Back to Departmental Colloquium: Fall 2009
Departmental Colloquium
Date: Thursday, Oct 29, 2009
Time: 4:15PM
Location: JWB 335
Oscar Garcia Prada
Consejo Superior de Investigaciones Cientificas
Title |
Geometry of surface group representations |
Abstract |
Given a compact real surface S and a semisimple Lie group G, we consider the moduli space R(S,G) of representations of the fundamental group of S in G (sometimes called the character variety). This moduli space plays a central role in many problems in geometry, topology and physics. By considering a complex structure on the surface S (thus making it a Riemann surface), the moduli space of representations is in bijection with a moduli space of holomorphic objects, known as Higgs bundles. We explain this correspondence and show how to use it to study the topology of R(S,G). We give special attention to the case where G is the isometry group of a non-compact Hermitian symmetric space. In this situation the moduli space has special components that can be regarded in some sense as generalizations of the Teichmueller space of S (which can be identified with a component of the character variety when G=PSL(2,R)). |
Representation Theory
Algebraic Geometry
Commutative Algebra