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Abstract: Over the past decade, a local theory of K-stability for Kawamata log terminal (klt) singularities has emerged. This theory studies minimizers of a normalized volume function and associates a K-semistable Fano cone to any given klt singularity. In many cases, this construction significantly generalizes the notion of the metric tangent cone for singular Kähler–Einstein spaces. The lecture is intended for a broad mathematical audience.
Bio: Chenyang Xu, born in 1981 in Chongqing, China, is a distinguished mathematician specializing in algebraic geometry. After earning his Ph.D. from Princeton University in 2008 under the mentorship of János Kollár, Xu held academic positions at institutions including MIT, the University of Utah, and Peking University, before returning to Princeton as a professor. His research focuses on birational geometry, the minimal model program, and the K-stability of Fano varieties. Xu's contributions have been recognized with several prestigious awards: the 2016 ICTP Ramanujan Prize for his work in birational geometry, the 2017 Future Science Prize in Mathematics and Computer Science for fundamental contributions to the field, the 2019 New Horizons in Mathematics Prize for advances in the minimal model program and moduli of algebraic varieties, and the 2021 Frank Nelson Cole Prize in Algebra for developing an algebraic theory of moduli for K-stable Fano varieties and pioneering new approaches to singularities in the minimal model program using K-stability. He was also an invited speaker at the 2018 International Congress of Mathematicians (ICM).
