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-4851 Classification of Equationally Complete Theories
- Math-4852 Spectral Shapes of Group-Based Graph Operators
- Math-4853 Noise Sensitivity and Exceptional Times in Spin-System Dynamics
- Math-4854 Percolation Thresholds During Planar Majority Dynamics
- Math-4855 Continuity of the Zero-Level Gaussian Percolation Transition
- Math-4856 Bounded Negativity for Rational Surfaces
- Math-4857 Vertex Algebra Partition Functions and Siegel Modular Forms
- Math-4858 Canonical Bicombings and Group Actions on Injective Spaces
- Math-4859 Non-Helly Coarse-Helly Actions and Coarse-Median Artin Groups
- Math-4860 Fixed Points for Infinite-Dimensional Locally Elliptic Actions
- Math-4861 Fixed Points, Expanding Combings, and Lattices in Metric Geometry
- Math-4862 Fixed Subgroups of Right-Angled Artin Group Automorphisms
- Math-4863 Simultaneous Regularization of Cremona Subgroups
- Math-4864 Convergence of Fully Discrete Hyperbolic Balance-Law Schemes
- Math-4865 Density of Specializations of High-Genus Galois Covers
- Math-4866 Local-Global Density of Galois Cover Specializations
- Math-4867 Exceptional Reducibility Sets in Polynomial Specialization
- Math-4868 Integral Universality of Goodwillie-Weiss Knot Invariants
- Math-4869 Sharp-Interface Limits of Periodic Phase-Transition Equations
- Math-4870 Annular Recurrent Fatou Components of Hénon Maps
- Math-4871 Projective-Free Lie Modules of Symmetric Groups
- Math-4872 Vertices, Sources, and Filtrations of Symmetric-Group Modules
- Math-4873 Covariance Estimation Without Logarithmic Oversampling
- Math-4874 Intermediate Dimensions of Nonergodic Directions on Translation Surfaces
- Math-4875 Strong Approximation of $L^p$ Convolution Operators
- Math-4876 Elementary Equivalence of Universal Sofic Groups
- Math-4877 Reducibility and Manifold Realization of Finite Poincaré Complexes
- Math-4878 Typical Geometry and Systoles of Large-Genus Surfaces
- Math-4879 Borel–Serre-Type Compactifications for General Lattices
- Math-4880 Zucker-Type Cohomology for Satake-Compactified Curve Moduli
- Math-4881 Ordinary Versus Immersive Simplicial Volume
- Math-4882 Rigidity of Large-Radius Convex Subsets in Buildings
- Math-4883 Finiteness of Hyperbolic-Volume-Generated Homology Seminorms
- Math-4884 Virtual Nonorderability of Cocompact Arithmetic Groups
- Math-4885 Optimal Mesh Selection with A Posteriori Error Estimates
- Math-4886 Uniqueness for Spatially Dependent Two-Phase Diffusion
- Math-4887 Numerical and Nef Dimensions of Line Bundles
- Math-4888 Algebraic Dimension from Positive Normal Bundles
- Math-4889 Intrinsic Characterizations of Regular Model Sets
- Math-4890 Spherical Designs with Square Cardinality
- Math-4891 Connectivity and Hamilton Circles in Locally Finite Graphs
- Math-4892 Coloring Dense Triangle-Free Graphs and Hajós' Conjecture
- Math-4893 Dissipation and Decay for Nonlinear Wave Equations
- Math-4894 High-Order Variational Integrators for Degenerate Lagrangians
- Math-4895 Langlands-Dual Parametrization of Shifted Quantum Affine Modules
- Math-4896 Normal Schubert Varieties in Full Affine Flag Varieties
- Math-4897 Weihrauch Determinacy and Degree Structure Questions
- Math-4898 Smooth Interior Regularity for Complex Monge–Ampère Equations
- Math-4899 Exact Flat Choir Numbers and Dimension-Sixteen Tori
- Math-4900 Hyperkähler Compactification of Projective Fibrations