Brendon Rhoades: Quotient rings and shadow play

Abstract: The Schensted correspondence is a fundamental bijection between permutations of size $n$ and pairs of $n$-box standard Young tableaux of the same shape. We describe a quotient ring whose standard monomial theory encodes the Viennot shadow formulation of the Schensted correspondence. This quotient ring is obtained by applying the orbit harmonics method to the locus of $n$-by-$n$ permutation matrices; we outline what happens when one uses other matrix loci. The orbit harmonics quotients are related to old and new equivariant log-concavity conjectures.