Preprints

The arithmetic fundamental lemma: An update. Science China Mathematics

Weil representation and Arithmetic Fundamental Lemma,arXiv:1909.02697.

Kudla--Rapoport cycles and derivatives of local densities, (with Chao Li), arxiv:1908.01701.

On Shimura varieties for unitary groups, (with M. Rapoport, B. Smithling), arxiv.

Arithmetic diagonal cycles on unitary Shimura varieties, (with M. Rapoport, B. Smithling), arxiv.

A majority of elliptic curves over Q satisfy the Birch and Swinnerton-Dyer conjecture. (with Manjul Bhargava, Christopher Skinner) preprint, Arxiv.

Indivisibility of Heegner points in the multiplicative case. (with Christopher Skinner) submitted, Arxiv.

Triple product L-series and Gross-Kudla-Schoen cycles. (with Xinyi Yuan, Shou-Wu Zhang). preprint.

 

Publications

Shtukas and the Taylor expansion of L-functions (II) (with Zhiwei Yun), Ann. of Math., Vol. 189 (2019), no. 2, 393-526.

Periods, cycles, and $L$-functions: a relative trace formula approach Proceedings ICM-2018. Beamer file

On p-adic Waldspurger formula. (with Yifeng Liu, Shou-Wu Zhang). Duke. Math. J., Vol. 167 (2018), 743--833.

Shtukas and the Taylor expansion of L-functions (with Zhiwei Yun), Ann. of Math., Vol. 186 (2017), no. 3, 767--911.

Oberwolfach report of talk in 08/2015)

Regular formal moduli spaces and arithmetic transfer conjectures (with M. Rapoport, B. Smithling), Math. Annalen., 2018, Vol. 370, 1079--1175.

On the arithmetic transfer conjecture for exotic smooth formal moduli spaces. (with M. Rapoport, B. Smithling). Duke Math. J., Vol. 166, Number 12 (2017), 2183--2336.

Selmer groups and the indivisibility of Heegner points. Cambridge Journal of Math., Vol. 2 (2014), No. 2, 191--253.

The Birch--Swinnerton-Dyer conjecture and Heegner points: a survey. Current Developments in Mathematics, Volume 2013, 169--203.

Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups. Ann. of Math. Vol. 180 (2014), Issue 3, 971--1049

Appendix: Spherical characters for a strongly tempered pair. (with Atsushi Ichino)

Automorphic period and the central value of Rankin-Selberg L-function. J. Amer. Math. Soc. 27 (2014), 541-612.

On the Arithmetic Fundamental Lemma in the minuscule case (with Michael Rapoport, Ulrich Terstiege), Compositio Mathematica, 2013, volume 149, issue 10, pp. 1631-1666. Arxiv.

Harmonic analysis for relative trace formula. in ?Automorphic Representations and L-Functions", edited by: D. Prasad, C. S. Rajan, A. Sankaranarayanan, and J. Sengupta, Tata Institute of Fundamental Research, 2013, Mumbai, India. ISBN-10: 93-80250-49-5, ISBN-13: 978-93-80250-49-6

On the smooth transfer conjecture of Jacquet-Rallis for n=3, The Ramanujan Journal Ramanujan's 125th anniversary special volume, 2012, Volume 29, Issue 1-3, pp 225-256

Gross-Zagier formula and arithmetic fundamental lemma, in Fifth International Congress of Chinese Mathematicians. Part 1, 2, 447-459, AMS/IP Stud. Adv. Math., 51, pt. 1, 2, Amer. Math. Soc., Providence, RI, 2012.

On arithmetic fundamental lemmas, Invent. Math., Volume 188, Number 1 (2012), 197-252.

The Gross-Zagier formula on Shimura curves (with Xinyi Yuan, Shou-Wu Zhang). Annals of Math. Studies vol. 184, Princeton University Press, 2012.

The Gross-Kohnen-Zagier theorem over totally real fields (with Xinyi Yuan, Shou-Wu Zhang). Compositio Math. 145 (2009), no. 5, 1147-1162.