I am a PhD candidate in mathematics at Leiden University, working in the field of noncommutative
geometry. My supervisor is Dr. Bram
Mesland.
From 2013 to 2018, I studied physics and mathematics at Peking University, China. From 2018 to
2021, I studied mathematics at Georg-August-Universität Göttingen, Germany, specialising in
noncommutative geometry and its application in topological insulators. I wrote my master thesis
under the supervision of Prof. Dr. Ralf
Meyer.
I use tools and viewpoints from noncommutative geometry to study index theory and mathematical
physics, in particular, those arising from the study of topological insulators.
- Starting from the seminal work of Jean Bellissard and his collaborators, C*-algebras and
K-theory have become prominent in understanding topological insulators. The
"noncommutative essence" of the real world fits naturally into the language of
noncommutative C*-algebras and NCG. Recently, motivated by the work of Bourne and Mesland on the
index theory of aperiodic topological insulators, and Meyer's work on groupoid correspondences, I am
reconsidering the structure of those C*-algebras that are used to model topological insulators.
An ongoing work of mine tries to use more "modern" techniques of groupoids and inverse semigroups to study them.
-
Another mainstream of my research lies in understanding "index theory at finite resolution",
namely, how to achieve nice numerical results using finite-dimensional data of physical
systems.
There were several very successful attempts, among which there is Schulz-Baldes and Loring's
spectral localisers. My ongoing work aims at a more systematic approach to this method.
Besides mathematics, I am also an enthusiastic long-distance runner.
NCG-Leiden / Noncommutative geometry reading seminar
I am a maintainers of NCG-Leiden (together
with Yufan Ge and Francesca Arici), a webpage collecting and announcing the information of
local NCG seminars at Leiden University. In
2024 spring semester, Francesca Arici and Bram Mesland are running a research seminar
on Wednesdays from 15:15-16:15. If you want to be added to the mailing list for this seminar,
please contact Francesca Arici or Bram Mesland.
In March 2024, Adam Rennie gave a mini-course on connections and curvatures in NCG,
based on joint work of him and Bram Mesland.
In previous semesters, we have run reading seminars on noncommutative geometry of foliations
(2023 fall), groupoid
C*-algebras (2022 fall) and KK-theory
(2022 spring).
Notes / Handouts
I have taken notes for several lectures and seminars. Some of them are below. They may be
incomplete and contain mistakes. Please use at your own risk.
- Groupoid
C*-algebras. My notes of Leiden NCG reading seminar on Groupoid
C*-algebras, 2022 fall semester. The notes contain fundaments of groupoids and their
C*-algebras, as well as some special topics based on the participants' own interest.
- KK-theory. My
notes
of Leiden NCG reading seminar on K(K)-theory,
2022 spring semester. We covered the basic knowledge of KK-theory in the first half,
including
the approaches of Kasparov and Cuntz. In the second half we turned to more research-related
fields based on speakers' own interest.
- Coarse
geometry
and groupoids. My notes of Nick Wright's talk on the coarse Baum-Connes
conjecture at Autumn School on Large
Scale Geometry, with an emphasis on the coarse groupoid construction of Skandalis,
Tu
and Yu. The interest of mine lies in the fact that the groupoid models of Roe C*-algebras
provide more explicit comparison maps between different models of aperiodic topological
insulators, and hence have potential physical applications.
- Localisation
algebras and K-homology. A handout provided for a talk in the Local NCG seminar
at Radboud University Nijmegen, 2023 spring semester. It is mainly based on Guoliang Yu's
article "Localization algebras and the coarse Baum-Connes conjecture", in which a new
picture of
K-homology is given to simplify the higher index map.
- Introduction to index
theory. A
handout provided for a talk at Leiden NCG reading seminar on Deformation quantisation
and
index theory, 2021 fall semester. It provides a basic introduction to the
Atiyah-Singer index theorem, and highlights the role of K-theory of C*-algebras.
- Completely bounded
maps. A handout provided for a talk at Leiden Functional Analysis
seminar
on Completely bounded maps
and
operator algebras, 2021 fall semester. It is based on Chapter 8 of Vern Paulsen's
book
"Completely bounded maps and
operator algebras".
Talks
Teaching
- 2023 Fall: Teaching assistant of Dutch national Mastermath course “Functional Analysis”.
- 2023 Spring: Teaching assistant of Leiden undergraduate course “Differentiable Manifolds
II”.
- 2022 Fall: Teaching assistant of Dutch national Mastermath course “Functional Analysis”.
- 2022 Spring: Teaching assistant of Leiden undergraduate course “Differentiable Manifolds
II”.
- 2021 Fall: Teaching assistant of Dutch national Mastermath course “Functional Analysis”.
Events / Conferences and workshops
Personal activities / Hobbies
I am an eager runner, and a learner in German and Dutch.
Running
I enjoy long-distance running. As an undergraduate student at Peking university, I was a member
of PURA (Peking university runners'
association). I paused running for several
years but rediscovered my passion during the pandemic in 2021. Despite of those enumerous
annoying injuries, running
brings me far more pleasure and confidence.
Uitslagen:
- 26/11/2023: Halve Marathon @ Spijkenisse Marathon, Netherlands. Finish in 1:38:29.
-
10/03/2024: Halve Marathon @ NN
CPC Loop Den Haag
Halve Marathon, Netherlands. Finish in 1:37:48.
-
12/05/2024: Halve Marathon @ De 33e Leiden Marathon, Netherlands. Finish in 1:35:33.
Languages and linguistics
Ich lerne Deutsch und Niederländisch. Ich interessiere mich auch für die Geschichte der
germanischen Sprachen.
Links
Here are some links of my own interest.
People: my colleagues, friends and collaborators
- Bram Mesland, my supervisor,
assistant professor at Leiden university.
- Francesca Arici, assistant professor
at Leiden university.
- Marcel de Jeu, associate professor at
Leiden university.
- Yufan Ge, my friend and colleague, PhD student
at Leiden university.
- Yi Shan, my friend, PhD student
at ENS.
Mathematics and physics
TeXniques
Beyond mathematics