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-4751 Connections Between CGLMP Inequalities and Quantum Field Theory
- Math-4752 Positive Maps and Multipartite Bound Entanglement
- Math-4753 Systematic Multiscale Design of Hierarchical Materials
- Math-4754 Relationship Between Two-Species Condensates
- Math-4755 Physical Interpretation of Elliptic Partition Functions
- Math-4756 Physical Regularity Criteria for Massless Scattering Theory
- Math-4757 Bounded Local Observables in Factorizing Quantum Field Theories
- Math-4758 Renormalization through Langmann–Szabo Duality
- Math-4759 Geometric Spin–Statistics under Weakened Assumptions
- Math-4760 Spectral Geometry and Cyclic Homology of $SU_q(2)$
- Math-4761 Scaling Limits of Tensor Products in AQFT
- Math-4762 Heterotic Mirror Symmetry for Bundled Calabi–Yau Manifolds
- Math-4763 Deformations and Massless Spectra of Smooth Deligne–Mumford Stacks
- Math-4764 Infrared Equivalence of Stack Presentations
- Math-4765 Gauge Fixing for Quantum Vertex Algebra Deformations
- Math-4766 Hoop Conjecture for Black-Hole Formation
- Math-4767 Orthotropic Extensions of Anisotropic Creep-Damage Models
- Math-4768 Nonperturbative Infrared Behavior of Nonamenable Sigma Models
- Math-4769 Continuous-Spectrum Analysis of Nelson-Type Models
- Math-4770 Higher-Dimensional Thermodynamic Limits
- Math-4771 Quantum Zeta Functions for Mirror Calabi–Yau Threefolds
- Math-4772 Mechanisms Producing Equatorial Superrotation
- Math-4773 Topographic Rossby Waves and Inertial-Wave Coexistence
- Math-4774 Linear Baroclinic Prediction of Ocean Eddies
- Math-4775 Global Well-Posedness and Uniqueness of Gravity-Capillary Waves
- Math-4776 Density of Current–Current Correlation Measures
- Math-4777 Wang–Ostrik Finiteness Conjecture for Fusion Categories
- Math-4778 Current Criteria for Phase Separation in Driven Systems
- Math-4779 Rigid Order–Disorder Interfaces in Continuous-Spin Models
- Math-4780 Stability of Schwarzschild Black Holes Under Perturbation
- Math-4781 Thermal Conductivity Under Asymmetric Momentum Noise
- Math-4782 Energy Transmission in Strongly Pinned Networks
- Math-4783 Constitutive Models for Oscillatory Micellar Sedimentation
- Math-4784 Massless and Point-Charge Limits of the Pauli–Fierz $g$-Factor
- Math-4785 First-Principles Derivation of Adaptive-Resolution Molecular Dynamics
- Math-4786 Efficient Coarse-Grained Free-Energy Computation
- Math-4787 Nonconvex Gradient Gibbs States and Free Energy
- Math-4788 Critical Transition and Pattern Scales in Shear Turbulence
- Math-4789 Homogeneous Factorizations Producing Type-II Arveson Systems
- Math-4790 E0-Semigroups from Free Product Systems
- Math-4791 Adapted Cocycles and Tensor Subsystems of Free Filtrations
- Math-4792 Recovering Spatial Tensor Systems by Intersection
- Math-4793 Ambient-Algebra Independence of Exchangeable Independence
- Math-4794 Extremal Exchangeability Beyond Natural Noncommutative Products
- Math-4795 Extending Dilated E0-Semigroups Beyond GNS Representations
- Math-4796 Future Restrictions of Inner Automorphic Dilations
- Math-4797 Classification of Spatial and Nonspatial Markov Semigroups
- Math-4798 Multiparameter E0-Semigroups from Free Product Systems
- Math-4799 Group-Valued Lévy Processes with Type-II Arveson Systems
- Math-4800 Efficient Reduced Free-Energy Computation for Atomistic Systems