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Alexander Thomas, PMA 9.166 : New approach to character varieties: nilpotent is the new holomorphic
Thursday, March 23, 2023, 03:30pm - 04:30pm
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, Alex Nolte and Charlie Reid.
Location: PMA 9.166

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