Relative character varieties and parabolic Higgs bundles

February 23 to March 3 2018

Organizers: Nicolas Tholozan, Jérémy Toulisse and Tengren Zhang.

We will study the relative character varieties of surface groups into reductive Lie groups, that is, the representations of the fundamental group of a punctured surface with prescribed holonomy at the punctures. After focusing on the Teichmüller theory for punctured surfaces, we will study the theory of harmonic maps from non-compact surfaces. We will then study the non-Abelian Hodge correspondence for parabolic Higgs bundles (with logarithmic and higher order poles). 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:

Compactification of moduli spaces of representations (2018)

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

Workshop on Higgs bundles and harmonic maps (2015)

Workshop on Higher Teichmüller theory (2013)

Scientific Program:

Relative character varieties and their symplectic structure (Brice Loustau)

Coordinates on Teichmüller space of a punctured surface and its decoration (Federica Fanoni)

Hitchin representations for surfaces with boundary (Giuseppe Martone)

Bounded cohomology, Toledo invariant and maximal representations (Alexis Gilles)

Harmonic maps between surfaces with cusps, cones and funnels (Charles Ouyang)

Cubic differentials and convex projective structures with boundary (Dai Xian)

A review of the non-Abelian Hodge correspondance for closed surfaces (Xuesen Na)

Parabolic vector bundles and unitary representations (Brian Collier)

Non-abelian Hodge correspondance for non-compact surfaces (David Alfaya)

Parabolic Higgs bundles for representations into real Lie groups (Qiongling Li)

The relative PSL(2,R)-character varieties (Daniele Alessandrini)

Wild non-Abelian Hodge theory (Andy Sanders)

Participants:

Daniele Alessandrini

David Alfaya

Brian Collier

Federica Fanoni

Alexis Gilles

Johannes Horn

Qiongling Li

Brice Loustau

Giuseppe Martone

Xuesen Na

Charles Ouyang

Evgenii Rogozinnikov

Andy Sanders

Nicolas Tholozan

Jérémy Toulisse

Tengren Zhang

Dai Xian