My recent research topics are mostly about p-adic Hodge theory via Fargues-Fontaine Curve and Breuil-Kisin-Fargues modules, I also have projects on (phi, Gamma)-modules, p-adic Langlands program and eigenvarieties. 

• Here is my thesis. I define and study a category I called the category of arithmetic  Breuil-Kisin-Fargues modules, and showed it is universal in the sense that it can be used to study compatibilities in integral p-adic Hodge theory. I could also use it to give a new formulation of the p-adic monodromy theorem for p-adic Galois representations.

Publications and Preprints:

• (with Tong Liu, Yong Suk Moon, and Koji Shimizu.) Log prismatic F-crystals and purity. (arXiv version)

• (with Qingyuan Jiang, and Yucheng Liu) Continuum envelops on Fargues-Fontaine curves and elliptic curves. (arXiv version)

• (with Tong Liu, Yong Suk Moon, and Koji Shimizu.) Completed prismatic F-crystals and crystalline Zp-local systems. Compos. Math. 160(2024), 5, 1101-1161. (arXiv version)

• (with Tong Liu.) A prismatic approach to (φ, Ĝ)-modules and F-crystals. J. Eur. Math. Soc. 2023. (arXiv version)

• (with Tong Liu.) A new method for overconvergence of (φ, Γ)-modules. (arXiv preprint). 2022.

• Arithmetic Breuil-Kisin-Fargues modules and comparison of integral p-adic Hodge theories. (arXiv preprint updated my 2019 paper on the same topic, submitted). 2022.

• A_inf has uncountable Krull dimension. (2023 version, arXiv submitted). 2020

Expository notes:

• Non-decompleteness of Kummer tower. (draft). 2020.

• Here is a talk I gave in Prof. Shahidi's class on the Littlewood-Richardson rule of Schur functor and a small programming.

• Also a talk I gave in Prof. Shahidi's class: An introduction on Bruhat-Tits theory with application to the computation of intertwining operator of SU(2,1). I calculated the Bruhat-Tits building for SU(2,1) and use it to prove Theorem 3.1 in the paper ``The unramified principal series of p-adic groups" of  W. Casselman. (available upon request)

Invited talks:

• Arithmetic Breuil-Kisin-Fargues modules and their moduli, Dec 2020, Purdue University 

• Arithmetic Breuil-Kisin-Fargues modules and their moduli, Dec 2020, Southern University of Science and Technology

• Why does the ring R[[x]] have infinite dimension when R is non-discrete valued?. Feb 2020, Student Colloquium, Purdue University

• p-adic Langlands correspondence for tori and eigenvarieties, 2017, Shanghai Jiao Tong University

Seminar (co-)organized and seminar attended:

• Finite flat group schemes and Barsotti-Tate groups study seminar in Spring 2016.

• Crystalline cohomology study seminar in Spring 2017. (with my friends Feng Hao and Andres Figuerola).

• We have the Rigid Analytic Space and Berkovich Space Seminar in Spring 2017, and I gave talks in it.

• Geometric class field theory in Fall 2017 - Spring 2018.

• Fargues-Fontaine Curve in Fall 2018.

• We have the Prismatic cohomology study seminar in Fall 2019.

Conferences attended: 

• Winter School on Shimura Varieties and Related Topics, Nov 29-Dec 3, 2019, ECNU, Shanghai, China

• Padova school on Serre conjectures and the $p$-adic Langlands program, May 27 - June 14, 2019, Padua, Italy

• Pop-up Conference in Number Theory, Nov 2 - 4, 2018, University of Illinois at Chicago, IL

• Groupes alg\'ebriques et g\'eom\'etrisation du programme de Langlands, May 25 - June 23, 2018, l'ENS de Lyon, France

• Iwasawa Theory, March 3 - 7, University of Arizona in Tucson, AZ

• Automorphic Forms and The Langlands Program, July 24 - Aug. 4, 2017, MSRI, Berkeley, CA

• $p$-adic Hodge Theory and Automorphic Forms, June 5 - 9, 2017, BICMR, Beijing

• Perfectoid Spaces, March 11 - 15, 2017, University of Arizona in Tucson, AZ

• The 7th International Congress of Chinese Mathematicians (ICCM),  Aug. 6 - 11, 2016, Beijing

• Workshop on the $p$-adic Langlands Correspondence, July 13 - 20, 2016, AMSS, Beijing

• The $p$-adic Langlands Program and Related Topics, May 16-20, 2016, Indiana University

• Workshop on the Patched Eigenvariety, July 26 - 31, 2015, AMSS, Beijing

• Conference on Arithmetic Geometry in honor of Katz's 71st birthday, May 11 - 15, 2015, AMSS, Beijing

Useful links:

Roadmap of the geometrization conjecture of the local Langlands programm in Fargues' homepage.