Speaker: Teresa Yu
University of Notre Dame
Will give an Algebraic Geometry and Commutative Algebra Seminar entitled:
Module theory in infinite-dimensional equivariant commutative algebra
Abstract: A foundational result in equivariant commutative algebra is Cohen's theorem that the infinite variable polynomial ring R=C[x1, x2, x3,…] is Noetherian up to the action of the infinite symmetric group. This result has led to uniformity and finiteness theorems for finite-dimensional structures in algebraic geometry, statistics, and algebraic topology, and more generally motivates the study of the equivariant commutative algebra of R. In this talk, we will survey the module-theoretic aspects of this field, with particular emphasis on the infinite GL and symmetric group settings. Along the way, we will see how FI-modules, originally introduced in the context of representation stability, provide a useful bridge between finite-dimensional representation theory and infinite-dimensional equivariant algebra.
Date: 09-10-2026
Time: 3:30 pm
Location: 258 Hurley Hall