Email: the part of my name starting with y and ending with g + at + math.columbia.edu

Office address:

Department of Mathematics, Columbia University

Room 415, MC 4436

2990 Broadway

New York, NY 10027

## 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

*The PDFs linked below are in general more updated than the arxiv versions.

- Fine Deligne-Lusztig varieties and Arithmetic Fundamental Lemmas. (With Xuhua He and Chao Li) [pdf] [arxiv]
*Preprint. (Submitted)* - Twisted orbital integrals and irreducible components of affine Deligne-Lusztig varieties. (With Rong Zhou) [arxiv]
*Preprint. (Submitted)* - 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.* - 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]

*To appear in Vol. 2 of the Paris Book Project (edited by T. Haines and M. Harris).*

##### 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

- Mar 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

## Seminars

Links to learning seminars of which I am/was a (co-)organizer.

- Learning seminar on Local Langlands. Spring 2019 (Co-organized with Sam Mundy)
- Learning seminar on Local Langlands. Fall 2018 (Co-organized with Sam Mundy) program
- Learning seminar on Beyond Endoscopy. Spring 2018 (Co-organized with Chao Li and Pak-Hin Lee)
- Learning seminar on the geometry of fundamental lemmas. Fall 2017 (Co-organized with Chao Li and Pak-Hin Lee)
- Graduate student seminar on higher dimensional class field theory, Fall 2014
- Graduate student seminar on Gross-Zagier and Kolyvagen, Fall 2013 (Co-organized with Rong Zhou)

## Teaching

- In Spring 2019, I am 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. Review sessions. (Containing some notes)
- 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. Recitation talks. (Containing some 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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