Mathematics
Open problems, research attempts and community review.
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 Global Attractors for Expanding Torus Symmetric Spacetimes
- Math-4902 Thermodynamic Fluid–Solid Phase Transitions
- Math-4903 Variance Feedback in Cloud Boundary-Layer Models
- Math-4904 Higher-Order Failure of the Quantum Linear Boltzmann Limit
- Math-4905 Long-Time Landau–Pekar Dynamics of Strongly Coupled Polarons
- Math-4906 Logarithmic Entanglement Enhancement from Partial Delocalization
- Math-4907 Loop Operators and Microscopic Nonabelian Anyons
- Math-4908 Sharp Free Energy of the Two-Dimensional Heisenberg Ferromagnet
- Math-4909 Conformal Field Theory Realizations of Subfactors
- Math-4910 Equivalent Bicommutant Categories from Nonisomorphic Conformal Nets
- Math-4911 Classification of Subnets of Conformal Nets
- Math-4912 Small-Weight Quantum Operations on Lattice Conformal Nets
- Math-4913 Hypergroup Correspondence for Discrete Conformal Subnets
- Math-4914 Canonical Equivalence of Complex and Lagrangian Quantizations
- Math-4915 Monolithic versus Staggered Magnetomechanical Relaxation
- Math-4916 Numerical Schemes for Coupled Fracture and Dissipation
- Math-4917 Bilinear Forms behind Resistor and Ising Integrable Equations
- Math-4918 Emergence of Isotropic Big-Bang Singularities
- Math-4919 Bartnik’s Stationary Vacuum Extension Conjecture
- Math-4920 Asymptotics of Expanding Vacuum Spacetimes Near Singularities
- Math-4921 Weak Cosmic Censorship for Vacuum Spacetimes
- Math-4922 Kasner Singularities Beyond the Subcritical Regime
- Math-4923 Self-Consistent Motion of Massive Charged Particles in Relativity
- Math-4924 Weak Bianchi Identities Across Timelike Singularities
- Math-4925 Initial Data for Physical Late-Time Schwarzschild Wave Tails
- Math-4926 Interior Singularity Structure of Dynamically Formed Black Holes
- Math-4927 Local Weak Cosmic Censorship in Charged Spherical Collapse
- Math-4928 Equality of Capacity–Volume and ADM Mass
- Math-4929 Completeness of Realignment and SIC-POVM Entanglement Tests
- Math-4930 Spin-Alignment Entropy Conjecture
- Math-4931 Trigonometric and Elliptic R-Matrices from Three-Dimensional WZW Models
- Math-4932 $u$-Equations for Arbitrary Hyperbolic Surfaces
- Math-4933 Affine–Virasoro Derivation of Nekrasov Blow-Up Identities
- Math-4934 Fivebrane Filtrations and Holomorphic Field Theories
- Math-4935 Conformal Invariance of Interacting Long-Range Fermionic Models
- Math-4936 Euclidean Extension of Hierarchical Susceptibility Asymptotics
- Math-4937 Mathematical Construction of the Negative-Phase Coulomb Category
- Math-4938 Knots–Quivers Correspondence for All Knots
- Math-4939 Instance-Independent Drivers in Quantum Annealing
- Math-4940 Fluctuation Limits for Moderately Interacting Particle Systems
- Math-4941 Continuation of Nordheim Condensation Beyond Dirac-Mass Formation
- Math-4942 Quantum-Symmetric Classes of Artin–Schelter Regular Algebras
- Math-4943 Periodic Ground States in Gross–Pitaevskii Theory
- Math-4944 Adiabatic Expansions for Gapless Quantum Systems
- Math-4945 Accelerated Information Propagation in Bosonic Lattices
- Math-4946 Aubin–Talenti Optimizers for Critical Dirac Potentials
- Math-4947 Lee–Huang–Yang Upper Bound for Hard-Sphere Bosons
- Math-4948 Modular Generators for Massive Double Cones
- Math-4949 Local Density Approximation for the Canonical Functional
- Math-4950 Higher-Dimensional Semiclassical Kinetic-Energy Corrections