Xinyi Yuan

Xinyi Yuan is an algebraist and number theorist who is currently an assistant professor of mathematics at the University of California, Berkeley. Yuan's research interests include Arakelov geometry, Diophantine equations, Shimura varieties and automorphic forms. In particular, his work focuses on arithmetic intersection theory, algebraic dynamics, Diophantine equations and special values of L-functions.

As a high schooler, Yuan received a gold medal at the International Mathematical Olympiad.^[1] Yuan obtained his A.B. in mathematics from Peking University in 2003 and his Ph.D. in mathematics from the University of California, Berkeley in 2008 under the direction of Shou-Wu Zhang.^[2] 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.^[3]

He spent time at the Institute for Advanced Study, Princeton University, and Harvard University before joining the Berkeley faculty in 2012.^[4]

Yuan was appointed a Clay Research Fellow for a three-year term from 2008 to 2013.^[5] 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.^[6][7]

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 Math. 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 Math. Studies vol. 184, Princeton University Press, 2012.
• (with Wei Zhang, Shou-Wu Zhang) "Triple product L-series and Gross-Kudla-Schoen cycles", preprint.
• (with Shou-Wu Zhang) "On the averaged Colmez conjecture", preprint.

References