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:

Currently working remotely due to Covid-19.

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.

## Papers & Preprints

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

- Proof of (Fourier-Jacobi) arithmetic fundamental lemma for the minuscule case (with Chao Li) [pdf]

An appendix to Yifeng Liu,*Fourier-Jacobi cycles and arithmetic relative trace formula,*preprint - 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 certain Shimura varieties of abelian type (with Mark Kisin and Sug Woo Shin)

In preparation. - Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties (with Rong Zhou) [pdf] [arxiv]
*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 - Oberwolfach report on my thesis in this workshop.
- Introduction to the Langlands-Kottwitz method. [pdf]

A chapter in the book*Shimura Varieties, London Mathematical Society Lecture Note Series: 457*(edited by T. Haines and M. Harris).

##### Preprints/In Preparation

##### Published

##### Oberwolfach Report

##### Paris Book Project

## Expository Writings

- I wrote my minor thesis in August, 2014, under the supervision of Prof. Wilfried Schmid.
- Algebraic K-theory and special values of L-functions: Beilinson's conjectures. (Talk notes at Juvitop 2015.)
- Tamagawa numbers. (Talk notes expanded from two talks in Trivial Notions, in 2014 and 2016.)
- Review of Faltings's explicit deformation theory for p-divisible groups.

## Invited Talks

- Dec, 2019, Intensive Lecture Series at Korea Institue for Advanced Study, Seoul, Korea
- Nov 20, 2019, Harvard Number Theory Seminar
- Oct 14, 2019, Berkeley Arithmetic Geometry and Number Theory Seminar
- Sep 15, 2019, AMS Fall Central Sectional Meeting, Wisconsin-Madison
- Jun 27, 2019, Korea Institue for Advanced Study, Seoul, Korea
- Jun 14, 2019, The 8th International Congress of Chinese Mathematicians (ICCM 2019), Plenary Speaker, Beijing, China
- Mar 19, 2019, Conference in honor of Prof. Michael Rapoport's 71st birthday, Beijing, China
- Nov 1, 2018, University of Maryland Algebra-Number Theory Seminar
- Oct 19, 2018, Columbia University Automorphic Forms and Arithmetic Seminar
- Jun 30, 2018, Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China
- Jun 25, 2018, Summer School on Representation Theory and the GGP Conjecture, BICMR, Beijing, China
- Jan 2,4,5, 2018, Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China
- Nov 4, 2017, JHU-UMD Algebra and Number Theory Day, University of Maryland
- Oct 26, 2017, Caltech Number Theory Seminar
- Oct 25, 2017, UCLA Number Theory Seminar
- Sep 26, 2017, University of Chicago Number Theory Seminar
- Sep 25, 2017, Northwestern Number Theory Seminar
- Jun 15, 2017, Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China
- Jun 13, 2017, Beijing International Center for Mathematical Research, Beijing, China
- May 25, 2017, Workshop: Harmonic Analysis and the Trace Formula, MFO, Oberwolfach, Germany
- May 1, 2017, Minnesota Automorphic Forms and Number Theory Seminar
- Mar 13, 2017, Michigan University Group, Lie and Number Theory Seminar
- Feb 14, 2017, Yale University Algebra and Number Theory Seminar
- Jan 31, 2017, Johns Hopkins University Number Theory Seminar
- Nov 11, 2016, Columbia University Automorphic Forms and Arithmetic Seminar
- Oct 20, 2016, Princeton University/IAS Number Theory Seminar
- Oct 12, 2016, Harvard Number Theory Seminar

## Teaching

- In Fall 2020, I am teaching Math 405, Linear Algebra.
- In Spring 2020, I was teaching GU4042 Intro to Modern Algebra II.
- In Fall 2019, I was teaching Complex Variables, and Representations of Finite Groups.
- In Spring 2019, I was teaching Complex Variables, and Representations of Finite Groups.
- In Fall 2018, I was teaching GU4042 Intro to Modern Algebra II.
- In Spring 2018, I was teaching UN3007 Complex Variables, and GU4041 Intro to Modern Algebra I.
- In Fall 2017, I was teaching GU4042 Intro to Modern Algebra II.
- In Fall 2016, I was the course assistant of Math 25a Honours Linear Algebra.
- In Fall 2015, I was the course assistant of Math 25a Honours Linear Algebra.
- In Fall 2014, I taught a tutorial on complex multiplication with Rong Zhou. Website.
- In Fall 2014, I was the course assistant of Math 223a Algebraic Number Theory. Notes.
- In Fall 2013, I was the teaching fellow of Math 21a Multivariable Calculus and Linear Algebra.

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

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