Shou-Wu 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.

The native form of this personal name is Zhang Shou-Wu. This article uses Western name order when mentioning individuals.
Shou-Wu Zhang
Shou-Wu Zhang in 2014
Born (1962-10-09) October 9, 1962
Hexian, Anhui, China
NationalityAmerican
Alma mater
Known for
Awards
Scientific career
FieldsMathematics
Institutions
ThesisPositive Line Bundles on Arithmetic Surfaces (1991)
Doctoral advisorLucien Szpiro
Other academic advisorsWang Yuan
Doctoral students
Influences

Biography

Early life

Shou-Wu Zhang was born in Hexian, Ma'anshan, Anhui, China on October 9, 1962.[1][2][3] Zhang grew up in a poor farming household and could not attend school until eighth grade due to the Cultural Revolution.[1] 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.[1][2] 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.[1][2][4]

Education

Zhang was admitted to the Sun Yat-sen University chemistry department in 1980 after scoring poorly on his mathematics entrance examinations but later transferred to the mathematics department after feigning color blindness and received his bachelor's degree in mathematics in 1983.[5][1][2][3][4][6] He then studied under analytic number theorist Wang Yuan at the Chinese Academy of Sciences where he received his master's degree in 1986.[1][4][3][6] In 1986, Zhang was brought to the United States to pursue his doctoral studies at Columbia University by Dorian M. Goldfeld.[1][2] He then studied under Goldfeld, Hervé Jacquet, Lucien Szpiro, and Gerd Faltings, and then completed his PhD at Columbia University under Szpiro in 1991.[7][1][2][4][3][6]

Career

Zhang was a member of the Institute for Advanced Study and an assistant professor at Princeton University from 1991 to 1996.[3][6] In 1996, Zhang moved back to Columbia University where he was a tenured professor until 2013.[1][5][3][6] He has been a professor at Princeton University since 2011.[5][6]

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.[5] 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.[5]

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.[5] 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).[5]

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.[5] 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).[5][8] 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 analogue of the Manin–Mumford conjecture.[9][5]

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.[10]

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).[11][12][5] He was also an invited speaker at the International Congress of Mathematicians in 1998.[13][5][6][14]

Selected publications

Arakelov theory
  • Zhang, Shou-Wu (1992), "Positive line bundles on arithmetic surfaces", Annals of Mathematics, 136 (3): 569–587, doi:10.2307/2946601, JSTOR 2946601.
  • Zhang, Shou-Wu (1993), "Admissible pairing on a curve", Inventiones Mathematicae, 112 (1): 421–432, Bibcode:1993InMat.112..171Z, doi:10.1007/BF01232429.
  • 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.
  • Szpiro, Lucien; Ullmo, Emmanuel; Zhang, Shou-Wu (1997), "Equirépartition des petits points", Inventiones Mathematicae, 127 (2): 337–347, Bibcode:1997InMat.127..337S, doi:10.1007/s002220050123.
  • Zhang, Shou-Wu (1998), "Equidistribution of small points on abelian varieties", Annals of Mathematics, 147 (1): 159–165, doi:10.2307/120986, JSTOR 120986.

Heights and Heegner points

Arithmetic dynamics
gollark: > This channel is for discussion and media related to meteorology and climatology! > The siren is not the "Go play outside" signal!
gollark: Also heretics.
gollark: I still have two cult roles and I can use it.
gollark: You *don't* have access? Weird.
gollark: Probably a lot of people. I think the statistic is that 2-ish people die worldwide, per second, and my research suggests that slipping is more frequent than dying.

References
  1. "从放鸭娃到数学大师" [From ducklings to mathematics master] (in Chinese). Academy of Mathematics and Systems Science. 11 November 2011. Retrieved 5 May 2019.
  2. "專訪張壽武：在數學殿堂里，依然懷抱小學四年級的夢想" [Interview with Zhang Shou-Wu: In the mathematics department, he still has his dream from fourth grade of elementary school] (in Chinese). Beijing Sina Net. 3 May 2019. Retrieved 5 May 2019.
  3. "旅美青年数学家张寿武" [Zhang Shouwu, a young mathematician in the United States] (in Chinese). He County Government. 2 November 2017. Retrieved 5 May 2019.
  4. "专访数学家张寿武：要让别人解中国人出的数学题" [Interview with mathematician Zhang Shouwu: Let others solve the math problems of Chinese people] (in Chinese). Sina Education. 4 May 2019. Retrieved 5 May 2019.
  5. Leong, Y. K. (July–December 2018). "Shou-Wu Zhang: Number Theory and Arithmetic Algebraic Geometry" (PDF). Imprints. No. 32. The Institute for Mathematical Sciences, National University of Singapore. pp. 32–36. Retrieved 5 May 2019.
  6. "专访数学家张寿武：数学苍穹闪烁中国新星" [Interview with mathematician Zhang Shouwu: A new Chinese star flashing in the mathematical sky] (in Chinese). Zhishi Fenzi. 4 December 2017. Retrieved 5 May 2019.
  7. Shou-Wu Zhang at the Mathematics Genealogy Project
  8. Zhang, Wei (2013). "The Birch–Swinnerton-Dyer conjecture and Heegner points: a survey". Current Developments in Mathematics. 2013: 169–203. doi:10.4310/CDM.2013.v2013.n1.a3..
  9. Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. (2019). "Current trends and open problems in arithmetic dynamics". Bulletin of the American Mathematical Society. 56 (4): 611–685. arXiv:1806.04980. doi:10.1090/bull/1665.
  10. "February 2018". Notices of the American Mathematical Society. 65 (2): 191. 2018. ISSN 1088-9477.
  11. 2016 Class of the Fellows of the AMS, American Mathematical Society, retrieved 2015-11-16
  12. "Shou-Wu Zhang". John Simon Guggenheim Foundation. Retrieved 31 January 2019.
  13. "ICM Plenary and Invited Speakers". Retrieved 31 January 2019.
  14. Zhang, Shou-Wu (1998). "Small points and Arakelov theory". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 217–225.
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