Yihang Zhu

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.

Preprints/In Preparation

• 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.



Published

• 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



Other Published Writings

• 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
  Camb. J. Math., to appear.


• 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).


• Oberwolfach report on my thesis in this workshop.