Research interests

I like to think about problems in number theory, algebraic geometry, and algebraic topology. Currently, I am working on projects related to the following topics.

• Galois representations

• Arithmetic of algebraic varieties

• Hypergeometric motives

• Rational homotopy theory

Publications and preprints

Warning: The papers posted on the arXiv may differ from the published versions!

• Some remarks on strong multiplicity one for paramodular forms (with Zhining Wei, Pan Yan, and Shaoyun Yi), 2023.                            (In preprint). [arXiv]

• On the essential torsion finiteness of abelian varieties over torsion fields (with Jeff Achter and Lian Duan), 2023.                            Nagoya Mathematical Journal (to appear). [arXiv]

• Smoothness of components of the Emerton-Gee Stack for GL2 (with Anthony Guzman, Kalyani Kansal, Iason Kountouridis, and Ben Savoie), 2022.                                                                                                                                                                                          Transactions of the AMS (to appear). [arXiv]

• Nonsplitting of the Hilbert exact sequence and the principal Chebotarev density theorem (with Lian Duan, Kelly Emmrich, and Ning Ma), 2021.                                                                                                                                                                                                 Submitted. [arXiv]

• Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces (with Lian Duan).                       Mathematical Research Letters, Volume 28, No. 5, 2021, 1353-1378. [arXiv] [Journal]

• Weight elimination in two dimensions when p=2, 2017.                                                                                                                                Mathematical Research Letters, Volume 29, No. 3, 2022, 887-902. [arXiv] [Journal]

In preparation

• Rank five compatible systems of Galois representations and the Tate conjecture of elliptic surfaces (with Lian Duan and Ariel Weiss).

Invited talks

• Tianyuan Mathematical Center in Northeast China Seminar, Xiamen University.   May. 2023

• Institute of Mathematical Sciences Seminar, ShanghaiTech University.   Nov. 2022

• Automorphic Forms and Representation Theory Seminar, Purdue University.   Jan. 2021

• Junior Number Theory Days, Johns Hopkins University.   Dec. 2020

• Junior Colloquium, Johns Hopkins University.   Nov. 2020

• Colloquium, Capital Normal University.   Nov. 2020

• Peking Online International Number Theory Seminar, Beijing University.   May. 2020 [slide]

• Algebra Seminar, University of Pennsylvania.   Feb. 2020

• FRAGMENT Seminar, Colorado State University.   Nov. 2019