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