Math-4026 Universal CLE Metrics as Chemical-Distance Limits
- Math-4027 Random Moduli of General Brownian Surfaces
- Math-4028 Selective Decay in Forced-Dissipative Flows
- Math-4029 Legendrian Augmentations and Matroid Realizations
- Math-4030 Unimodular Placing Triangulations after Lattice Dilation
- Math-4031 Restrictions of Toric Vector Bundles to Embedded Varieties
- Math-4032 The Numerical Unramified Plancherel Conjecture
- Math-4033 The Local Geometric Langlands Conjecture
- Math-4034 Derived Geometric Satake for the Basic Object
- Math-4035 Removing Dual-Group Invariants from Plancherel Geometry
- Math-4036 Plancherel Algebras of Dual Hyperspherical Varieties
- Math-4037 Spectral Exchange of Period and L-Sheaves
- Math-4038 q-Hodge Filtrations and Habiro Descent
- Math-4039 Mixed-Chromatic Cohomology Beyond the Extreme Case
- Math-4040 Surjectivity of the p-Adic Hitchin Morphism
- Math-4041 Class-Breadth Inequalities for Odd-Prime Groups
- Math-4042 Modular S-Transform Equivalence for Strongly Finite Vertex Algebras
- Math-4043 Topological Invariance of Helicity
- Math-4044 Aperiodic Stable Transitivity Near Anosov Flows
- Math-4045 Fractal-Time Local Smoothing
- Math-4046 Legendre–Assouad Bounds for Fractal Local Smoothing
- Math-4047 Fractal-Time Local Smoothing Between Lebesgue Spaces
- Math-4048 Categorical Künneth Formula for Étale Motives
- Math-4049 Optimal List Decoding and Recovery of Random Code Ensembles
- Math-4050 Two Erdős Problems on Partial Block Designs