New approach to character varieties: nilpotent is the new holomorphic

Geometry Topology Seminar
Monday, March 13, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Alexander Thomas – U. Heidelberg – athomas@mathi.uni-heidelberg.de
Alex Nolte

The study of representations of fundamental groups of surfaces into Lie groups is captured by the character variety. One main tool to study character varieties are Higgs bundles, a complex geometric tool. They fail to see the mapping class group symmetry. I will present an alternative approach which replaces Higgs bundles by so-called higher complex structures, given in terms of commuting nilpotent matrices. The resulting theory has many similarities to the non-abelian Hodge theory. Joint with Georgios Kydonakis and Charlie Reid.