Meromorphic quadratic differentials and geometric structures on surfaces

Geometry & Topology
Event time: 
Monday, August 28, 2017 - 3:00pm to 4:00pm
431 DL
Subhojoy Gupta
Speaker affiliation: 
Indian Institute of Science
Event description: 

Let $Q(X)$ be the vector space of holomorphic quadratic differentials on a Riemann surface $X$ of genus greater than one. This parametrizes the following two spaces of geometric objects on the underlying topological surface $S$: First, by a theorem of Wolf, and independently Hitchin, $Q(X)$ provides a parametrization of marked hyperbolic structures, namely the Teichmuller space of S. Second, by a theorem of Hubbard and Masur, there is a bijective correspondence between $Q(X)$ and measured foliations on $S$. In this talk I shall describe generalisations of these results to the case when $Q(X)$ is replaced by the space of meromorphic quadratic differentials with poles of higher order. The proofs involve harmonic maps of infinite energy. Part of this is joint work with Michael Wolf.

Special note: 
Note unusual day