Algebra/Topology Seminar by Jeremy Miller

Talk by Jeremy Miller (Purdue University)

Title: Secondary representation stability and ordered configuration spaces

Abstract: I will describe a notion called secondary representation stability. In joint work with Jennifer Wilson, I proved that this phenomenon is present in the homology of ordered configuration spaces of non-compact surfaces. While representation stability in this context can be formulated in terms of stabilizing by bringing a particle in from infinity, secondary representation stability involves bringing in two particles which orbit each other. In particular, this stability pattern involves comparing homology groups in different homological degrees. This project can be thought of as a representation theoretic analogue of secondary homological stability in the sense of Galatius-Kupers-Randal-Williams.