Brendon Rhoades, UC, San Diego

Abstract: Let $x$ be an $n \times n$ matrix of variables and let S be the polynomial ring in these variables over a field. Inspired by the Permuted Kernel Problem in cryptography, we introduce a quotient $S/I$ of $S$ by a homogeneous ideal $I$ generated in degrees 1 and 2 which has surprising connections to increasing subsequences in permutations. We describe connections between $S/I$ and log concavity conjectures of Chen and Novak-Rhoades.