Yuezhao Li
Avatar of Yuezhao Li
PhD candidate in mathematics
Mathematical Institute
Leiden University
Netherlands
Email: y.li@math.leidenuniv.nl

I am a PhD candidate in mathematics at Leiden University, working in the field of noncommutative geometry. My supervisor is Prof. 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 study the application of noncommutative geometry to index theory and mathematical physics. Work of mine in progress is devoted to understanding topological insulators using tools from noncommutative geometry and C*-algebras, following the pioneering work of Jean Bellissard. Another keen interest of mine is unbounded KK-theory, a novel framework for Connes' noncommutative differential geometry initiated by Bram Mesland, soon joined by brilliant mathematicians including Walter van Suijlekom, Jens Kaad, Simon Brain, Adam Rennie and many others.

Besides mathematics, I am also an enthusiastic long-distance runner.

2024 Spring Semester: I am tutoring the Dutch national mastermath course "Operator Algebras" taught by Martijn Caspers and Bram Mesland. The noncommutative geometry research group of Leiden university is running a research seminar on NCG and related topics.


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 the upcoming month (March 2024), Adam Rennie will give a mini-course on connections and curvatures in NCG, based on ongoing 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.

Until now I have participated in (and finished) one half-marathon. More to achieve in 2024.

Languages and linguistics

Ich lerne Deutsch und Niederländisch. Ich interessiere mich auch für die Geschichte der germanischen Sprachen.


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