New approach to character varieties: nilpotent is the new holomorphic

Series
Geometry Topology Seminar
Time
Monday, March 13, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alexander Thomas – U. Heidelberg – athomas@mathi.uni-heidelberg.dehttps://thomas-math.wixsite.com/maths/english-version
Organizer
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.