We meet (online) every other Thursday at 1pm (Mexico City/Central time). If you'd like to participate, please contact Bernardo Villarreal (villarreal at matem dot unam dot mx) so we can add you to our email list. A link to the meeting will be sent the day of the talk.
Feb 18. Simon Gritschacher, University of Copenhagen
Title: On the second homotopy group of spaces of commuting elements in Lie groups
Abstract: In this talk we will consider the topological space of n-tuples of pairwise commuting elements in a Lie group G. This space arises as a moduli space of flat connections on principal G-bundles over the n-torus. We will describe homotopy and homology calculations. One of our main results is the description of the second homotopy group of the space of commuting pairs in any compact Lie group. The connection with gauge theory will be discussed. This is joint work with Alejandro Adem and José Manuel Gómez.
Mar 4. Sam Nariman, Purdue UniversityTitle: Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups
Abstract: I will discuss a remarkable generalization of Mather’s theorem by Thurston that relates the identity component of diffeomorphism groups to the classifying space of Haefliger structures. The homotopy type of this classifying space plays a fundamental role in foliation theory. However, it is notoriously difficult to determine its homotopy groups. Mather-Thurston theory relates the homology of diffeomorphism groups to these homotopy groups. Hence, this h-principle type theorem has been used as the main tool to get at the homotopy groups of Haefliger spaces. We talk about generalizing Thurston's method to prove analogue of MT for other subgroups of diffeomorphism groups that was conjectured to hold. Most h-principle methods use the local statement about M=R^n to prove a statement about compact manifolds. But Thurston's method is intrinsically compactly supported method and it is suitable when the local statement for M=R^n is hard to prove. As we also shall explain Thurston's point of view on this "local to global" method implies non abelian Poincare duality.
Mar 18. Alexander Kupers, University of Toronto
Title: E_2-algebras and the unstable homology of mapping class groups
Abstract: We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.
Apr 15. Kristine Bauer, University of Calgary
Apr 29. Rachael Boyd, Max Planck Institute for Mathematics
May 13. Jeffrey Carlson, Imperial College London
May 27. Mona Merling, University of Pennsylvania
Jun 10. Dan Petersen, Stockholm University
Jun 24. Calista Bernard, Stanford University