Yihang Zhu's Homepage

About me: I am an Assistant Professor at University of Maryland, College Park.
Previously I was a Ritt Assistant Professor at Columbia University, after receiving my Ph.D. in 2017 from Harvard University, under the supervision of Prof. Mark Kisin.

Email: yhzhu + at + umd.edu

Office address:

2111 Kirwan Hall.
If you want to meet me virtually send me an email.

photo by S.W.S.

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.

Recent teaching

Spring 2023. Representation theory 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), updated notes
Spring 2021, Math 621: Algebraic Number Theory II. updated notes

Papers & Preprints

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

Preprints

[significantly revised] The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties.
[pdf] [arxiv]
PhD Thesis. (Submitted)

The stable trace formula for Shimura varieties of abelian type
(with Mark Kisin and Sug Woo Shin)
[pdf] [arxiv]

Stabilizers of irreducible components of affine Deligne-Lusztig varieties
(with Xuhua He and Rong Zhou)
[pdf] [arxiv] (Submitted)

Published

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)
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)
[arxiv]
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]

Seminars

I am one of the organizers of the Algebra-Number Theory Seminar at UMD

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

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