ABSTRACT

Finding Kähler-Einstein (KE) metrics on algebraic varieties has been an intense topic of research for decades. For varieties with non-positive first Chern classes, the existence of KE metrics goes back to the work of Aubin and Yau. The situation is more subtle when the first Chern class is positive, and in this case the Yau-Tian-Donaldson conjecture predicts that the existence of KE metrics is equivalent to a purely algebro-geometric stability condition (so-called K-stability) of the varieties. This conjecture was confirmed in the smooth case by Chen-Donaldson-Sun and Tian, and it remains a challenge to understand the singular case. In this talk, I'll explain why this conjecture is closely related to some finite generation problem in birational geometry and discuss some recent advances that in particular lead to a full solution of the conjecture. Based on joint work with Yuchen Liu and Chenyang Xu.

ZOOM INFO

ID: 615 1075 3736

Password: 617344

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https://zoom.com.cn/j/61510753736?pwd=UEZvMzhTbzQzWVppYzJaREUyeEJIdz09

BRIEF BIO

Ziquan Zhuang received his B.A. from Peking University in 2014 and Ph.D. from Princeton University in 2019. He is currently a CLE Moore instructor at MIT, working on birational geometry and K-stability.