Speaker: Prof. Laura Schaposnik (University of Illinois at Urbana-Champaign)
I. An introduction to Higgs bundles
-16:00-17:00, November 3, 2014
We shall introduce classical Higgs bundles and their moduli space from a geometric and Lie theoretic point of view, motivating their study through representation theory. Then, we will extend these concepts to Higgs bundles whose structure group are complex Lie groups, as well as real forms, and finalize by introducing the Hitchin fibration of the moduli space of Higgs bundles.
II. Spectral data for complex Higgs bundles
-15:30-16:30, November 4, 2014
Spectral data has been used for many years to study Higgs bundles whose structure groups are complex Lie groups. During the talk we shall recall these constructions for Higgs bundles whose structure groups are classical complex Lie groups, and mention how Langlands duality can be seen through this description of the fibres of the Hitchin fibration as abelian varieties.
Ⅲ. Spectral data for complex Higgs bundles
-13:00-14:00, November 5, 2014
By looking at real Higgs bundles as fixed points of certain involution on the moduli spaces of complex Higgs bundles, one is able to obtain define spectral data, leading to geometric interpretations of the moduli spaces. We shall dedicate this lecture to the study of spectral data for real Higgs bundles, in particular, showing how one gets a finite covering of the Hitchin base for split real forms, and how in other cases the fibres are non-abelian spaces.
Ⅳ. Spectral data for complex Higgs bundles -15:30-16:30, November 6, 2014
Ⅳ. Spectral data for complex Higgs bundles
-15:30-16:30, November 6, 2014
-The details will be posted.
Place: Room 404, Math Science bldg.
Date: November 3-6, 2014