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.
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.
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
Seminar organized:
In fall 2024, I organized Learning group on Condensed Mathematics with Shizhang Li, Yihang Zhu, and Foling Zou
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.
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.