Zhang Wei (mathematician)

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Note: This article places the family name before the person's first name. This is the usual order in Chinese. Zhang is the family name here, Wei is the first name.

Zhang Wei ( Chinese  张伟 , Pinyin Zhāng Wěi ; born July 18, 1981 in the Dachuan district of the city of Dazhou in the Sichuan province of the People's Republic of China ) is a Chinese mathematician who studies number theory, automorphic forms and algebraic geometry.

Zhang Wei obtained his bachelor's degree from Peking University and received his PhD from Columbia University with Shou-Wu Zhang in 2009 (Modularity of generating functions of special cycles on Shimura varieties). Afterwards he was a Benjamin Pierce Instructor at Harvard University as a post-doctoral student from 2010 . He is currently (2016) a professor at Columbia University.

Zhang deals with algebraic cycles , trace formulas and special values ​​of L-functions . He became known when he proved the Kudla conjecture as a student in 2005 (topic of his dissertation). Stephen S. Kudla hypothesized in 1997 that a family of cycles constructed by him is generated on Shimura varieties of Siegel modular forms . Richard Borcherds proved the assumption for cycles of codimension 1. Zhang extended this to a higher dimension and, in addition to Borcherds, built on works by Hirzebruch / Zagier and Zagier / Gross / Kohnen (1986/1987). With Xinyi Yuan and Shou-Wu Zhang he generalized his result to totally real number fields . Shortly thereafter, they generalized proofs of Gross-Zagier formulas that connect heights of Heegner points on module curves (which, according to the work of Wiles and Taylor, also include elliptic curves ) with values ​​of the derivative of certain L-functions at s = 1 and were difficult to understand in the original works, about the proof of an arithmetic analogue of a formula by Jean-Loup Waldspurger . With Yun in 2015 he succeeded in a geometric interpretation of the higher terms of the Taylor series of L-functions.This was seen as a significant advance, which also allows the exact calculation of higher terms than the first (Gross / Zagier 1986) and second terms and a new perspective on the Birch and Swinnerton-Dyer conjecture .

In 2010 he received the SASTRA Ramanujan Prize and in 2016 the Morningside Gold Medal . For 2018 he received a New Horizons in Mathematics Prize . He is invited speaker at the International Congress of Mathematicians in Rio de Janeiro 2018 (Periods, cycles, and L-functions: a relative trace formula approach). For 2019 he was awarded the Clay Research Award .

Fonts (selection)

Except for the writings mentioned in the footnotes

  • with Zhiwei Yun : Shtukas and the Taylor expansion of L -functions, Annals of Mathematics, Volume 186, 2018, pp. 767–911

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Hirzebruch, Zagier Intersection number of curves on Hilbert modular surfaces and modular forms of Nebotypus , Inv.Math., Volume 36, 1976, pp. 57-113
  3. ^ Yuan, Shou-Wu Zhang, Wei Zhang The Gross-Kohnen-Zagier theorem over totally real fields , Composition Mathematica, Volume 145, 2009, pp. 1147–1162
  4. ^ Gross, Zagier Heegner Points and Derivatives of L Series , Inventiones Mathematicae, Volume 84, 1986, pp. 225-320, Part II Gross, Kohnen, Zagier Mathematische Annalen, Volume 278, 1987, pp. 497-562. The Gross-Zagier theory plays an important role both in the Gaussian class number problem and in the theory of the Birch and Swinnerton-Dyer conjecture .
  5. ↑ Yuan, Shou-Wu Zhang, Wei Zhang Heights of CM points I: Gross-Zagier formula , Preprint 2009, appears as a book in Annals of Mathematical Studies, Princeton University Press
  6. ↑ Yun, Zhang, Shtukas and the Taylor expansion of L-functions, Arxiv 2015
  7. ^ Hartnett, Math quartet joins forces on unified theory , Quanta Magazine, December 2015
  8. ↑ Arxiv
  9. ^ Clay Research Award 2019
personal data
SURNAME Zhang, Wei
ALTERNATIVE NAMES 张伟
BRIEF DESCRIPTION Chinese mathematician
DATE OF BIRTH July 18, 1981
PLACE OF BIRTH Dachuan , Dazhou, Sichuan Province, People's Republic of China