Shou-Wu Zhang

Shou-Wu Zhang (born October 9, 1962) is a Chinese-American mathematician known for his work in number theory and arithmetic geometry.

He is currently a Professor of Mathematics at Princeton University.

Shou-Wu Zhang was born in Hexian, Ma'anshan, Anhui, China on October 9, 1962.

Zhang grew up in a poor farming household and could not attend school until eighth grade due to the Cultural Revolution.

He spent most of his childhood raising ducks in the countryside and self-studying mathematics textbooks that he acquired from sent-down youth in trades for frogs.

By the time he entered junior high school at the age of fourteen, he had self-learned calculus and had become interested in number theory after reading about Chen Jingrun's proof of Chen's theorem which made substantial progress on Goldbach's conjecture.

Zhang was admitted to the Sun Yat-sen University chemistry department in 1980 after scoring poorly on his mathematics entrance examinations, but he later transferred to the mathematics department after feigning color blindness and received his bachelor's degree in mathematics in 1983.

He then studied under analytic number theorist Wang Yuan at the Chinese Academy of Sciences where he received his master's degree in 1986.

In 1986, Zhang was brought to the United States to pursue his doctoral studies at Columbia University by Dorian M. Goldfeld.

He then studied under Goldfeld, Hervé Jacquet, Lucien Szpiro, and Gerd Faltings, and then completed his PhD at Columbia University under Szpiro in 1991.

Zhang was a member of the Institute for Advanced Study and an assistant professor at Princeton University from 1991 to 1996.

In 1996, Zhang moved back to Columbia University where he was a tenured professor until 2013.

Zhang has received a Sloan Foundation Research Fellowship (1997) and a Morningside Gold Medal of Mathematics (1998).

He was also an invited speaker at the International Congress of Mathematicians in 1998.

In a series of works in the 2000s, Zhang proved a generalization of the Gross–Zagier theorem from elliptic curves over rationals to modular abelian varieties of GL(2) type over totally real fields.

In particular, the latter result led him to a proof of the rank one Birch-Swinnerton-Dyer conjecture for modular abelian varieties of GL(2) type over totally real fields through his work relating the Néron–Tate height of Heegner points to special values of L-functions in.

Eventually, established a full generalization of the Gross–Zagier theorem to all Shimura curves.

In arithmetic dynamics, posed conjectures on the Zariski density of non-fibered endomorphisms of quasi-projective varieties and proposed a dynamical analogue of the Manin–Mumford conjecture.

He is also a Clay Foundation Prize Fellow (2003), Guggenheim Foundation Fellow (2009), Fellow of the American Academy of Arts and Sciences (2011), and Fellow of the American Mathematical Society (2016).

He has been a professor at Princeton University since 2011 and is an Eugene Higgins Professor since 2021.

Zhang is on the editorial boards of: Acta Mathematica Sinica, Algebra & Number Theory, Forum of Mathematics, Journal of Differential Geometry, National Science Review, Pure and Applied Mathematics Quarterly, Science in China, and Research in Number Theory.

He has previously served on the editorial boards of: Journal of Number Theory, Journal of the American Mathematical Society, Journal of Algebraic Geometry, and International Journal of Number Theory.

Zhang's doctoral thesis Positive line bundles on Arithmetic Surfaces proved a Nakai–Moishezon type theorem in intersection theory using a result from differential geometry already proved in Tian Gang's doctoral thesis.

In a series of subsequent papers, he further developed his theory of 'positive line bundles' in Arakelov theory which culminated in a proof (with Emmanuel Ullmo) of the Bogomolov conjecture.

In 2018, proved the averaged Colmez conjecture which was shown to imply the André–Oort conjecture for Siegel modular varieties by Jacob Tsimerman.