Abstract: 

The space of Hermitian norms on a given complex vector space is a fundamental example of symmetric space of nonpositive curvature. The purpose of this talk is to describe the geometry of this space using elementary linear algebra, to realize its asymptotic cone as a space of non-Archimedean norms, and to apply this in the context of Mumford's Geometric Invariant Theory.

Bio: 

Sebastien Boucksom is a French mathematician specializing in complex and non-Archimedean geometry. After defending his PhD thesis in 2002 under the supervision of Jean-Pierre Demailly, he became a CNRS Junior Researcher at the Institut de Mathematiques de Jussieu in 2003, then a CNRS Senior Researcher in 2014, first at the Ecole Polytechnique, and then at the Institut de Mathematiques de Jussieu since 2022. He was an invited speaker at the 2018 ICM in Rio.

Video: http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Spaces_of_norms_and_Geometric_Invariant_Theory.html