Compactification of moduli spaces of representations

June 11-18 2017

Organizers: Brian Collier, Giuseppe Martone and Jérémy Toulisse.

We will study the different compactifications of moduli spaces of representations of surface groups into reductive Lie groups. After focusing on the different tools to compactify SL(2) character variety (Thurston compactification, Morgan-Shalen compactification, geodesic currents, limit of grafting and degenration of harmonic maps), we will focus on the current developement of these tools for higher rank Lie groups (tropicalization of coordinates, compactifications by action on buildings...). Each participant will give a 2h30 lecture on a topic that will be assigned before the workshop.

This Log Cabin workshop is based on the previous ones organized thanks to the GEAR network:

Workshop on Sp(4,R)-Anosov representations (2016)

Workshop on Higgs bundles and harmonic maps (2015)

Workshop on Higher Teichmüller theory (2013)

Here are the notes from the workshop.

Scientific Program:

Lie theory and symmetric spaces (Alexis Gilles)

The different compactifications of Teichmuller spaces: an overview (Sara Maloni)

Morgan-Shalen compactification of character varieties (Léo Bénard)

Limits of grafting (Ellie Dannenberg)

Buildings and limits of symmetric spaces (Qiongling Li)

Compactifications via affine buildings (Beatrice Pozzetti)

Tropical compactifications of character varieties (Daniele Alessandrini)

Higher lamination and tropicalization “à la Fock and Goncharov” (Tengren Zhang)

Loftin’s degenerations of projective structures (Xin Nie)

Degeneration of harmonic maps (Nicolas Tholozan)

Bordification of the moduli space of Higgs bundles (Laura Fredrickson)

Limits of opers as a generalization to grafting (Andy Sanders)

Participants:

Daniele Alessandrini

Léo Bénard

Brian Collier

Xian Dai

Ellie Dannenberg

Laura Fredrickson

Alexis Gilles

Qiongling Li

Brice Loustau

Sara Maloni

Giuseppe Martone

Xin Nie

Charles Ouyang

Beatrice Pozzetti

Andrew Sanders

Nicolas Tholozan

Jérémy Toulisse

Tengren Zhang