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-2251 Wikipedia geometry item 14: Nagata–Biran conjecture that if $X$ is a smooth algebraic surface and $L$ is an ample line bund…
- Math-2252 Zariski multiplicity conjecture on the topological equisingularity and equimultiplicity of varieties at singular points
- Math-2253 Finding matching upper and lower bounds for k-sets and halving lines
- Math-2254 Automorphism Problem for the Turing Degrees
- Math-2255 Shelah's categoricity conjecture for $L_{\omega_1,\omega}$
- Math-2256 Shelah's eventual categoricity conjecture
- Math-2257 Soft Phases in Two-Dimensional O(N) Models
- Math-2258 Long-Range Order for the Quantum Heisenberg Model
- Math-2259 Extended States with Extensive Disorder
- Math-2260 Localization in Two Dimensions
- Math-2261 Bounded Excess Electrons
- Math-2262 Asymptotics of Atomic Ionization Energy
- Math-2263 One-Dimensional Lieb-Thirring Constants
- Math-2264 Mutually Unbiased Bases in Dimension Six
- Math-2265 Finiteness of a Shafarevich–Tate group needed by the lifting method
- Math-2266 The density hypothesis for zeroes of the Riemann zeta function
- Math-2267 Generalized Riemann hypothesis for Selberg class
- Math-2268 Zilber–Pink conjecture
- Math-2269 No critical infinite cluster on transitive graphs
- Math-2270 Absence of bigeodesics in first-passage percolation
- Math-2271 5.16 (Walsh) — Hyperbolic groups with Kleinian-type boundaries
- Math-2272 Problem 2 — (Billiards in general polygons).
- Math-2273 Major problems 5 — The chromatic splitting conjecture, which is considerably more complicated to state.
- Math-2274 Morava K- and E-theory 1 — Show that pi_* L_K(n) S^0 is finitely generated over the p-adics in each degree.
- Math-2275 Morava K- and E-theory 5 — Find the shadow of the thick subcategory theorem in the K(n)-local category.
- Math-2276 Rationally connected irrational varieties with property (*)
- Math-2277 A transcendental-rank obstruction to surface hosts
- Math-2278 A cyclotomic resolution-Betti obstruction for the global canonical index
- Math-2279 A new-Lefschetz defect reduction for rational Hodge pairings
- Math-2280 A classwise CM implication and a one-product coniveau certificate
- Math-2281 Hot spots: high-dimensional refutation, product rules, and heat-flow quantifiers
- Math-2282 Lipschitz extension from Hilbert spaces into L1
- Math-2283 Finite-dimensional embeddings of doubling Hilbert subsets
- Math-2284 Higher-dimensional quantitative bi-Lipschitz parameterization and a scalar-curvature obstruction
- Math-2285 Correlation cancellation for multiplicative functions
- Math-2286 GPY lower bounds and distances between Gaussian primes
- Math-2287 Steinitz prefix bounds for arbitrary norms
- Math-2288 Cycle--clique Ramsey numbers and an endpoint-fan certificate
- Math-2289 A four-point Hamming barrier in Euclidean Ramsey theory
- Math-2290 Four concyclic points and bounded Euclidean Ramsey witnesses
- Math-2291 van der Waerden numbers and sparse forcing sets
- Math-2292 Polynomial growth of diagonal van der Waerden numbers
- Math-2293 Finite-field factorization and sparse-polynomial root testing
- Math-2294 Prime-factor advice in power-residue quotients
- Math-2295 Three zeta-like products, degree-count inversion, and the factorization boundary
- Math-2296 Logarithmic Brunn–Minkowski inequality and equality cases
- Math-2297 Log-Minkowski inequality for symmetric convex bodies
- Math-2298 $L_p$ Brunn–Minkowski inequality for symmetric convex bodies
- Math-2299 An ultrafilter-free local criterion for O2-ultrapower embeddability
- Math-2300 Positive consistency of Naimark's problem and a local hereditary reduction