Department of

Mathematics


Seminar Calendar
for events the day of Thursday, May 4, 2017.

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Thursday, May 4, 2017

12:00 pm in 243 Altgeld Hall,Thursday, May 4, 2017

The geometry of maximal SO(2,n) representations

Brian Collier   [email] (University of Maryland)

Abstract: Like Hitchin representations, the set of maximal representations of a surface group into a Lie group of Hermitian type form connected components of representations with Labourie's Anosov property. For such representations, Guichard and Wienhard have constructed geometric structures modeled on certain flag varieties. In this talk we will use Higgs bundle techniques to construct a unique maximal space-like surface in the pseudo-Riemannian hyperbolic space H2,n-1 associated to any maximal SO(2,n) representation. Using the geometry of this surface, we construct geometric structures on certain homogeneous bundles on the surface and prove that they agree with those of Guichard-Wienhard. As a corollary, we also prove (a generalization of) a conjecture of Labourie for all maximal representations into rank 2 Hermitian Lie groups.This is based on joint work with Nicholas Tholozan and Jérémy Toulisse.

1:00 pm in 314B Illini Union,Thursday, May 4, 2017

IGL Spring 2017 Open House

Abstract: The IGL end-of-semester Open House will take place from 1:00 pm to 4:00 pm in Room 314B Illini Union. Come see what the IGL teams have produced this semester! Please note change of location!

4:00 pm in 245 Altgeld Hall,Thursday, May 4, 2017

The L^2 metric on Hitchin’s moduli space

Rafe Mazzeo (Stanford)

Abstract: The much-studied moduli space of solutions to Hitchin’s equations on a Riemann surface carries a natural complete Weil-Petersson type metric. The large-scale structure of this metric is only now being revealed, first through an ambitious set of physics conjectures by Gaiotto-Neitzke-Moore, and now through techniques of geometric analysis. I will discuss this whole picture and report on recent work with Swoboda-Weiss-Witt.