Time：9:00-10:45, Thursday, Sep 8, 2022
ZOOM ID: 849 5118 4197
PASSCODE: 073628
Host: Dr. Chuanhao Wei, Institute for Theoretical Sciences, Westlake University
Speaker：Prof. Chenyang Xu, Princeton University
Title：K-stability and birational geometry
Abstract: The notion of K-stability for a Fano varieties was introduced by Tian in late 90s, to capture the existence of a Kähler-Einstein metric. A few years later, Donaldson showed it is an algebraic notion. In the last decade, it has gradually become clear to algebraic geometers that K-stability provides a rich algebraic theory in higher dimensional geometry. In particular, it can be used to solve the longstanding question of constructing moduli spaces for Fano varieties.
In the first part of the talk, Prof. Xu will survey the background of K-stability and how algebraic geometers' understanding of it has evolved. In particular, he will explain algebraic geometry plays a key role of establishing the equivalence between K-stability and the existence of a Kähler-Einstein metric, i.e. the Yau-Tian-Donaldson Conjecture, for all Fano varieties. In the second part, Prof. Xu wants to focus on the construction of moduli spaces, and explain how the recipe given by K-stability can be used to resolve the issues that mystify people for a long time.
