MATH 7610: Seminar in Geometry (Fall 2011)

Instructor:Allen Hatcher, Peter Kropholler, and Allen Knutson

This course will consist of three independent mini-courses of 4-5 weeks each:

I. “Stable Homology by Scanning,” lectures by Allen Hatcher

The goal here will be Galatius’ theorem that the automorphism group of a free group has the same homology as the symmetric group, in a stable range of dimensions. En route: the Madsen-Weiss theorem on the stable homology of mapping class groups of surfaces.

II. “Invitations to Group Theory,” lectures by Peter Kropholler

Scheduled September 28 – October 31

We’ll make a group theoretic excursion starting with two beautiful theorems, one of John Wilson and one of Dave Witte Morris. The study will draw attention to connections with 3-manifold theory and the theory of right orderable groups.

III. “Representation Theory of Lie Groups,” lectures by Allen Knutson

Scheduled to start November 2

This will be from as topological a viewpoint as possible, and with an eye towards infinite-dimensional groups (e.g. Kac-Moody groups and Diff(S^1)).