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

**Office address:**

Department of Mathematics, Columbia University

Room 415, MC 4436

2990 Broadway

New York, NY 10027

My CV.

photo by H. W.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 and other related spaces
- Automorphic representations, Arthur-Selberg trace formulas and endoscopy
- Representation theory of real and p-adic groups.

*The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties.*PhD Thesis. Updated version- Oberwolfach report on my thesis in this workshop.

*The stable trace formula for certain Shimura varieties of abelian type.*(With Mark Kisin and Sug Woo Shin.) In preparation.*Remarks on the arithmetic fundamental lemma.*(With Chao Li.) [pdf] (To appear in*Algebra and Number Theory*)*Arithmetic intersection on GSpin Rapoport-Zink spaces.*(With Chao Li.) [arxiv] preprint. (Submitted.)*Introduction to the Langlands-Kottwitz method.*To appear in Vol. 2 of the Paris Book Project*Stabilization of the trace formula, Shimura varieties, and arithmetic applications.*Edited by Clozel, Haines, Harris, Labesse, Ngo.

- I wrote my minor thesis in August, 2014, under the supervision of Prof. Wilfried Schmid. It is an exposition of the work of Miller-Schmid on automorphic distributions and the full holomorphy of the exterior square L-functions for $\DeclareMathOperator{\GL}{GL} \GL_{n, \mathbb Q}$.
- 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.

- Nov 4, 2017, JHU-UMD Algebra and Number Theory Day, Unversity 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

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

- Learning seminar on the geometry of fundamental lemmas. Fall 2017 (ongoing)
- 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)

- In Fall 2017, I am 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 two sets of 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); or 朱藝航 (traditional).