YMSC Topology Seminar | The equicritical stratification and stratified braid groups

Abstract：

Thinking about the configuration space of n-tuples in the complex plane as the space of monic squarefree polynomials, there is a natural equicritical stratification according to the multiplicities of the critical points. There is a lot to be interested in about these spaces: what are their fundamental groups (“stratified braid groups”)? Are they K(pi,1)’s? How much of the fundamental group is detected by the map back into the classical braid group? They are also amenable to study from a variety of viewpoints (most notably, they are related both to Hurwitz spaces and to spaces of meromorphic translation surface structures on the sphere). I will discuss some of my results thus far in this direction. Portions of this are joint with Peter Huxford.

Speaker

My work lies at the juncture of geometry/topology, geometric group theory, and complex algebraic geometry. I study the connections between mapping class groups (including braid groups), some closely-related topological spaces (surface bundles and configuration spaces), and moduli spaces of Riemann surfaces and Abelian differentials.