Tuesday, November 7, 2017
2:45 pm
Building 15, Room 104 – Building 15

Geometry and Topology Seminar

Stability in the homology of configuration spaces
Jenny Wilson, Department of Mathematics, Stanford University

This talk will illustrate some topological properties of the space F_k(M) of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of the configuration spaces F_k(M) 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 configuration spaces stabilize. In this talk I will explain these stability patterns, and describe a higher-order "secondary representation stability" phenomenon among the unstable homology classes. These results may be viewed as a representation-theoretic analogue of current work of Galatius–Kupers–Randal-Williams. The project is joint with Jeremy Miller.

Contact Mathematics Department mathinfo@caltech.edu at 626-395-4335
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