## Department Colloquium

### Wednesday, November 22nd, 2017

**Time:** 3:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Jenny Wilson

**Title:** Dynamics, geometry, and the moduli space of Riemann surfaces

**Abstract:** The ordered configuration space $F_k(M)$ of a manifold M is the space of ordered k-tuples of distinct points in M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which these spaces stabilize. In this talk, I will explain these stability patterns, and describe higher-order stability phenomena established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

**Jenny Wilson (Stanford University):** Jenny Wilson obtained her B.Sc. (with Honours) in Mathematics from Queen's University in 2009, and her Ph.D. in Mathematics from the University of Chicago in 2014. She then joined Stanford University, where she is Szego Assistant Professor. The awards received by Dr. Wilson while at Queen's University include the Irene MacRae Prize in Mathematics and Statistics, the Medal in Mathematics and Statistics, the Governor General's Academic Silver Medal, and the NSERC Undergraduate Student Research Award, all in 2009. She also received two NSERC Postgraduate Fellowships (PGS M in 2009-2010 and PGS D in 2011-2014), the McCormick Fellowship (2009-2011), the Lawrence and Josephine Graves Teaching Prize at the University of Chigago (2013), and the AMS-Simons Travel Grant (2015-2018). Jenny Wilson's research involves applications of commutative algebra and representation theory to study algebraic structures in topology and geometric group theory. In recent work, she has investigated

con guration spaces of points in a manifold, Torelli groups, and certain congruence subgroups.