**Preprints**

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

Shtukas and the Taylor expansion of L-functions (II) (with Zhiwei Yun), 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**

On p-adic Waldspurger formula. (with Yifeng Liu, Shou-Wu Zhang). to appear Duke. Math. J.

Shtukas and the Taylor expansion of L-functions (with Zhiwei Yun), Ann. of Math.

Oberwolfach report of talk in 08/2015)

Regular formal moduli spaces and arithmetic transfer conjectures (with M. Rapoport, B. Smithling), Math. Annalen.

On the arithmetic transfer conjecture for exotic smooth formal moduli spaces. (with M. Rapoport, B. Smithling). Duke Math. J.

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, 2013, TIFR.

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.