HD - Research

Research Interests

Number Theory, Algebraic Geometry

Research Topics: p-adic Hodge theory and p-adic geometry; more specifically, I am interested in coefficient theory in p-adic Hodge theory, p-adic Langlands program; representation theory of p-adic groups and the structures of p-adic groups; Stability conditions in algebraic geometry.
Keywords: prismatic F-crystals, (φ, Γ)-modules, Fargues–Fontaine curves, Prismatizations, F-Gauges, Banach–Colmez spaces, Bruhat–Tits theory; Bridgeland Stability.

Publications and Preprints:

(with Tong Liu.) A prismatic approach to (φ, Ĝ)-modules and F-crystals. J. Eur. Math. Soc. 28(2026), 6, 2581-2636. (arXiv version)
A_inf has uncountable Krull dimension. Math. Ann. (2025), 4, 5483-5490. (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)

p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy. (arXiv version)
(with Tong Liu, Yong Suk Moon, and Koji Shimizu.) Log prismatic F-crystals and purity. (arXiv version, submitted)
(with Yong Suk Moon and Koji Shimizu.) A log prismatic-crystalline comparison theorem. (arXiv version, submitted)
(with Yong Suk Moon and Koji Shimizu.) On log crystalline higher direct image. (arXiv version, submitted)
(with Qingyuan Jiang and Yucheng Liu.) Continuum envelops on Fargues-Fontaine curves and elliptic curves. (arXiv version)
(with Tong Liu.) A new method for overconvergence of (φ, Γ)-modules. (arXiv preprint, to be updated soon). 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.

Current Seminar and other Activities:

- BIMSA-YMSC Tsinghua Number Theory Seminar, every Monday, 10:00 – 11:00 (except holidays).
- Since the spring of 2025, I have organized the Learning seminar on Liquid Mathematics for Xue Tang Ban. The topic of this seminar is "Condensed GAGA from the liquid side."
- Shanwen and I are organizing a joint RUC-YMSC mini-workshop on formalized mathematics.

Expository notes:

Non-decompleteness of Kummer tower. (2020. This is now the appendix of "A new method for overconvergence of (φ, Γ)-modules", with Tong Liu)

Selected Research Talks

p-adic Hodge theory around rank-1 points | Jan 2026, ICCM, Shanghai, China
A prismatic Herr complex for Bloch–Kato Selmer group | Nov 2025, SIMIS, Shanghai, China
p-adic Hodge theory around Shilov points | Nov 2025, Wuhan University, China
A revisit of the Fundamental Lemma in p-adic Hodge theory | May 2025, Tianyuan Mathematics Research Center, Yunnan, China
p-adic Hodge theory and crystals | Jan 2025, ICCM, Shanghai, China
Bridgeland Stability Conditions Applied to the Fargues–Fontaine Curve | Jun 2024, Tsinghua University, China
A new method for overconvergence of étale (φ, Γ)-modules | Apr 2024, Nanjing University, China
The motivic part in Galois cohomologies: a prismatic approach | Dec 2023, Tsinghua University, Beijing, China
A purity result for semi-stable local systems | Aug 2023, USTC, Anhui, China
Overconvergence of Laurent F-crystals | Dec 2022, Frontiers in Mathematical Science, Sanya, China
Crystalline local systems and prismatic crystals | Dec 2021, Southern University of Science and Technology, China
On arithmetic Breuil-Kisin-Fargues modules and their moduli | Dec 2020, Purdue University & SUSTech
A_inf has uncountable Krull dimension | Feb 2020, Purdue University
A global depth preserving theorem for Langlands correspondence for tori and eigenvarieties | 2017, Shanghai Jiao Tong University

