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problems
Sharp global and almost-everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations, settling the sharpness question left open by the first-order theory.
For a measurable set Ω⊂ R^3, let E(Ω)=P(Ω)+frac12iint_Ω×Ωdx dy/|x-y|, where P is De Giorgi perimeter, and set V_*=5frac2-2^2/32^2/3-1≈3.51. The conjecture asks for the complete fixed-volume minimization picture. Chodosh and Gianocca prove…
Define φ_k(n) = ∑_1 ≤ a ≤ n, (a,n)=1 a^k and D_s = k ≥ s : φ_s(n) | φ_k(n) for every n. Is D_1 = 1, 3, 15, as conjectured by Büyükaşik and collaborators?
For a designated face of an undirected unweighted planar graph, how many distinct distance patterns can vertices have? Li and Parter (STOC 2019) proved an upper bound; Mozes, Wallheimer and Weimann conjectured the true answer matches their…
A polynomial-time algorithm for computing an optimal committee under any Thiele voting rule on the Voter Interval domain, resolving a ten-year-old open problem posed for Proportional Approval Voting by Elkind and Lackner and later extended…
Does the analytic Bertini restriction theorem for multiplier ideals hold locally, outside a pluripolar exceptional set of fibers? Proved in full generality.
What is the minimax optimal error rate for density estimation when observations are perturbed by Wasserstein-bounded contaminations? Chao and Dobriban's 2023 preprint left a gap between upper and lower bounds; the sharp rate is now…
Can a noetherian ring have a local cohomology module whose support is not closed - equivalently, one with infinitely many minimal primes? Huneke and Lyubeznik asked; the paper constructs such rings, so the answer is yes.
An asymptotic formula for p(k), the limiting probability that a random permutation has an invariant set of size k: it is asymptotically k^-δ(1+o(1)) times a smooth positive function, sharpening a line of estimates running through…
Denjoy's 1932 theorem says a C^1+bv circle diffeomorphism with irrational rotation number has no wandering interval. Whether it is sharp in regularity: for every concave modulus of continuity ω weaker than Lipschitz, there is a C^1+ω…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
In the list update problem, is the simple transposition rule optimal under IID requests? The question traces to Rivest's 1976 study of self-organizing lists. The paper proves transposition is within a small constant factor of the optimal…
Erdos Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system. The answer is exactly the class generated from private-vertex expansions of finite bipartite graphs by finite disjoint unions and…
Treglown conjectured, in a complementary form, that for every positive integer k every digraph D with mind^+(v), d^-(v) ≤ k-1 for all v has an equitable acyclic k-colouring. This implies the acyclic colouring versions of the…
Whether perfectly complete quantum key agreement can be built from quantumly secure one-way functions in a black-box way. It cannot: for any protocol where Alice and Bob exchange only classical messages, make at most q_A and q_B quantum…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of L_p(L_1) as a prominent remaining open…
The realisation problem asks which unital Banach algebras arise as the Calkin algebra B(X)/K(X) of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be…
Given online vectors v_t ∈ R^d with |v_t|_2 ≤ 1, can signs ε_t ∈ -1, 1 be chosen in O(dT) total time so that every prefix has ℓ_∞ discrepancy O(√log T) with high probability? The previous optimal algorithm ran in time exponential in T and…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.