Chennai Mathematical Institute


3.30 p.m., Seminar Hall
Higgs bundles and higher Teichmueller spaces

Oscar Garcia-Prada
ICMAT, Madrid.


It is well-known that the Teichmueller 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 into PSL(2,R) --- a component consisting entirely of Fuchsian representations. Higher Teichmueller spaces correspond to special components of the moduli space of representations when one replaces PSL(2,R) by a non-compact semisimple real Lie group of higher rank. The representations in these components share a number of properties with the Fuchsian ones in the PSL(2,R) case. In this talk, we will describe several classes of groups for which these spaces have been identified using Higgs bundle theory. We will finish by briefly commenting on the conjectural general picture.