Xinyi Yuan Department of Mathematics Columbia University 2990 Broadway New York, NY 10027 USA Office: 611 Mathematics Email: yxy@math.columbia.edu

About Me:

I am a Research Fellow of the Clay Mathematics Institute during 2008-2011, and I will be an assistant professor at Princeton University in Fall 2011.
      My research interest is Arakelov geometry, Shimura varieties and automorphic forms. Specifically, I work on arithmetic intersection theory, algebraic dynamics, and special values of L-functions. Please visit my CV, Research Statement, Publication List, Publication list with abstracts.

Education:

• Ph.D. Mathematics, Columbia University, New York, 2003-2008 (Thesis advisor: Shou-wu Zhang). 
• B.S. Mathematics, Peking University, Beijing, 2000-2003.

Employment:

• Assistant Professor, Department of Mathematics, Princeton University, 2011--.
• Research Fellow, Clay Mathematics Institute, 2008-2011.
• Ritt Assistant Professor, Department of Mathematics, Columiba University, 2010-2011.
• Post-doctor, Department of Mathematics, Harvard University, 2009-2010.
• Post-doctor, School of Mathematics, Institute for Advanced Study, 2008-2009.

Publication:
(The files may be slightly different from the published versions.)

(I) My works on Arakelov geometry and algebraic dynamics:

• Calabi-Yau Theorem and Algebraic Dynamics (with Shou-wu Zhang), preprint.
• Small Points and Berkovich Metrics (with Shou-wu Zhang), preprint.
• On Volumes of Arithmetic Line Bundles II, preprint.
• On Volumes of Arithmetic Line Bundles, Compositio Mathematicae 145 (2009), 1447-1464.
• Big Line Bundles over Arithmetic Varieties, Inventiones Mathematicae 173 (2008), no. 3, 603--649. For more background, please see my thesis.

(II) My works on automorphic forms, Shimura varieties and L-functions:

• A Relative Trace Formula Proof of the Gross-Zagier Formula (with Ye Tian and Wei Zhang), available soon.
• Triple Product L-series and Gross-Schoen Cycles (with Shou-wu Zhang and Wei Zhang), preprint.
• Gross-Zagier Formula on Shimura Curves (with Shou-wu Zhang and Wei Zhang), to be published by the Annals of Mathematics Studies.
• The Gross-Kohnen-Zagier Theorem over Totally Real Fields (with Shou-wu Zhang and Wei Zhang), Compositio Mathematicae 145 (2009), 1147-1162.

(III) My expository works:

• Algebraic Dynamics, Canonical Heights and Arakelov Geometry, 2011.

last updated by July 19, 2011