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-4851 Local Conformal Field Theories from Non-Semisimple Tensor Categories
- Math-4852 Conformal Field Theory Realization of the Asaeda–Haagerup Subfactor
- Math-4853 Weak Verlinde Formula beyond Rational Conformal Field Theory
- Math-4854 Existence of Time-Dependent Bivariational Quantum Dynamics
- Math-4855 Transferring Resonant Blowup to the Full Einstein System
- Math-4856 Local Well-Posedness of Lovelock Equations
- Math-4857 Weak Limits of Discrete Wave-Turbulence Spectra
- Math-4858 Joint Boltzmann–Grad and Long-Time Limits for Lorentz Gases
- Math-4859 Attainment of Constrained Domain-Wall Energies
- Math-4860 Phase Diagram of the Interacting Bose Gas
- Math-4861 Quantized Transport in Interacting Disordered Systems
- Math-4862 Classification of Quantizations of Symplectic and Poisson Manifolds
- Math-4863 Equivalence of Euclidean AdS/CFT Generating Functionals
- Math-4864 Zero-Velocity Lieb–Robinson Bounds for Disordered Spin Systems
- Math-4865 Sharp Spectral-Cluster Density Bounds on Manifolds
- Math-4866 Reconstruction of Many-Body Dynamics from One-Particle Density
- Math-4867 Ball-Shaped Minimizers of Competing Nonlocal Energies
- Math-4868 Analytical Foundations of Magnetoelastic Material Models
- Math-4869 Macroscopic Limits and Phase Diagrams of Ferroelectric Models
- Math-4870 Metric-Tensor Scaling in Liouville Quantum Gravity
- Math-4871 Strong-Interaction Limits of the Hohenberg–Kohn Functional
- Math-4872 Sharp Convergence Domains for Cluster Expansions
- Math-4873 Infinite-Dimensional K-Moment Problems in Quantum Field Theory
- Math-4874 QQ Systems for Spectral Determinants and Integrable Models
- Math-4875 Lower-Bounded Hamiltonians for Many-Body Point Interactions
- Math-4876 Quantum Backflow Bounds with External Potentials
- Math-4877 Variational GENERIC Structure and Preserving Integrators
- Math-4878 Euclidean Reconstruction of Relativistic Quantum Field Theories
- Math-4879 Symmetry Identities Beyond Renormalization-Group Methods
- Math-4880 Osterwalder–Schrader Positivity in Free Probability
- Math-4881 Quantum Optimal Transport for Mean-Field Dynamics
- Math-4882 Low-Parameter Hyperelastic Models of Brain Tissue
- Math-4883 Far-From-Threshold Buckling of Indented Spherical Shells
- Math-4884 Regularized Density-to-Potential Maps in Density Functional Theory
- Math-4885 Factorial Lattice-Regularity Bounds for Equilibrium Displacements
- Math-4886 Functional Differential Equations for Many-Body Green Functions
- Math-4887 Selecting Physical Solutions of Many-Body Green-Function Equations
- Math-4888 Topological Defects in Three-Dimensional Polycrystals
- Math-4889 Higher-Order Tsirelson, Kirchberg, and Connes Problems
- Math-4890 Linear Entropy and Rank Inequalities for Quantum Marginals
- Math-4891 Arithmetic Nature of Delocalized Eta Invariants
- Math-4892 All-Order Expansion of the Noncommutative $\Phi^4$ Model
- Math-4893 Axisymmetry of Spherical Near-Horizon Geometries
- Math-4894 Weak Cosmic Censorship in Asymptotically Flat Spacetimes
- Math-4895 Horizon Topology Changes and Stable Higher-Dimensional Black Holes
- Math-4896 Nonlinear Instability of Anti–de Sitter Spacetime
- Math-4897 Reverse Burnett Problem for Einstein–Vlasov Limits
- Math-4898 Area–Angular-Momentum Inequalities with Nonpositive Cosmological Constant
- Math-4899 Global Geometric Inequalities for Material Bodies
- Math-4900 Hawking Energy Limits and the Null Penrose Inequality