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
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).
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