EVENT DETAILS AND ABSTRACT

Title: The many uses of saddle connections
Speaker: Andrew Neitzke
Speaker Info: University of Texas, Austin
Brief Description:
Special Note:
Abstract:

Saddle connections are certain geodesic trajectories on Riemann surfaces which have been studied for some time, e.g. in Teichmüller theory and the theory of billiards. In joint work with Davide Gaiotto and Greg Moore we have found that these objects also appear in a wide range of other contexts. For example:

1. they are a key ingredient in the construction of hyperkähler metrics on complex integrable systems (Hitchin systems),
2. they control the analysis of certain families of ordinary differential equations (e.g. the semiclassical analysis of Schrödinger-type equations),
3. they provide simple examples of “Donaldson-Thomas invariants” as considered by algebraic geometers,
4. they correspond to the “mutations” which appear in some examples of the theory of cluster algebras.

I will give an overview of these developments, and (briefly) some new generalizations thereof.