Mathematics catalogue
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-12201 Strict Positivity for Fourth-Order Quantum Diffusion
- Math-12202 Vanishing and Uniqueness of Quantum Diffusion Solutions
- Math-12203 Bose–Einstein Condensation in Quantum Boltzmann Dynamics
- Math-12204 Boltzmann–Grad Limits for the Lorentz Gas
- Math-12205 Uniqueness in the Boltzmann–Nordheim Condensate Model
- Math-12206 Energy Cost of Density Defects in Fermi Seas
- Math-12207 Momentum-Space Scarring on Irrational Point-Scatterer Tori
- Math-12208 Semiclassical Measures and Exceptional Eigenmodes
- Math-12209 Quantum Variance Conjectures for Matrix Elements
- Math-12210 Many-Body Localization at Positive Density
- Math-12211 Classification of Gapped Ground-State Phases
- Math-12212 $L^2$-Cohomology of Strongly Centered Monopole Moduli Spaces
- Math-12213 Asymptotic Metrics for Higher-Rank Monopoles
- Math-12214 Nonlinear Stability of Subextremal Kerr Black Holes
- Math-12215 Nonaxisymmetric Stability of Extremal Kerr Waves
- Math-12216 Critical Ultrarelativistic Black-Hole Collision Solutions
- Math-12217 Regular Conformal Equations for Matter with Nonzero Trace
- Math-12218 Non-Disappearance of Nonnegative Scalar-Curvature Limits
- Math-12219 Resonant Mode Mixing in Anti-de-Sitter Instability
- Math-12220 Open Problems in Geometric Nonlinear Quantum Dynamics
- Math-12221 Multipartite Quantum Data Hiding with Separable States
- Math-12222 Absolutely Continuous Diffraction and Dynamical Spectra
- Math-12223 Periodic Gibbs Phases in Two Dimensions
- Math-12224 Quasicrystalline Gibbs Phases in Higher Dimensions
- Math-12225 Reflection-Positivity Research Questions
- Math-12226 Construction of K-Matrices for Coideal Subalgebras
- Math-12227 Quantum-Group and Affine-Hecke Solutions of Boundary qKZ Equations
- Math-12228 Analytic Structures for Nonformal Deformation Quantization
- Math-12229 Conformal Field Theory Realizations of Subfactors
- Math-12230 Four-Dimensional Standard-Subspace Nets with Minimal Length
- Math-12231 Bisognano–Wichmann Covariance for Standard-Subspace Nets
- Math-12232 Local Conformal Field Theories from Non-Semisimple Tensor Categories
- Math-12233 Conformal Field Theory Realization of the Asaeda–Haagerup Subfactor
- Math-12234 Weak Verlinde Formula beyond Rational Conformal Field Theory
- Math-12235 Existence of Time-Dependent Bivariational Quantum Dynamics
- Math-12236 Transferring Resonant Blowup to the Full Einstein System
- Math-12237 Local Well-Posedness of Lovelock Equations
- Math-12238 Weak Limits of Discrete Wave-Turbulence Spectra
- Math-12239 Joint Boltzmann–Grad and Long-Time Limits for Lorentz Gases
- Math-12240 Attainment of Constrained Domain-Wall Energies
- Math-12241 Phase Diagram of the Interacting Bose Gas
- Math-12242 Quantized Transport in Interacting Disordered Systems
- Math-12243 Classification of Quantizations of Symplectic and Poisson Manifolds
- Math-12244 Equivalence of Euclidean AdS/CFT Generating Functionals
- Math-12245 Zero-Velocity Lieb–Robinson Bounds for Disordered Spin Systems
- Math-12246 Sharp Spectral-Cluster Density Bounds on Manifolds
- Math-12247 Reconstruction of Many-Body Dynamics from One-Particle Density
- Math-12248 Ball-Shaped Minimizers of Competing Nonlocal Energies
- Math-12249 Analytical Foundations of Magnetoelastic Material Models
- Math-12250 Macroscopic Limits and Phase Diagrams of Ferroelectric Models