Selected Learning Seminar Talks

Application to the geometrization of the local Langlands correspondence | Mar 2025, Tianyuan Mathematics Research Center, Yunnan, China
What is a Bruhat-Tits Building? | Apr 2024, BIMSA, China
Espaces symétriques de Drinfeld et correspondance de Langlands locale | Dec 2023, MCM, Beijing, China
Line bundles on rigid spaces in the v-topology | Aug 2023, BICMR, Beijing, China
Minicourse on Breuil–Kisin classification of p-divisible groups and deformation | May 2023, BICMR, Beijing, China
Syntomification | May 2023, MCM, Beijing, China
Existence of crystalline lift | Feb 2023, BIMSA, Beijing, China
More on Fargues-Fontaine curve | Jan 2023, BICMR, Beijing, China
The category BC in terms of the Fargues–Fontaine curve | Dec 2022, MCM, Beijing, China
Complexes on the Hodge-Tate Divisor and Frobenius on WCart | Mar 2022, MCM, Beijing, China

Professional Services

Co-Organizer, BIMSA-YMSC Tsinghua Number Theory Seminar | 2023–Present, Tsinghua & BIMSA, China
Co-Organizer, RUC-YMSC mini-workshop on formalized mathematics | Apr 2026, Tsinghua & Remin University, China
Organizer, Liquid GAGA Learning Seminar | Spring 2026, YMSC, China
Co-Organizer, 2025 Symposium on Number Theory and Arithmetic Geometry | Dec 2025, TSIMF, Sanya, China
Organizer, Learning group on Condensed Mathematics | Spring and Fall 2025, YMSC, China
Co-Organizer, Happy P-day | Dec 2023, Tsinghua University
Organizer, Seminar on isocrystals with G-structures | Spring 2020, Purdue University
Organizer, Seminar on Fargues–Fontaine Curve | Fall 2018, Purdue University
Organizer, Geometric class field theory seminar | Fall 2017, Purdue University
Organizer, Crystalline cohomology student seminar | Spring & Fall 2017, Purdue University
Organizer, Finite flat group scheme and p-divisible group student seminar | Spring 2016, Purdue University

Conferences & Academic Visits (Selected)

Geometrization of the local Langlands correspondence | Feb 2026, CIRM, Marseille, France
p-adic aspects of the Langlands program | Feb 2026, CIRM, Marseille, France
International Congress of Chinese Mathematicians (ICCM) | Jan 2026, Shanghai, China
2025 Symposium on Number Theory and Arithmetic Geometry | Dec 2025, Sanya, China
Academic Visit at SIMIS | Nov 2025, Shanghai, China
Academic Visit at Wuhan University | Nov 2025, Wuhan, China
Workshop on Frontiers in Number Theory | May 2025, Tianyuan Center, Yunnan, China
Recent Advances in p-adic Geometry | Mar 2025, Tianyuan Center, Yunnan, China
The Fourth Cross-Strait Workshop on Arithmetic Geometry | Mar 2025, Nanjing, China
International Congress of Chinese Mathematicians (ICCM) | Jan 2025, Shanghai, China
Seminar on Moduli Spaces and Related Topics | Jun 2024, Tsinghua University, China
Conference on Arithmetic Geometry Nanking | Apr 2024, Nanjing, China
Workshop on p-adic Arithmetic Geometry (Spring & Fall) | 2023-2024, IAS, US
The Third Cross-Strait Workshop on Arithmetic Geometry | Aug 2023, Anhui, China
Reading Workshop on non-abelian p-adic Hodge Theory | Aug 2023, Beijing, China
Luojia Conference on Number Theory and Algebraic Geometry | Apr 2023, Wuhan, China
YMSC–MCM p-adic seminars (various topics) | 2022-2023, Beijing, China
Frontiers in Mathematical Science | Dec 2022, Sanya, China
Academic Visit at Southern University of Science and Technology | Dec 2021, Shenzhen, China
Winter School on Shimura Varieties and Related Topics | Nov 2019, Shanghai, China
Serre conjectures and the p-adic Langlands program | Jun 2019, Padua, Italy
Groupes algébriques et géométrisation du programme de Langlands | Jun 2018, l'ENS de Lyon, France
Automorphic Forms and The Langlands Program | Aug 2017, MSRI, Berkeley, CA
p-adic Hodge Theory and Automorphic Forms | Jun 2017, BICMR, Beijing
The 7th International Congress of Chinese Mathematicians (ICCM) | Aug 2016, Beijing
Workshop on the p-adic Langlands Correspondence | Jul 2016, 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.

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