#
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