You are here

Stability in the homology of configuration spaces

Jenny Wilson, Stanford
Tuesday, March 7, 2017 - 1:30pm
PDL C-36
Pre-seminar
When: Tuesday March 7, 1:30--2:15
Title: Representation stability 
 
Abstract: In this introductory talk I will explain how we can use representation theory to illuminate the structure of certain families of groups and topological spaces with actions of the symmetric groups, using the concept of "representation stability" developed by Church, Ellenberg, Farb, and others.  The main motivating example will be the pure braid groups. The talk will address the questions, "What should it mean for a sequence of S_n--representations to stabilize?",  "How can I detect this stability?", and "Where does it show up in the wild?"   
 
Seminar
When: Tuesday March 7, 2:30--3:20
Title:  Stability in the homology of configuration spaces
 
Abstract: Let F_k(M) denote the space of ordered k-tuples of distinct points in a connected, open manifold M. For a fixed manifold M, as k increases, we might expect the homology of the configuration spaces F_k(M) to become increasingly complicated. Church and others showed, however, that given the appropriate algebraic framework, there is a representation-theoretic sense in which these homology groups stabilize.  In this talk I will explain these stability patterns, and describe higher-order "secondary stability" phenomena among the unstable homology classes established in recent work joint with Jeremy Miller. 
 
 
Event Type: 
Share