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…

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…

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 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…

This paper simplifies the proof of the bound on the target dimension for reducing the dimension of high-dimensional polygonal curves using random projections, extending it to various distance measures…

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…

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

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…

This paper proves that single-vector embeddings require a larger representation size than multi-vector embeddings to approximate certain similarities.

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.

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

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…

This paper presents conditions for achieving optimal uniformity in Quasi-Monte Carlo estimators using Sobol' sequences and Artin-Schreier polynomials.

This paper identifies a technical oversight in Mossel and Peres (2005) theorem on designing Bernoulli factories for multivariable functions and provides a counterexample.