Research Areas

Arithmetic algebraic geometry (ℓ-adic and p-adic cohomology theories)

Education

Sep. 1985 - July 1989: Wuhan University, B. S.

Sep. 1989 - Aug. 1990: Selected by the Chern Program (陈省身项目) and the China Education Ministry to pursue Ph. D. in USA. Trained at the English Training Center at Guangzhou in Sun Yat-Sen University, and Beijing Language and Culture University.

Sep. 1990 - May 1995: Rice University (USA), Ph. D.

Work Experience

Aug. 1995 - Aug. 1997: Indiana University (USA), Visiting assistant professor.

Aug. 1997 - July 1999: Nankai University, Postdoctor.

July 1999 - June 2016: Nankai University, Professor.

June 2012 - June 2016: Director of the Chern Institute of Mathematics, Nankai University.

July 2016 - present: Tsinghua University, Professor.

Grant (after 2019)

1. Jan. 2022- Dec. 2026, National Science Foundation, Landau-Ginzburg model and exponen[1]tial sums, Grant No. 12171261. Director.

2. Dec. 2021-Nov. 2026, Key project of the Ministry of Science and Technology, Riemann hypothesis and distribution of prime numbers, Ministry of Science and Technology, Grant No. 2021YFA1000700. Participant. The director of the project is Jianya Liu.

3. Jan. 2016 - Dec. 2020: Key project of the National Science Foundation, Automorphic representations and arithmetic of algebraic varieties, Grant No. 11531008. Participant. The director of the project is Jianya Liu.

Publications

Research papers published in journals

[1] On the boundaries of special Lagrangian submanifolds, Duke Mathematical Journal 79 (1995), 405-422.

[2] An analogue of Bernstein’s theorem, Houston Journal of Mathematics 24 (1998), 415-419.

[3] On the construction of generalized Jacobians, L’Enseignement Mathématique 45 (1999), 17-50.

[4] On the semisimplicity of pure sheaves, Proceedings of the American Mathematical Society 127 (1999), 2529-2533.

[5] On the semisimplicity conjecture and Galois representations, Transactions of the American Mathematical Society 353 (2001), 4357-4369.

[6] (joint with Daqing Wan) Total degree bounds of Artin L-functions and partial zeta functions, Mathematical Research Letters 10 (2003), 33-41.

[7] (joint with Daqing Wan) Moment L-functions, partial L-functions, and partial exponential sums, Mathematische Annalen 328 (2004), 193-228.

[8] (joint with Chunlei Liu) Equidistribution of Gauss sums and Kloosterman sums, Mathematische Zeitschrift 249 (2005), 269-281.

[9] (joint with Daqing Wan) The L-functions of symmetric products of the Kloosterman sheaf, Journal für die reine und angewandte Mathematik (Crelle’s Journal) 589 (2005), 79-103.

[10] (joint with Daqing Wan) Mirror congruence for rational points on Calabi-Yau varieties, Asian Journal of Mathematics 10 (2006), 1-10.

[11] (joint with Daqing Wan) Trivial factors for L-functions of symmetric products of Kloosterman sheaves, Finite Fields and Their Applications 14 (2008), 549-570.

[12] (joint with Daqing Wan) L-functions of symmetric products of the Kloosterman sheaf over Z, Mathematische Annalen 342 (2008), 387-404.

[13] Weight of twisted exponential sums, Mathematische Zeitschrift 262 (2009), 449-472.

[14] A Tauberian theorem for ℓ-adic sheaves, Science in China 53 (2010), special issue dedicated to Wang Yuan, 2207-2214.

[15] Calculation of ℓ-adic local Fourier transformations, Manucripta Mathematica 133 (2010), 409-464.

[16] (joint with Daqing Wan) Functional equations of L-functions for symmetric products of the Kloosterman sheaf, Transactions of the American Mathematical Society 362 (2010), 5947-5965.

[17] Deformation of ℓ-adic sheaves with undeformed local monodromy, Journal of Number Theory 133 (2013), 675-691.

[18] A Thom-Sebastiani theorem in characteristic p, Mathematical Research Letters 21 (2014), 101-119.

[19] (joint with Daqing Wan) A class of incomplete character sums, Quarterly Journal of Mathe[1]matics 65 (2014), 1195-1211.

[20] ℓ-adic GKZ hypergeometric sheaves and exponential sums, Advances in Mathematics 298 (2016), 51-88.

[21] Deformations and rigidity of ℓ-adic sheaves, Advances in Mathematics 351 (2019), 947-966.

[22] (joint with Daqing Wan), On Katz (A, B)-exponential sums, Quarterly Journal of Mathematics 72 (2021) 773-793 .

[23] (joint with Peigen Li, Daqing Wan, Hao Zhang), p-adic GKZ hypergeometric complex, Math[1]ematische Annalen (to appear).

Books

[1] Algebraic Geometry, Tsinghua University Press (2006).

[2] Etale Cohomology Theory, Nankai Tracts in Mathematics 13, World Scientific (2011).