# Spectral Networks

**Organizers:** François Labourie and Jérémy Toulisse.

The goal of this reading seminar will be to study the fundamental article ¨Spectral Networks¨ of the physicists Davide Gaiotto, Gregory W. Moore and Andrew Neitzke (and the articles related). Their work is a source of many conjectures.

A rank n spectral network on a surface S is a combinatorial object (roughly, a decorated graph). Such a spectral network allows to construct a desabelianization, that is, to associate a representation of the fundamental group of S into GL(n,C) to a (abelian) representation into GL(1,C) of a covering of S, called the spectral curve. This construction is related to many other constructions, such as:

No specific background will be needed to understand the lectures.

# Sessions:

**November 16th:**

**November 30th:**

**February 8th:**

- Jérémy Toulisse: Spectral Networks II
- François Labourie: Quadratic differentials, laminations, trees and compactification III

**March 29th:**

**April 26th:**

- Indira Chatterji: Introduction to buildings
- Carlos Simpson: WKB exponents and construction of a pre-building for SL(3)