Spaces of norms, geometric invariant theory and K-stability

Sebastien Boucksom, CNRS-CMLS, Ecole Polytechnique

Online Talk 

*Please note the change in time*

The space of Hermitian norms on a given complex vector space is a fundamental example of Riemannian symmetric space, whose geometry can be explicitly analyzed in terms of basic algebra; this includes its cone at infinity, which can be realized as a space of non-Archimedean norms. Such spaces, and convex functions thereon, naturally arise in the context of Mumford's geometric invariant theory, and the more recent algebro-geometric notion of K-stability. 

The purpose of this talk is to provide an elementary introduction to this circle of ideas, hinting at more recent developments related to the Yau-Tian-Donaldson conjecture.