Wednesday March 29th, 2023 | |
| Time: | 1:00 PM - 2:30 PM |
| Title: | From complex to non-Archimedean geometry - and back: Lecture 2: Pluripotential theory and the YTD conjecture |
| Speaker: | Sebastien Boucksom, Sorbonne Universite |
| Location: | SCGP 102 |
| Abstract: | |
| The general purpose of this series of lectures is to illustrate the use of non-Archimedean geometry in the study of complex geometric objects in the large (logarithmic) scale, first in the classical finite-dimensional setting of Geometric Invariant Theory (GIT), and then in the infinite-dimensional context of the Yau-Tian-Donaldson (YTD) conjecture. The first lecture will be devoted to the large scale geometry of spaces of norms, and their relation to GIT and the classical Hilbert-Mumford criterion. The second lecture will review the fundamental ingredients in the variational approach to the YTD conjecture, emphasizing the geometric properties of the space of Kähler potentials and its completion. Finally, the third lecture will introduce the non-Archimedean counterparts to these spaces, their relation to K-stability, and their use in the recent progress accomplished towards the general case of the YTD conjecture. | |