Xinyi Yuan

Xinyi Yuan (Chinese: 袁新意) is a Chinese mathematician who is currently a professor of mathematics at Peking University working in number theory, arithmetic geometry, and automorphic forms. In particular, his work focuses on arithmetic intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions.

The native form of this personal name is Yuan Xinyi. This article uses Western name order when mentioning individuals.
Xinyi Yuan
Yuan in 2017
Alma materColumbia University
Peking University
Awards
  • Clay Research Fellow (2008)
Scientific career
FieldsMathematics
InstitutionsPeking University
University of California, Berkeley
Institute for Advanced Study
Princeton University
Harvard University
ThesisEquidistribution Theory over Algebraic Dynamical Systems (2008)
Doctoral advisorShou-Wu Zhang

Education

Yuan is from Macheng, Huanggang, Hubei, and graduated from Huanggang Middle School in 2000.[1] That year, he received a gold medal at the International Mathematical Olympiad while representing China.[2] Yuan obtained his A.B. in mathematics from Peking University in 2003 and his Ph.D. in mathematics from the Columbia University in 2008 under the direction of Shou-Wu Zhang.[3] His article "Big Line Bundles over Arithmetic Varieties," published in Inventiones Mathematicae, demonstrates a natural sufficient condition for when the orbit under the absolute Galois group is equidistributed.[4]

Career

He spent time at the Institute for Advanced Study, Princeton University, and Harvard University before joining the Berkeley faculty in 2012.[5]

Yuan was appointed a Clay Research Fellow for a three-year term from 2008 to 2013.[6] Together with a number of other collaborators, Yuan was profiled in Quanta Magazine and Business Insider for, among other things, his research on L-functions.[7][8]

Research

Together with Shou-Wu Zhang, Yuan proved the averaged Colmez conjecture which was later shown to imply the André–Oort conjecture for Siegel modular varieties by Jacob Tsimerman.[9][10]

Publications (selected)
  • (with Tong Zhang) "Effective Bound of Linear Series on Arithmetic Surfaces", Duke Math. J. 162 (2013), no. 10, 1723–1770.
  • "On Volumes of Arithmetic Line Bundles", Compositio Math. 145 (2009), 1447–1464.
  • "Big Line Bundles over Arithmetic Varieties", Invent. Math. 173 (2008), no. 3, 603–649.
  • (with Tong Zhang) "Relative Noether inequality on fibered surfaces", Advances in Mathematics 259 (2014), 89–115.
  • (with Shou-Wu Zhang) "The arithmetic Hodge index theorem for adelic line bundles", Math. Ann. (2016), 1–49.
  • (with Wei Zhang, Shou-Wu Zhang) "The Gross–Kohnen–Zagier theorem over totally real fields", Compositio Math. 145 (2009), no. 5, 1147–1162.
  • (with Wei Zhang, Shou-Wu Zhang) "The Gross–Zagier formula on Shimura curves", Annals of Mathematics Studies vol. 184, Princeton University Press, 2012.
  • (with Wei Zhang, Shou-Wu Zhang) "Triple product L-series and Gross–Kudla–Schoen cycles", preprint.
  • Yuan, Xinyi; Zhang, Shou-Wu (2018). "On the averaged Colmez conjecture". Annals of Mathematics. 187 (2): 553–638. arXiv:1507.06903. doi:10.4007/annals.2018.187.2.4.
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References
  1. "黄冈中学近14年来未出省状元 发展过程中矛盾凸显". Xinhua News Agency. 6 April 2015. Retrieved 3 August 2017.
  2. "Xinyi Yuan – Official IMO Results", International Mathematical Olympiad. Retrieved on 4 December 2016.
  3. "Xinyi Yuan CV", UC Berkeley. Retrieved on 3 December 2016.
  4. "Big line bundles over arithmetic varieties", Inventiones Mathematicae. Published September 2008. Retrieved on 4 December 2016.
  5. "IAS Member – Xinyi Yuan", Institute of Advanced Study. Retrieved on 4 December 2016.
  6. "Xinyi Yuan", Clay Mathematics Institute. Retrieved on 3 December 2016.
  7. "Math Quartet Joins Forces on Unified Theory", Quanta Magazine. Retrieved on 3 December 2016.
  8. "Math Quartet Joins Forces on Unified Theory", Business Insider. Retrieved on 4 December 2016.
  9. "February 2018". Notices of the American Mathematical Society. 65 (2): 191. 2018. ISSN 1088-9477.
  10. Yuan, Xinyi; Zhang, Shou-Wu (2018). "On the averaged Colmez conjecture". Annals of Mathematics. 187 (2): 553–638. arXiv:1507.06903. doi:10.4007/annals.2018.187.2.4.
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