Peter Gothen

Departamento de Matemática Pura, Universidade do Porto

Classification of surface group representations.
We study representations of the fundamental group of a closed oriented surface of genus $g \geq 2$ in a non-compact Lie group $G$. Two such representations are said to be deformation equivalent if there is a continuous path of representations joining them. We explain an approach to determine when two such representations are equivalent in the case when the quotient of $G$ by its maximal compact subgroup is an hermitian symmetric space. Our approach is analytic in nature and exploits the relation between surface group representations and Higgs bundles on Riemann surfaces.