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-4751 Stability of the Prékopa–Leindler Inequality
- Math-4752 Convex Body Uniqueness from Tangential Hyperplane Sections
- Math-4753 Positive-Definite Functions of Minkowski Functionals
- Math-4754 Existence of Noncircular Degenerate Herman Rings
- Math-4755 Locally Omitted Values in Completely Invariant Fatou Components
- Math-4756 Complete Invariance of Singular-Value Basins
- Math-4757 Wandering Domains of Polynomial-Type Quasiregular Maps
- Math-4758 Existence of Ahlfors Islands Maps Between Compact Surfaces
- Math-4759 Closure Conjectures for Infinite Stable Fields
- Math-4760 Genus Three Hecke Trace Formula
- Math-4761 Invariant Homogeneous Valuations on Convex Bodies
- Math-4762 Nodal Geometry of Second $p$-Laplacian Eigenfunctions
- Math-4763 Interpolation of Sobolev Extension Domains and Jacobian Signs
- Math-4764 Sharp Korn–Sobolev Constants and Shape-Preserving Approximation
- Math-4765 Finite Forcibility and Structure of Extremal Graph Limits
- Math-4766 Sharp Connectivity-Preserving Tree Deletion Bounds
- Math-4767 Connectivity-Preserving Paths in Antisymmetric Digraphs
- Math-4768 Cocycle Superrigidity for Bernoulli Actions
- Math-4769 Realization of Sober Spaces as Primitive Ideal Spaces
- Math-4770 Gluing Primitive Ideal Spaces of Amenable Algebras
- Math-4771 Maximal Coarse Baum–Connes Assembly for Expander Quotients
- Math-4772 Character-Degree Criteria for Nilpotent Blocks
- Math-4773 Atypicality Detection by Ambidextrous Modified Dimensions
- Math-4774 Irreducible Specht Modules for Type-A Hecke Algebras
- Math-4775 Asymptotic Counts of Periodic Rational Polygon Billiards
- Math-4776 Measure Equivalence of Limit and Free Groups
- Math-4777 Hyperbolic-Group Boundaries Homeomorphic to Trees of $\mathbb{CP}^{2}$
- Math-4778 Cohomological Dimensions of Elementary Amenable Groups
- Math-4779 Coarse-Manifold Fillings in S-Arithmetic Lattices
- Math-4780 Proper Minimal Embeddings of Open Surfaces
- Math-4781 Mutation Generation of E-Invariant-Zero Representations
- Math-4782 Infinite Cycles and Bose–Einstein Condensation
- Math-4783 Submetries of Compact Ptolemy Spaces
- Math-4784 $\varepsilon$-Regularity Estimate for Donaldson's Equation
- Math-4785 Holomorphic-Curve Structure of Calabi–Yau Blow-Up Sets
- Math-4786 Continuation of Kähler–Ricci Flow through Singularities
- Math-4787 Bigness of Subvarieties with Ample Normal Bundle
- Math-4788 Projection-Locus Smoothness and Cohomology Vanishing
- Math-4789 Numerical Characterization of $q$-Ampleness
- Math-4790 Orbit Closures of Full Cartan Torus Actions
- Math-4791 Linear Representations of Ascending Free-Group Mapping Tori
- Math-4792 Minimum Density of Area-Minimizing Hypersurface Singularities
- Math-4793 Free Toral Rank versus Free $p$-Rank
- Math-4794 Dyer–Lashof Finite Generation of Tate Cohomology
- Math-4795 Commensurability Classes of Hyperbolic Knot Complements
- Math-4796 Reachability and Power Avoidance in Infinite Words
- Math-4797 Digit Sum Bias and Nonvanishing Hankel Determinants
- Math-4798 Infinite Words Avoiding Equal-Length, Equal-Sum Factors
- Math-4799 Almost Aleph-One-Categoricity of Compact Kähler Spaces
- Math-4800 Quasimonomial Valuations Computing Asymptotic Log Canonical Thresholds