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-5001 Monoidal Invariance of Hopf-Algebra Cohomological Dimension
- Math-5002 Dimension Rigidity of Quantum Automorphism-Group Factors
- Math-5003 Lévy–Khintchine Decomposition for Star-Bialgebras
- Math-5004 Morita Classification of Quantum SU-Two Projective Representations
- Math-5005 Separated Augmentation Filtrations and Quantum Group Generation
- Math-5006 Genuine Finite-Growth Nichols Algebras over Nonabelian Groups
- Math-5007 Floer Cohomology and Contact Loci of Jets
- Math-5008 Igusa Bounds for Finite-Ring Exponential Sums
- Math-5009 Negativity of Log Divisors on Q-Acyclic Surfaces
- Math-5010 Deciding Positivity in Star Algebras
- Math-5011 Thinness of Hyperbolic Hypergeometric Monodromy Groups
- Math-5012 Indecomposable Representations of Quantum Loop Algebras
- Math-5013 Structure of Cohomological Hall Algebras of Preprojective Algebras
- Math-5014 Primitive Generators of Preprojective Cohomological Hall Algebras
- Math-5015 Affine Springer Cohomology and Quantum-Group Centers
- Math-5016 Unitarity from Nilpotent-Orbit Boundary Codimension
- Math-5017 Hypercube Decomposition of Kazhdan–Lusztig Polynomial Derivatives
- Math-5018 Diamond-Complete Hypercube Formulas for Kazhdan–Lusztig Polynomials
- Math-5019 Quantum Grothendieck Rings Beyond Simply-Laced Types
- Math-5020 Semicuspidal and Schur Algebras of Affine Quivers
- Math-5021 Stable Hyperbolicity of Closed Geodesics for Riemannian Metrics
- Math-5022 Gradient Flows and Ball Topology of Amplituhedra
- Math-5023 The $L_p$ Aleksandrov Problem for Integral Curvature Measures
- Math-5024 Maximum-Volume Sections of $ell_p$ Balls
- Math-5025 Report-Proved Logarithmic Treewidth Bound
- Math-5026 Polynomial $chi$-Bounds for Pivot-Minor-Closed Classes
- Math-5027 Small Induced-Universal Graphs for Planar Graphs
- Math-5028 Rainbow Turán Number of Cycles
- Math-5029 Density Threshold for Rainbow Clique Subdivisions
- Math-5030 Blow-Ups of Clique Subdivisions in Dense Graphs
- Math-5031 Maximum Twin-Width of $n$-Vertex Graphs
- Math-5032 Hitting Maximum Independent Sets in Bounded-Chromatic Graphs
- Math-5033 Reconstruction of Point Sets from $k$-Decks
- Math-5034 Chromatic Number of Almost-Linear Graph Unions
- Math-5035 Subgraph Query Complexity for Fixed Pattern Graphs
- Math-5036 Set-Theoretic Dichotomy for Borel-Quotient Automorphisms
- Math-5037 Dynamical Comparison for Amenable Minimal Nonamenable-Group Actions
- Math-5038 Cocompact Amenable Subgroups of Type-I Groups
- Math-5039 Quadratic Schreier Growth for Torsion-Free Solvable Groups
- Math-5040 Entropy and Nondiagonal Asymptotic Pairs
- Math-5041 Higgs Bundles Arising from p-Adic Representations
- Math-5042 Riemann–Hilbert Correspondence for Étale and v-Sheaves
- Math-5043 Higher-Order Vanishing Ideals in Polynomial Interpolation
- Math-5044 Dimensions of Planar Spline Spaces in Intermediate Degrees
- Math-5045 Geometry and Combinatorics of Planar Spline Dimensions
- Math-5046 Six Problems in Borel Graph Combinatorics
- Math-5047 Finite-Mean Coding Radius for Finitely Dependent Processes
- Math-5048 Finitary-Factor Characterization of Markov Random Fields
- Math-5049 Simultaneous Spatial and Informational Coding Efficiency
- Math-5050 Solution Concepts for Stable SDEs with Distributional Drift