Peking University, November 16, 2020: The 2021 Frank Nelson Cole Prize in Algebra is awarded to Xu Chenyang, an alumnus of the School of Mathematical Sciences at Peking University. He leads a group developing an algebraic theory of moduli for K-stable Fano varieties and working out a radically new approach to the singularities of the minimal model program using K-stability.
Xu’s (single-authored) paper “A minimizing valuation is quasi-monomial” proves a conjecture of Jonsson and Mustaţă on log canonical thresholds and also a conjecture of Li Chi on normalized volumes. In a series of papers with various coauthors (in particular, the papers “Boundedness of moduli of varieties of general type” with Hacon and McKernan and “Uniqueness of K-polystable degenerations of Fano varieties” with Blum), new powerful methods were introduced, and they established a general framework for moduli of K-stable Fano varieties and gave detailed descriptions in many cases. This opens up a completely new area of moduli theory, which earlier was assumed to apply only to general type and Calabi-Yau varieties. This can be viewed as a vast expansion of the minimal model program initiated by Shigefumi Mori.
Xu Chenyang was born in Chongqing, China, in 1981. He did his undergraduate studies at Peking University and his graduate studies at Princeton University, with János Kollár. He held a postdoctoral position at the Massachusetts Institute of Technology (MIT). Xu was hired as a junior faculty at the University of Utah in 2011. He joined the Beijing International Center for Mathematical Research at Peking University in 2012 and was promoted to professor there in 2013. In 2018, he moved to MIT, and in 2020 he became a professor at Princeton University. Xu’s main research area is the birational geometry of higher dimensional algebraic varieties, and he likes to explore its connections to other fields.
The Cole Prize in Algebra is awarded every three years for a notable research memoir in algebra that has appeared during the previous six years. This prize and the Cole Prize in Number Theory were established in 1928 to honor Frank Nelson Cole (1861–1926) on the occasion of his retirement as secretary of the AMS after 25 years of service.