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-4801 Triple-Point Theta Divisors at Odd Two-Torsion Points
- Math-4802 Rank Versus Heegaard Genus of Hyperbolic Three-Manifolds
- Math-4803 Residually Finite Torsion Groups with Restricted Subgroups
- Math-4804 The $\ell^2$-Betti Spectrum of the Lamplighter Group
- Math-4805 Normalized Mod-p Cohomology in Arithmetic Lattice Towers
- Math-4806 Energy Thresholds for Landau–Lifshitz Dynamics
- Math-4807 Decidability of Semieffective Divisors on Blown-Up Projective Space
- Math-4808 Alpha Bounds for Uniform Fat-Point Schemes
- Math-4809 Green–Lazarsfeld Gonality Conjecture
- Math-4810 Volumes of Line Bundles as Periods
- Math-4811 Arrangement Complexity and Random-Complex Homology Thresholds
- Math-4812 Unconditional Reproducing-Kernel Bases in Model Spaces
- Math-4813 Universality Classes for Interacting Particle Fluctuations
- Math-4814 Tempered Embeddings of Unimodular Quasi-Affine Spaces
- Math-4815 The Haagerup Property for Mapping Class Groups
- Math-4816 Finsler Realizations of the Bers Compactification
- Math-4817 Minimal-Dimensional Cocompact Models for Mapping Class Groups
- Math-4818 Transferring Hypocoercivity to Larger Banach Spaces
- Math-4819 Semigroup Generation by Sums of Unbounded Operators
- Math-4820 Evolution-Semigroup Generators for Nonautonomous Operator Families
- Math-4821 Edge-Disjoint Hamilton Cycles in Random Graphs
- Math-4822 Saturation Numbers for Cycles
- Math-4823 Local Coloring and Transitive Sets in Tournaments
- Math-4824 Functional Inequality on the Boolean Cube
- Math-4825 Maximum Simplicial Depth of Point Configurations
- Math-4826 Maximum Density of Directed Simplices in Tournaments
- Math-4827 Directed Trees in Slightly Larger Tournaments
- Math-4828 Chromatic Boundedness of Wheel-Free Graphs
- Math-4829 Highly Chromatic Subgraphs with Controlled Odd Cycles
- Math-4830 Sparse Quadrilateral Removal at the Extremal Threshold
- Math-4831 Smoothness on Products of Perfect Sets
- Math-4832 Precipitous Ideal Separation at Higher Cardinals
- Math-4833 Functional Characterization of Thompson Group Amenability
- Math-4834 Face Vectors of Flag Simplicial Complexes
- Math-4835 Finiteness from Face-Number Bounds for Manifolds with Boundary
- Math-4836 Loop-Space Localization and Witten-Type Interpolation
- Math-4837 Moment Polyhedra of Noncompact Coadjoint Orbits
- Math-4838 Multiplicity-Free Quantization and Orbit Counts
- Math-4839 Quantization of Nilpotent Coadjoint Orbits by Degeneration
- Math-4840 Positivity of Cohomological and K-Theoretic Quiver Coefficients
- Math-4841 Generic Bases for Cluster Algebras
- Math-4842 Graphical Non-Abelian Hodge Correspondence
- Math-4843 Character Multiplicities and Kac–Moody Roots
- Math-4844 Tree Modules for Roots of Acyclic Quivers
- Math-4845 Local Gross–Prasad Multiplicity for Orthogonal Groups
- Math-4846 Gross–Prasad Labels for Multiplicity-One Pairs
- Math-4847 Plancherel Support of Spherical Homogeneous Spaces
- Math-4848 Arthur Parameters from Automorphic Descent Integrals
- Math-4849 Integrability Under Hirota–Kimura Discretization
- Math-4850 Lipschitz Equivalence of Dust-Like Self-Similar Sets