Top Open Problems
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-4201 Composite of Unrelated Decidability Questions
- Math-4202 Squarefree Group Orders in Elliptic-Curve Reductions
- Math-4203 Zeta Moments from Shifted Divisor Correlations
- Math-4204 Three Problems from an Analytic Number Theory Session
- Math-4205 Elliptic-Curve Bijections and Additive Bases from Restricted Primes
- Math-4206 Simplicial Volumes of Surface Bundles
- Math-4207 Monodromy of Universal Plane-Curve Bundles
- Math-4208 Coherence and Finiteness Properties of Surface-Bundle Groups
- Math-4209 Multiple Kodaira Fiberings and Relative Irregularity
- Math-4210 Non-Liftable Monodromy of Surface Bundles
- Math-4211 Asymptotic Point Counts on Curve Moduli Spaces
- Math-4212 Boundedness of Tautological Kappa Classes
- Math-4213 Hyperbolic Three-Manifold Groups in $\operatorname{SL}_3(\mathbb Z)$
- Math-4214 Multiplicity Inequality for Quotients by Perfect Ideals
- Math-4215 Toric Reembeddings for Embedded Local Uniformization
- Math-4216 Large Regularity Quadratic Ideals with Linear First Syzygies
- Math-4217 Model Theory and Analysis of Surreal Exponential Fields
- Math-4218 Elementary Equivalence of Differential Generalized Series Fields
- Math-4219 Arithmetic Integer Parts of Surreal and Real Closed Fields
- Math-4220 Residue Fields of O-Minimal Exponential Fields
- Math-4221 Model Theory of Residue Exponential Fields
- Math-4222 Elementary Embeddings of Residue Exponential Fields
- Math-4223 Equiangular Lines and Few-Angle Spherical Codes
- Math-4224 Enumeration and Structure of Higher-Dimensional Permutations
- Math-4225 Maximum-to-Average Independence Ratios in Triangle-Free Graphs
- Math-4226 Regular Graphs Beating Clique Homomorphism Densities
- Math-4227 Positive Association in Random Proper Colorings
- Math-4228 Homotopy Equivalence of Negative Curvature and Anosov Metric Spaces
- Math-4229 Contractibility of Anosov Metric Spaces on Surfaces
- Math-4230 Infinite Components of Positive Ricci Metric Moduli
- Math-4231 Components of Nonnegative Curvature Metrics on Homotopy Spheres
- Math-4232 Flat Bands on Nonpositively Curved Surfaces
- Math-4233 Frame Bundle Rigidity of Negatively Curved Manifolds
- Math-4234 Ricci Flow of Anosov Metrics on Surfaces
- Math-4235 Convergence of Complex-Balanced Systems with Boundary Equilibria
- Math-4236 Polynomial-Rate Approximation of Stochastic Differential Equations
- Math-4237 Explicit Low-Discrepancy Sets and Efficient Dispersion
- Math-4238 Optimal Minimal Dispersion in High Dimensions
- Math-4239 Monotonicity Constants for Expected Random-Simplex Volumes
- Math-4240 Practical Criteria for Metrizable Universal Minimal Flows
- Math-4241 Cardinals Carrying Aronszajn Trees
- Math-4242 Eliminating Special Aronszajn Trees Along Radin Clubs
- Math-4243 Radin Forcing and Simultaneous Tree Properties
- Math-4244 Tree Property at Successors of Countable Limit Alephs
- Math-4245 Meager Ideal Equalities at Uncountable Regular Cardinals
- Math-4246 Smooth Moduli Spaces of Tame Algebras
- Math-4247 Optimal Degree Bounds for Sum-of-Squares Representations
- Math-4248 Certificates of Global Optimality for Thomson Configurations
- Math-4249 Bounding Generic Completion Rank by Maximum-Likelihood Threshold
- Math-4250 Colin de Verdière Invariants and Four-Dimensional Panellings