Yihang Zhu 朱艺航

Professor Yau Mathematical Sciences Center Tsinghua University. Brief Bio: I received my Ph.D. in 2017 from Harvard University, under the supervision of Prof. Mark Kisin. I was a Ritt Assistant Professor at Columbia University from 2017 to 2020, and Assistant Professor at University of Maryland from 2020 to 2023. 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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Recent teaching

• 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
• 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 To appear.


• Stabilizers of irreducible components of affine Deligne-Lusztig varieties
  (with Xuhua He and Rong Zhou)
  [pdf] [arxiv]
  J. Eur. Math. Soc. To appear.


• 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 © 2019-2023 Yihang Zhu.