Geometry Seminar

Date: October 26, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Dylan Allegretti , University of Sheffield

Title: The monodromy of meromorphic projective structures

Abstract: A projective structure on an oriented surface S is an atlas of charts mapping open subsets of S into the Riemann sphere. There is a natural map from the space of projective structures to the PGL(2,C) character variety of S which sends a projective structure to its monodromy representation. In this talk, I will describe a meromorphic analog of this construction. I will introduce a moduli space parametrizing projective structures with poles at a discrete set of points. I will explain how, in this setting, the object parametrizing monodromy data is a type of cluster variety. This is joint work with Tom Bridgeland.