Speaker: Rohit Nagpal (U. Wisconsin)
Title: S_{infty}-equivariant modules over polynomial rings in infinitely many variables

Abstract: Let R be the polynomial ring k[x_1, x_2, ldots] in countably many variables. Cohen proved that S_{infty}-stable ideals in R satisfy the ascending chain condition. This makes the category of smooth equivariant R-modules a noetherian category. Smooth modules over R appear naturally in algebraic statistics and chemistry, and so it makes sense to study this category in detail. The first step in this direction is to understand its spectrum. In this talk, we describe this spectrum. In particular, we show that the S_{infty}-stable ideal I_n generated by n-variable discriminants is in this spectrum. We show that every nonzero S_{infty}-stable ideal must contain I_n for some large n, and so these ideals are of primary interest. We also mention some new algebraic properties of discriminants. This is a part of an ongoing project with Andrew Snowden.