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-4801 Local Approximations of Electronic Spectral Projectors
- Math-4802 Mathematical Classification of Atomic Chemical Groups
- Math-4803 Stability of Atomic Ground-State Quantum Numbers
- Math-4804 Sigma Models with Noncommutative Target Spaces
- Math-4805 Geometric Collapse in the Toroidal Six-Vertex Model
- Math-4806 Rooted-Tree Expansions of Renormalized Two-Point Functions
- Math-4807 Nonlinear Stability of the Full Kerr Family
- Math-4808 Uniqueness of Stationary Black-Hole Exteriors
- Math-4809 Weak Cosmic Censorship for Einstein–Vlasov
- Math-4810 Strong Cosmic Censorship for Spherical Einstein–Vlasov Collapse
- Math-4811 Physical Realizability of Quantum Computation
- Math-4812 Casimir-Connection Monodromy and Quantum Weyl Groups
- Math-4813 Large-Scale Mechanisms Driving Atmospheric Monsoons
- Math-4814 Oceanic Mid-Depth Stratification and Overturning Circulation
- Math-4815 Potential Temperature and Potential Vorticity Inversion
- Math-4816 Predictive Thermostated Dynamics and Subgrid Reservoir Modeling
- Math-4817 Nonlinear Coupling of Buoyancy Reversal and Radiation
- Math-4818 Errors in Long Equatorial Wave Models
- Math-4819 Coupling and Learning Strategies for Climate Supermodels
- Math-4820 Strict Positivity for Fourth-Order Quantum Diffusion
- Math-4821 Vanishing and Uniqueness of Quantum Diffusion Solutions
- Math-4822 Bose–Einstein Condensation in Quantum Boltzmann Dynamics
- Math-4823 Boltzmann–Grad Limits for the Lorentz Gas
- Math-4824 Uniqueness in the Boltzmann–Nordheim Condensate Model
- Math-4825 Energy Cost of Density Defects in Fermi Seas
- Math-4826 Momentum-Space Scarring on Irrational Point-Scatterer Tori
- Math-4827 Semiclassical Measures and Exceptional Eigenmodes
- Math-4828 Quantum Variance Conjectures for Matrix Elements
- Math-4829 Many-Body Localization at Positive Density
- Math-4830 Classification of Gapped Ground-State Phases
- Math-4831 $L^2$-Cohomology of Strongly Centered Monopole Moduli Spaces
- Math-4832 Asymptotic Metrics for Higher-Rank Monopoles
- Math-4833 Nonlinear Stability of Subextremal Kerr Black Holes
- Math-4834 Nonaxisymmetric Stability of Extremal Kerr Waves
- Math-4835 Critical Ultrarelativistic Black-Hole Collision Solutions
- Math-4836 Regular Conformal Equations for Matter with Nonzero Trace
- Math-4837 Non-Disappearance of Nonnegative Scalar-Curvature Limits
- Math-4838 Resonant Mode Mixing in Anti-de-Sitter Instability
- Math-4839 Open Problems in Geometric Nonlinear Quantum Dynamics
- Math-4840 Multipartite Quantum Data Hiding with Separable States
- Math-4841 Absolutely Continuous Diffraction and Dynamical Spectra
- Math-4842 Periodic Gibbs Phases in Two Dimensions
- Math-4843 Quasicrystalline Gibbs Phases in Higher Dimensions
- Math-4844 Reflection-Positivity Research Questions
- Math-4845 Construction of K-Matrices for Coideal Subalgebras
- Math-4846 Quantum-Group and Affine-Hecke Solutions of Boundary qKZ Equations
- Math-4847 Analytic Structures for Nonformal Deformation Quantization
- Math-4848 Conformal Field Theory Realizations of Subfactors
- Math-4849 Four-Dimensional Standard-Subspace Nets with Minimal Length
- Math-4850 Bisognano–Wichmann Covariance for Standard-Subspace Nets