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-4101 Kernel Presentation for Multiple Eisenstein Relations
- Math-4102 Rational Dimensions of Critical Modular $L$-Values
- Math-4103 Algebraicity Under Central-Binomial Untwisting
- Math-4104 Socles of Products from Lusztig Components
- Math-4105 Homological Interpretation of Semidistributive Rowmotion
- Math-4106 Connectivity of Cluster-Tilting Exchange Graphs
- Math-4107 Common Refinements of PL-Homeomorphic Simplicial Complexes
- Math-4108 Thiagarajan Grid-Free Decidability Conjecture
- Math-4109 Wall Structures on Symmetric-Group Cayley Graphs
- Math-4110 Hilbert-Space Coarse Embeddings of Coarse Median Spaces
- Math-4111 Metric Properness of Wreath-Product Actions on Median Graphs
- Math-4112 Median Actions and Kazhdan Property for Brin Group 2V
- Math-4113 Hyperbolic Cubulability, Residual Finiteness, and Local Medianity
- Math-4114 Cubulability and Residual Finiteness of Hyperbolic Groups
- Math-4115 Cartan-Hadamard Theorem without Uniform Local Medianity
- Math-4116 Asymptotic-Cone Characterization of Hierarchically Hyperbolic Spaces
- Math-4117 Property T for Random Free-Product Quotients above One-Third Density
- Math-4118 Blowup Residues, Stability, and Rates for Mass-Critical gKdV
- Math-4119 Higher Sobolev Norm Growth for Half-Wave Maps
- Math-4120 Metastability and Massive-Arratia Limits for Weakly Interacting Diffusions
- Math-4121 Abstract Cohomology of Pro-$p$ Groups in Cross Characteristic
- Math-4122 $E_\infty$ Structures from Frobenius Lifts
- Math-4123 Splitting Projective Modules with Vanishing Top Chern Class
- Math-4124 Odd-Dimensional Projective-Module Splitting
- Math-4125 Automorphisms of Rational Surfaces with Antipluricanonical Curves
- Math-4126 Commuting Locally Nilpotent Derivations Conjecture
- Math-4127 Automorphisms of Weyl-Algebra Automorphism Groups
- Math-4128 Birational Asymmetry Between Representations and Their Duals
- Math-4129 Birational Equivalence of Twisted Algebraic-Group Representations
- Math-4130 Cayley Degrees of Simple Algebraic Groups
- Math-4131 Reconstructing Complete Local Rings from Finite Quotients
- Math-4132 Agreement of Mean Curvatures on Overlapping Varifolds
- Math-4133 Nonnegativity in Complete Indices of Bruhat Intervals
- Math-4134 Face Bounds for Minkowski Sums of Polytopes
- Math-4135 Clustered Colorings of Triangulated Grids
- Math-4136 Embedding Obstructions from Missing Simplicial Faces
- Math-4137 Neighborliness of Centrally Symmetric Polytopes
- Math-4138 Facial Structure of Intersections of Unit Balls
- Math-4139 Relevant Islands in the Parabolic Anderson Model
- Math-4140 Conformal Type of Surfaces Spread over the Sphere
- Math-4141 Universal Holomorphic Functions under Composition Operators
- Math-4142 Completely Invariant Julia Sets of Rational Semigroups
- Math-4143 Minimal Rational Curves on Almost Homogeneous Varieties
- Math-4144 Kawaguchi–Silverman Arithmetic Degree Conjecture
- Math-4145 Root Separation and Rational Values of Littlewood Polynomials
- Math-4146 Torsion Specializations of Sections of Abelian Schemes
- Math-4147 Northcott Property for Rings of Integers in Bounded-Degree Composita
- Math-4148 The Dynamical Mordell–Lang Conjecture for Endomorphisms
- Math-4149 Uniform Lower Bounds for Specialized Canonical Heights
- Math-4150 Distinct Number Fields from Fibers of Rational Functions