Mathematics Seminar
Date: Wednesday, 8 January 2025
Time: 3:30 PM
Venue: Seminar Hall
Non-maximal Toledo components
Oscar Garcia-Prada
ICMAT, Madrid.
08-01-25

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Abstract

The well-known Milnor-Wood inequality gives a bound on the Toledo invariant of a representation of the fundamental group of a compact surface in a group of Hermitian type. While a lot is known regarding the counting of maximal Toledo connected components, and their role in higher Teichmueller theory, the non-maximal case remains elusive. Exploiting the non-abelian Hodge correspondence and the theory of Higgs bundles, in this talk, I will present a strategy to count the number of such non-maximal Toledo components. This is joint work with Brian Collier and Jochen Heinloth.