Yihang Zhu's Homepage

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

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.

Learning groups

Fall 2024. Learning group on Condensed Mathematics

Recent teaching

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

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]

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

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Yihang Zhu 朱艺航