Speaker: Robin Deeley (U Colorado)

Title: Minimal dynamical systems

Abstract: A self-homeomorphism of a compact Hausdorff space is called minimal if each of its orbits is dense. I will discuss the following question: given a compact Hausdorff space does there exist a minimal homeomorphism on it? Although the answer is no, a similar question has a positive answer for any finite CW-complex. I will also discuss a number of explicit examples of minimal dynamical systems. All of our constructions are motivated by questions in C*-algebra theory. Nevertheless no knowledge of C*-algebras is required for the talk. This is joint work with Ian Putnam and Karen Strung.

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.