Time：10:00-11:30, Wednesday, February 4 2026
Venue：E14-212
Host：Xin Fu, ITS
Speaker：Pengfei Huang, Nanjing University
Title：Symmetric spaces for groups over involutive algebras and applications
Abstract：Symplectic groups and (indefinite) orthogonal groups over noncommutative involutive algebras provide new way of realizing classical Lie groups. When in particular, the involutive algebra is Hermitian or the complexification of a Hermitian algebra, one can identify the corresponding maximal compact subgroups. This new perspective allows for the realization of various geometric models for the symmetric space of these groups. In this talk, we will try to illustrate such ideas and describe the tangent spaces for each of the models, as well as the application to Higgs bundles. If time permits, we will also talk about the description of Hitchin morphisms in terms of models. This is a joint work with Kydonakis, Rogozinnikov and Wienhard.
