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-3751 Finite-Order Projections outside the Assembly-Map Image
- Math-3752 Lower Bounds for Reduced Structure Groups
- Math-3753 Duplicate Reduced-Structure-Group Lower Bound
- Math-3754 Counting Hyperbolic Manifolds with Fixed Cusp Number
- Math-3755 Full Support for Singular Hitchin Systems
- Math-3756 Zero-Free One-Forms on Compact Kähler Varieties
- Math-3757 Local Fundamental Groups of Rational Singularities
- Math-3758 Fundamental Groups of Five-Dimensional Log-Canonical Singularities
- Math-3759 Virtual Nilpotence of Rational Log-Canonical Local Groups
- Math-3760 Equality Cases for Singularities of Theta Divisors
- Math-3761 Dimension Bounds for Theta Divisor Singularities
- Math-3762 First Hochschild Cohomology of Nontrivial-Defect Blocks
- Math-3763 Optimal Character-Ratio Bounds for Almost Quasisimple Groups
- Math-3764 Finitely Generated Cohomology in Stable Module Categories
- Math-3765 Abelian Fields Generated by Height-Zero Characters
- Math-3766 Asymptotic Counting Near Curved Submanifolds
- Math-3767 Ramanujan Bounds for Siegel Cusp-Form Coefficients
- Math-3768 Gap Distribution of Prime Multiples Modulo One
- Math-3769 Tropical Curve Counts for Smooth Cubic Log Divisors
- Math-3770 Classification of Critical CR Yamabe Solutions
- Math-3771 Bergman-Kernel Asymptotics at Curvature-Vanishing Points
- Math-3772 Singer’s Unobstructedness Conjecture for Anti-Self-Dual Four-Manifolds
- Math-3773 Tomas–Stein Extremizers on the Circle
- Math-3774 Favard Length and Lipschitz Graph Structure
- Math-3775 Analytic Self-Maps and Automorphism Groups of Cantor Sets
- Math-3776 Rational Point Counts near Hypersurfaces
- Math-3777 $L^p$ Ranges for Radial Projection Estimates
- Math-3778 Quasi-Modularity of Elliptic-Curve Stable-Map Classes
- Math-3779 Elliptic-Cover Cycles and the Gorenstein Kernel
- Math-3780 Chow Vanishing for Lagrangian-Fibered Hyperkähler Varieties
- Math-3781 Cohomological Dimension of Stein Meromorphic Function Fields
- Math-3782 Stability of Brill–Noether Triples
- Math-3783 Logarithmic Hilbert Schemes for Divisor-Stratified Varieties
- Math-3784 Algebraicity of Endoscopic Tate Classes
- Math-3785 Eisenstein Maps and Modular Symbols in Cyclotomic K-Theory
- Math-3786 Nontriviality of Heegner-Point Kolyvagin Systems
- Math-3787 Steinness of Local Shimura Varieties
- Math-3788 Poincaré Duality for Pro-Étale Cohomology of Stein Varieties
- Math-3789 Finite Generation of Group-Ring Cohomology
- Math-3790 Positive Scalar Curvature Information from Rosenberg Indices
- Math-3791 Stable K-Area and Nonvanishing Rosenberg Indices
- Math-3792 Rosenberg Indices and Codimension-Two Curvature Obstructions
- Math-3793 Numerical Criterion for Deformed Hermitian–Yang–Mills Metrics
- Math-3794 Smoothing and Deforming Metric Cones by Ricci Expanders
- Math-3795 Polynomial Time Zeta Functions for Hyperelliptic Curves
- Math-3796 Three Closed Reeb Orbits Beyond Lens Spaces
- Math-3797 Persistence Exponents of Multiply Integrated Brownian Motion
- Math-3798 Index Bounds for Minimal-Hypersurface Volume
- Math-3799 BMO Blowup Criteria for Incompressible Flow Potentials
- Math-3800 Extremal Bounds for Intersecting $K(d)$-Families