Xinyi Yuan

Xinyi Yuan 2017

Xinyi Yuan (* 1981 near Wuhan ) is a Chinese mathematician.

Yuan went to school in Huanggang (Huanggang High School) and received the gold medal at the 2000 International Mathematical Olympiad. From 2000 he studied mathematics at the University of Beijing with a bachelor's degree in 2003 and received his doctorate in 2008 from Columbia University with Shou-Wu Zhang (Equidistribution Theory over Algebraic Dynamical Systems). As a post-doctoral student he was at the Institute for Advanced Study and at Harvard University in 2009/10 . In 2010/11 he was Ritt Assistant Professor at Columbia University. From 2012 he was Assistant Professor and from 2018 Associate Professor at the University of California, Berkeley .

He deals with arithmetic geometry, especially Arakelow geometry , algebraic dynamics, Shimura varieties , automorphic forms and Diophantine equations , and works closely with the Chinese mathematicians Zhang Wei , Xinwen Zhu and Zhiwei Yun (Zhang Wei is a fellow student from Beijing and also did his doctorate with Shou-Wu Zhang) in the Langlands program . In his dissertation he proved an arithmetic analogue of a theorem by Yum-Tong Siu , which among other things results in the proof of a uniform distribution theorem for orbits of the absolute Galois group . With Zhang Wei and Shou-Wu Zhang, he proved Gross-Zagier formulas for quaternionic Shimura curves over totally real number fields .

With Shou-Wu Zhang he proved the averaged Colmez conjecture (after Pierre Colmez ). It expresses the folding height of Abelian varieties with complex multiplication as a linear combination of logarithmic derivatives of Artin L-functions . According to Jacob Tsimerman, it implies the André-Oort conjecture for principally polarized Abelian varieties.

From 2008 to 2013 he was a Clay Research Fellow.

Fonts

Big Line Bundles over Arithmetic Varieties , Inventiones mathematicae, Volume 173, 2008, pp. 603-649. Arxiv
On Volumes of Arithmetic Line Bundles , Compositio Mathematica, Volume 145, 2009, pp. 1447-1464. Arxiv , part 2, Arxiv
with Zhang Wei , Shou-Wu Zhang: The Gross – Kohnen – Zagier theorem over totally real fields, Compositio Mathematica , Volume 145, 2009, pp. 1147–1162,
with Zhang Wei, Shou-Wu Zhang: The Gross-Zagier formula on Shimura curves , Annals of Mathematics Studies 184, Princeton University Press, 2012.
Algebraic Dynamics, Canonical Heights and Arakelov Geometry , 5th Int. Congress of Chinese Mathematicians, 2012, Parts 1-2, American Mathematical Society, pp. 893-929.
with Tong Zhang: Effective Bound of Linear Series on Arithmetic Surfaces , Duke Mathematical Journal, Volume 162, 2013, pp. 1723-1770. Arxiv
with Tong Zhang: Noether inequality on fibered surfaces , Advances in Mathematics, Volume 259, 2014, pp. 89–115. Arxiv
with Shou-Wu Zhang: The arithmetic Hodge index theorem for adelic line bundles , Mathematische Annalen, Volume, 2016, pp. 1–49. Arxiv , part 2, Arxiv
with Zhang Wei, Shou-Wu Zhang: Triple product L-series and Gross – Kudla – Schoen cycles , preprint.
with Ye Tian, Shou-Wu Zhang: Genus periods, genus points and congruent number problem , Asian J. Math., Volume 21, 2017, pp. 721–773, Arxiv
with Shou-Wu Zhang: On the averaged Colmez conjecture , Annals of Mathematics, Volume 187, 2018, pp. 553–638, Arxiv