Chinese-American mathematician (born 1962)In this Chinese name, the family name is Zhang.

Shou-Wu Zhang (Chinese: 张寿武; pinyin: Zhāng Shòuwǔ; 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.

Contents

• 1 Biography
  • 1.1 Early life
  • 1.2 Education
  • 1.3 Career
• 2 Research
• 3 Awards
• 4 Selected publications
  • 4.1 Arakelov theory
  • 4.2 Bogomolov Conjecture
  • 4.3 Gross--Zagier formulae
  • 4.4 Arithmetic dynamics
• 5 References
• 6 External links

Biography

Early life

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.

Education

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 *ytic 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.

Career

Zhang was a member of the Ins*ute for Advanced Study and an *istant professor at Princeton University from 1991 to 1996. In 1996, Zhang moved back to Columbia University where he was a tenured professor until 2013. 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.

Research

Zhang's doctoral thesis Positive line bundles on Arithmetic Surfaces (Zhang:1992) 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 (Zhang:1993, 1995a, 1995b, Szpiro, Ullmo & Zhang:1997), he further developed his theory of 'positive line bundles' in Arakelov theory which culminated in a proof (with Emmanuel Ullmo) of the Bogomolov conjecture (Zhang:1998).

In a series of works in the 2000s (Zhang:2001b, 2004, Yuan, Zhang & W. Zhang:2009), 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 (Zhang:1997, 2001a). Eventually, Yuan, Zhang, and W. Zhang:(2013) established a full generalization of the Gross–Zagier theorem to all Shimura curves.

In arithmetic dynamics, Zhang:(1995a, 2006) posed conjectures on the Zariski density of non-fibered endomorphisms of quasi-projective varieties and Ghioca, Tucker, and Zhang:(2011) proposed a dynamical *ogue of the Manin–Mumford conjecture.

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

Awards

Zhang has received a Sloan Foundation Research Fellowship (1997) and a Morningside Gold Medal of Mathematics (1998). 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 was also an invited speaker at the International Congress of Mathematicians in 1998.

Selected publications

Arakelov theory

• Zhang, Shou-Wu (1993), "Admissible pairing on a curve", Inventiones Mathematicae, 112 (1): 421–432, Bibcode:1993InMat.112..171Z, doi:10.1007/BF01232429, S2CID:120229374.
• Zhang, Shou-Wu (1995a), "Small points and adelic metrics", Journal of Algebraic Geometry, 8 (1): 281–300.
• Zhang, Shou-Wu (1995b), "Positive line bundles on arithmetic varieties", Journal of the American Mathematical Society, 136 (3): 187–221, doi:10.1090/S0894-0347-1995-1254133-7.
• Zhang, Shou-Wu (1996), "Heights and reductions of semi-stable varieties", Compositio Mathematica, 104 (1): 77–105.
• Zhang, Shou-Wu (2010), "Gross–Schoen cycles and Dualising sheaves", Invent. Math., 179 (1): 1–73.
• Yuan, Xinyi; Zhang, Shou-Wu (2017), "The arithmetic Hodge index theorem for adelic line bundles", Math. Ann., 367: 1123–1171.

Bogomolov Conjecture

• Szpiro, Lucien; Ullmo, Emmanuel; Zhang, Shou-Wu (1997), "Equirépar*ion des pet... points", Inventiones Mathematicae, 127 (2): 337–347, Bibcode:1997InMat.127..337S, doi:10.1007/s002220050123, S2CID:119668209.
• Zhang, Shou-Wu (1998), "Equidistribution of small points on abelian varieties", Annals of Mathematics, 147 (1): 159–165, doi:10.2307/120986, JSTOR:120986.

Gross--Zagier formulae

• Zhang, Shou-Wu (1997), "Heights of Heegner cycles and derivatives of L-series", Inventiones Mathematicae, 130 (1): 99–152, Bibcode:1997InMat.130...99Z, doi:10.1007/s002220050179, S2CID:10537873.
• Zhang, Shou-Wu (2001), "Heights of Heegner points on Shimura curves", Annals of Mathematics, 153 (1): 27–147, arXiv:math/0101269, doi:10.2307/2661372, JSTOR:2661372, S2CID:119624920.
• Yuan, Xinyi; Zhang, Shou-Wu; Zhang, Wei (2009), "The Gross–Kohnen–Zagier Theorem over Totally Real Fields", Compositio Mathematica, 145 (5): 1147–1162, doi:10.1112/S0010437X08003734.
• Yuan, Xinyi; Zhang, Shou-Wu; Zhang, Wei (2013), The Gross–Zagier formula on Shimura curves, Annals of Mathematics Studies, vol.:184.
• Liu, Yifeng; Zhang, Shou-Wu; Zhang, Wei (2018a), "A p-adic Waldspurger formula", Duke Mathematical Journal, 167 (4): 743–833.
• Yuan, Xinyi; Zhang, Shou-Wu (2018b), "On the averaged Colmez conjecture", Annals of Mathematics, 187 (2): 553–638, arXiv:1507.06903, doi:10.4007/annals.2018.187.2.4, S2CID:118916754.

Arithmetic dynamics

• Zhang, Shou-Wu (2006), "Distributions in algebraic dynamics", in Yau, Shing-Tung (ed.), Essays in geometry in memory of S.S. Chern, Surveys in Differential Geometry, vol.:10, Somerville, MA: International Press, pp.:381–430, doi:10.4310/SDG.2005.v10.n1.a9, MR:2408228.
• Ghioca, Dragos; Tucker, Thomas J.; Zhang, Shou-Wu (2011), "Towards a dynamical Manin-Mumford conjecture", International Mathematics Research Notices, 22: 5109–5122, doi:10.1093/imrn/rnq283, MR:2854724.

References

External links

• Princeton home page
• Shou-Wu Zhang at the Mathematics Genealogy Project