Jan 18, 2024
Higgs bundles and the topology of higher Teichmüller spaces
Algebraic Geometry and Number Theory Seminar
Date: January 18, 2024 |
1:00 pm –
3:00 pm
Speaker:
Oscar Garcia-Prada, ICMAT, Madrid
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Language:
English
It is well-known that the Teichmüller space of a compact surface can be identified with a connected component of the moduli space of representations of the fundamental group of the surface in PSL(2,R). Higher Teichmüller spaces are generalizations of this for certain non-compact real Lie groups of higher rank. Using the theory of Higgs bundles, we can exploit the non-abelian Hodge correspondence and the more recently obtained Cayley correspondence, to address the study of the topology of higher Teichmüller spaces. In particular, we will compute the intersection cohomology of certain singular higher Teichmüller spaces.
