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.

## 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.

**[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) - 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 - 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]

##### Preprints

##### Published

##### Other Published Writings

## 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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