Yihang Zhu 朱艺航

Professor Tsinghua University Yau Mathematical Sciences Center Brief Bio: I received my Ph.D. in 2017 from Harvard University, under the supervision of Prof. Mark Kisin. Before the current position, I was a Ritt Assistant Professor at Columbia University and Assistant Professor at University of Maryland. Email: yhzhu + at + tsinghua.edu.cn Office address: 清华大学静斋205 Jingzhai 205, Tsinghua University

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Research Interest

Number theory and automorphic representations. More specifically, I am interested in the interaction of the following topics as predicted in the Langlands Program:

• Arithmetic of Shimura varieties, Rapoport-Zink spaces, affine Deligne-Lusztig varieties, etc.
• Automorphic representations, Arthur-Selberg trace formulas and endoscopy
• Representation theory of real and p-adic groups.

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Learning groups

• Fall 2025 - Spring 2026. Learning group on Categorical Local Langlands after Xinwen Zhu (MCM-YMSC p-adic Geometry Learning Seminar)
• Spring 2025. Learning group on Canonical Integral Models of Shimura Varieties
• Fall 2024. Learning group on Condensed Mathematics

Recent teaching

• Spring 2026. p-adic Geometry. (cotaught with Hansheng Diao) Notes for my part
• Fall 2025. Algebraic Number Theory II. Notes
• Spring 2025. Algebraic Number Theory I. Notes
• Fall 2024.
  • Topics in the Langlands Program (II).

    Teaching jointly with Bin Xu. I teach the first half on Eisenstein series. course summary and exercises.

  • Joint Lecture Series in Modern Number Theory (the Mordell Conjecture)
• Summer 2024. Introduction to the Langlands Program (summer school at PKU). notes.pdf (Update: added notes of final lecture.)
• Spring 2024.
  • Topics in the Langlands Program.
  • Joint Lecture Series in Modern Number Theory (the Mordell Conjecture)
• Fall 2023.
  • The Hodge-Tate period map on the perfectoid Shimura variety

    Notes.

  • History of Class Field Theory (in Chinese) 类域论的历史 1 2 3 (You may need to refresh the video website twice.)
• Spring 2023. Representations of p-adic groups. Notes
• Spring 2022. Topic course on Shimura varieties. Notes
• Summer 2021. Mini course at BICMR: Counting points on Shimura varieties. (website), Notes

  Erratum: Exercise 4.4, Every semi-simple element admits at most one polar decomposition. The polar decomposition exists if and only if all eigenvalues in the algebraic closure have integral valuations.

• Spring 2021, Math 621: Algebraic Number Theory II. Notes

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Papers & Preprints

*Some of the PDFs linked below are more updated than the arxiv versions.

Preprints

• The stable trace formula for Shimura varieties of abelian type
  

  (with Mark Kisin and Sug Woo Shin)
  [pdf] [arxiv]
  Revision coming! To appear in Ann. Math. Stud.

Published

• The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties.
  

  [pdf] [arxiv]
  Astérisque, 453 (2024). DOI : 10.24033/ast.1225



• Stabilizers of irreducible components of affine Deligne-Lusztig varieties
  

  (with Xuhua He and Rong Zhou)
  [pdf] [arxiv]
  J. Eur. Math. Soc., (2024), published online first. DOI 10.4171/JEMS/1414



• Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties
  

  (with Rong Zhou)
  [pdf]
  Camb. J. Math., 8 (2020), No. 1, 149–241. doi:10.4310/CJM.2020.v8.n1.a3



• Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas
  

  (with Xuhua He and Chao Li)
  [pdf]
  Forum Math. Sigma, 7 (2019), E15. doi:10.1017/fms.2019.45 (Open Access)



• Arithmetic intersection on GSpin Rapoport-Zink spaces
  

  (with Chao Li)
  [pdf]
  Compos. Math., 154 (2018), No. 7, 1407-1440. doi:10.1112/S0010437X18007108



• Remarks on the arithmetic fundamental lemma
  

  (with Chao Li)
  [pdf]
  Algebra Number Theory , 11 (2017), No. 10, 2425-2445. doi:10.2140/ant.2017.11.2425




Other Published Writings

• Report for the Oberwolfach workshop Automorphic Forms, Geometry and Arithmetic (Aug 2021)
  

  [pdf]



• Proof of the arithmetic fundamental lemma in the minuscule case
  

  (with Chao Li)
  [pdf]
  An appendix to Yifeng Liu, Fourier-Jacobi cycles and arithmetic relative trace formula
  Camb. J. Math., 8 (2020), No. 1, 149–241. DOI: 10.4310/CJM.2021.v9.n1.a1



• Introduction to the Langlands-Kottwitz method.
  

  [pdf]
  A chapter in the Paris Book Project Shimura Varieties, London Mathematical Society Lecture Note Series: 457
  (edited by T. Haines and M. Harris, 2020).



• Report for the Oberwolfach workshop Harmonic Analysis and the Trace Formula (May 2017)
  

  [pdf]

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My name in Chinese characters: 朱艺航 (simplified); 朱藝航 (traditional).

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Background picture is originally the table of local Dynkin diagrams in Tits, J. Reductive groups over local fields. Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, pp. 29--69.
Copyright © 2019-2026 Yihang Zhu.