Finite Generation and K-Stability

Explore a lecture on finite generation and K-stability presented by Ziquan Zhuang from the Massachusetts Institute of Technology. Delve into recent advancements in birational geometry, focusing on the finite generation property of valuations and its relationship to key questions in K-stability. Examine the connections to the Yau-Tian-Donaldson conjecture and the K-moduli conjecture. Gain insights into the algebraic conditions that characterize solutions to the Kähler-Einstein problem on Fano varieties. This talk serves as the second part of a joint presentation with Chenyang Xu, offering a comprehensive look at cutting-edge research in algebraic geometry and complex differential geometry.