This paper constructs an epsilon-cover of the joint value set of m constant-degree polynomials over a convex set H in the linfty-norm, with size n^(O(log(mn)/ε^2)), given that the polynomials have a c…

The paper explains a method for finding the number of solutions to a system of multivariate polynomial inequalities over a finite field and applies it to find formulas for the number of contiguous sup…

This paper studies set-defined graph classes and proves that bounded unions of shift-colorable graphs form the fundamental obstruction to chromatic number boundness in these classes.

The paper develops an explicit multi-linear polynomial form for binary polynomial optimization problems after eliminating a subset of variables, allowing for characterization of new special classes wi…

This paper studies the existence of polynomial measures of dependence between two random variables that satisfy the data processing inequality and vanish on independence. It proves that no such polyno…

The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the…

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

The paper formalizes Razborov's flag algebra method for finite simple graphs and creates a compiler to transform certificate data into algebraic proofs checked by Lean.

This paper presents a quantum attack on Module-LWE based lattice schemes like ML-KEM, demonstrating a polynomial-time quantum algorithm with a high success probability.

The paper studies the resources required to batch verify Boolean functions and provides lower bounds on the witness-query tradeoff based on approximate degree.

This paper introduces a robust OR polynomial framework to derive certificates for positive semidefinite matrices across OR constraints, and applies it to acute-free families and multicolor Ramsey numb…

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper studies ranking and aggregation under Kendall tau distance with matroid or flag matroid constraints on prefixes.