Zoom link:  https://princeton.zoom.us/j/91248028438

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The Hamilton-Tian Conjecture implies that any smooth complex Fano variety admits a degeneration to a Fano variety admitting a Kahler-Ricci soliton, which is a type of canonical metric. In this talk, I will discuss an algebraic analogue of this statement phrased in the language of K-stability. Applications of this result include (1) any possibly singular Fano variety admits a two step degeneration to a Fano variety admitting a Kahler-Ricci soliton and (2) the moduli theory of K-unstable Fano varieties. This talk is based on joint work with Yuchen Liu, Chenyang Xu, and Ziquan Zhuang.

The main results build on previous work of Han and Li and a recent finite generation result of Liu, Xu, and Zhuang.