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-4901 Kodaira Dimensions of Abelian-Differential Moduli Spaces
- Math-4902 Scalar-Curvature Rigidity on Wrapped Sphere Complements
- Math-4903 Positive Energy Conditions and Spaces of Initial Data
- Math-4904 Sharp Width Bounds for Positive-Scalar-Curvature Bands
- Math-4905 Rigidity in Scalar-Curvature Band Width Inequalities
- Math-4906 Fillability of Bartnik Boundary Data Under Scalar Curvature Bounds
- Math-4907 Equivalence of Weak Scalar-Curvature Notions for Continuous Metrics
- Math-4908 Preservation of Positive-Scalar-Curvature Obstructions Under Surgery
- Math-4909 Surgery Stability of Positive Ricci Curvature
- Math-4910 Core Metrics and Positive Ricci Curvature on Simply Connected Manifolds
- Math-4911 Contractible Positive-Scalar-Curvature Three-Manifolds
- Math-4912 Exponential Frames for Measurable Sets
- Math-4913 Density and Balian–Low Theory for Gabor Schauder Bases
- Math-4914 Universal Wavelet Generators for Dense Affine Sets
- Math-4915 Positive Characters of Simply Connected Groups
- Math-4916 Power-Law Fixed-Radius Circle Discrepancy
- Math-4917 Low-Randomness Constructions of Low-Discrepancy Point Sets
- Math-4918 Random-Order Discrepancy Bounds for Lattice Point Sets
- Math-4919 Existence and Convergence in Irreversible Fracture Evolution
- Math-4920 Relative Isoperimetric Partitions of Convex Regions
- Math-4921 Multiphase Models with Multiple Conserved Quantities
- Math-4922 Crystallization from Many-Particle Interaction Potentials
- Math-4923 Brauer Obstructions to Rational Points over Surface Function Fields
- Math-4924 Betti-Preserving Initial Ideals in Fixed Coordinates
- Math-4925 Gorenstein Initial Ideals with Minimal Generators
- Math-4926 Powers of Linearly Presented Primary Ideals
- Math-4927 Charalambous–Reeves Standard-Matching Conjecture
- Math-4928 Fractional Helly Theorems for Bounded HVC Dimension
- Math-4929 Rational 1-Connectedness Under Higher Fano Conditions
- Math-4930 Positivity of Landau–Ginzburg TERP Structures
- Math-4931 Integrality of Constrained Polytope Families
- Math-4932 Nonnegative Stretched Clebsch–Gordan Coefficients
- Math-4933 Universality of Real Table Polytopes
- Math-4934 A Weakened Wills Inequality for Convex Bodies
- Math-4935 Finite-Dimensional Approximation of Bounded Analytic Functions
- Math-4936 Holomorphic Structures on Vector Bundles over Complex Surfaces
- Math-4937 Hydrodynamics of Ergodic Kob–Andersen Models
- Math-4938 Strong Disorder and Polymer Superdiffusivity
- Math-4939 Free Finite-Group Actions on Products of Spheres
- Math-4940 Minimum Coincidence Components of Homotopic Map Pairs
- Math-4941 Three-Cocycles in the Hyperfinite Type $\mathrm{II}_1$ Factor
- Math-4942 Boundary and Hyperbolic Dimensions of Symmetric Spaces
- Math-4943 Least Dimension for Curvature-Finiteness Counterexamples
- Math-4944 Jacobi Fields and Neck Sizes of Coplanar Unduloids
- Math-4945 Liouville Theorems for Periodic Elliptic Equations
- Math-4946 Bound-State Moments and Embedded Singular Spectrum
- Math-4947 Limiting Cycle Distributions of Birational Maps
- Math-4948 Global Solutions and Sharp-Interface Limits in Three Dimensions
- Math-4949 Low-Moment Detection of Reductive Subgroups
- Math-4950 Surface Chromatic Width and Bounded-Facewidth Snarks