course: Minimal surfaces and Hitchin components.
speaker: Francois Labourie (Université Paris-Sud 11, Orsay, Paris)abstract: As a generalisation of results for SL(3,R) (proved independently by the author and Loftin) and for SL(2,R)xSL(2,R) (Schoen), I will explain that for any rank 2 semisimple split real group G and any Hitchin representation rho in G, there exists a unique rho-equivariant minimal surface in the corresponding symmetric space. As a corollary all the corresponding Hitchin components are parametrised; in a mapping class group invraiant way, by a pair (J,Q) where J is a complex structure on the surface and Q a holomorphic differential. A weaker result subsist for general cyclic Higgs bundles as introduced and studied by Baraglia. I will start by explaining what is a Higgs bundle, and I will also explain basic Lie Theory. A basic knowledge of Lie groups (not assuming root theory) will be appreciated.
timetable:
Tue 3 Jun, 11:30 - 12:30, Aula Dini
Wed 4 Jun, 11:30 - 12:30, Aula Dini
Thu 5 Jun, 11:30 - 12:30, Aula Dini
Thu 5 Jun, 16:15 - 17:15, Aula Dini
Fri 6 Jun, 9:00 - 10:00, Aula Dini
documents:
LABOURIE - Introduction to Higgs bundles
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