photo: ZC and the sea of clouds atop the Niubeishan mountain

Zhe Chen

My name in Chinese: 陈哲(simplified)

E-mail: zhechencz [at] gmail [dot] com

I obtained my PhD degree in the summer of 2017 at Durham University, UK.
Since then I have been working at Department of Mathematics, Shantou University, China.

Research

My research interests are around representation theory and number theory, with a focus on representations of profinite groups of Lie type.

Some writings: (some corrections)

(with Yongqi Feng) Class numbers and invariant characters of sl_2(F_p). Preprint.
(with Yushan Pan) A remark on decomposing the canonical representation of the Drinfeld curve. A preliminary version.
Hopf algebra and the duality operation for gl_n(F_q). Preprint.
On a stability of higher level Coxeter unipotent representations. Manuscripta Mathematica, 2025.
(with Alexander Stasinski) The algebraisation of higher level Deligne--Lusztig representations II: odd levels. Preprint.

The above paper establishes the explicit character formula for higher level Deligne--Lusztig representations on general elements, when the parameter is strongly generic. In the special case of GL_n, this result can be rephrased in terms of regular semisimple conjugation orbits, as presented in the slides; note that the last page of the slides contains a conjecture that is unconditional on all parameters, which appears originally in our paper "On a stability...".

Intersections of Deligne--Lusztig varieties and Springer fibres. Preprint.
Twisting operators and centralisers of Lie type groups over local rings. Journal of Algebra, 2022.
Flags and orbits of connected reductive groups over local rings. Mathematische Annalen, 2020.
A note on cusp forms and representations of SL_2(F_p). Journal of Group Theory, 2021.
Green functions and higher Deligne--Lusztig characters. Documenta Mathematica, 2018.
On the inner products of some Deligne--Lusztig-type representations. International Mathematics Research Notices, 2020.
Generic character sheaves on reductive groups over a finite ring. Journal of Pure and Applied Algebra, 2021.
(with Alexander Stasinski) The algebraisation of higher Deligne--Lusztig representations. Selecta Mathematica, 2017.
On generalised Deligne--Lusztig constructions, Durham PhD thesis, 2017. Official version. My thesis template.

Some activities:

CH@TAG: a half-day (semi-)scientific popularisation seminar (Jan 2025); seminar poster. "CH@TAG" is short for "Cheng-Hai.Alegbra.Topology.Arithmetic.Geometry.day", in which "day" comes also from "TAG".
Lectures at SUSTech, "Cohomology and Coxeter unipotent representations: the story of GL_3" (Aug 2023). Click here for the lecture notes.
Three (online) talks at Xiamen University, "Deligne–Lusztig constructions over finite fields and finite rings I,II,III" (May--Jun 2022). Videos are recorded in this website.
A modular Deligne--Lusztig theory seminar (2017--2018). Click here for more details.

Teaching

Undergraduate Courses Info (internal link).
Graduate Courses Info: (Spring 2025) Basics of algebraic groups and group schemes (rough plan).

Miscellaneous

Weiqi (also known as Baduk and Go) is an ancient board game, built on a few simple rules. I continued this hobby in UK via the friendly Durham Go club. Currently I am around 2~3 dan.