I am an Associate Professor in the Department of Mathematics at Columbia University. I completed my Ph.D at Princeton University in 2018. My advisor was Professor Richard Taylor. Before that, I was an undergraduate at Peking University.
I am interested in algebraic number theory, especially p-adic aspects of the Langlands program.
Email address: lp3224[at]columbia[dot]edu
Prescribed lifts of 2-dimensional representations, with Matthew Emerton, Toby Gee and Xinwen Zhu, arXiv:2606.25485
On the locally analytic completed cohomology of modular curves (survey paper), submitted to the Proceedings of the 2025 International Congress of Basic Science, arXiv:2603.27937
Some vanishing results for the rational completed cohomology of Shimura varieties, with Kai-Wen Lan, arXiv:2603.27932
On locally analytic vectors of the completed cohomology of modular curves II. Ann. of Math. (2) 203 (1), 121-281, (January 2026)
A note on some p-adic analytic Hecke actions. J. Eur. Math. Soc. 27 (2025), no. 8, pp. 3297–3311 arXiv:2012.11845
On locally analytic vectors of the completed cohomology of modular curves. Forum of Mathematics, Pi , Volume 10 , 2022 , e7
The Fontaine-Mazur conjecture in the residually reducible case. J. Amer. Math. Soc. 35 (2022), 1031-1169. arXiv:1901.07166
First covering of Drinfel'd upper half plane and Banach representations of GL_2(Q_p). Alg. Number Th. 11 (2017) 405-503. arXiv:1510.03006