Yuezhao Li

I am a postdoctoral researcher at Beijing International Center for Mathematical Research, Peking University. I study noncommutative geometry (NCG) and its applications in index theory and mathematical physics.

My research is mainly about the mathematical ideas of topological phases of matter. A current interest of mine is to understand interacting particule systems and their invariants in the framework of quantum spin systems. Previously, I use techniques from bivariant K-theory to provide a conceptual framework of the spectral localiser due to Loring and Schulz-Baldes. This may shed some light on understanding the index theory of spectral truncations in the sense of Connes and van Suijlekom, and the operator system K-theory of van Suijlekom. I have also studied topological phases of non-interacting systems and their invariants using techniques from K-theory, groupoid C*-algebras and coarse geometry.

Contact: liyuezhao AT bicmr.pku.edu.cn

See also my CV, my ResearchGate and LinkedIn, as well as some other things about myself, including running, languages, coding, etc.

Short bio

Oct 2026–now: postdoctoral researcher (research assistant) at BICMR, Peking University.
Mar–Aug 2026: postdoctoral researcher at MPIM Bonn.
2021–2025: PhD student of the NCG research group at Leiden, supervised by Dr. Bram Mesland.
2018–2021: Master student in mathematics at Georg-August-Universität Göttingen, thesis written with Prof. Dr. Ralf Meyer.
2013–2018: Bachelor student in physics at Peking University.

My calendar in 2026

Starting October 2026, I am a postdoctoral researcher at Peking University, China. During 1 March – 31 August, 2026, I was a postdoctoral researcher at Max Planck Institute for Mathematics at Bonn, Germany. Recent events in 2026:

1–4 September: Research visit to Universiteit Leiden, Netherlands.
7–11 September: Conference Interactions between operator algebras, K-theory and homotopy theory. Münster, Germany.
14–16 September: Workshop K-theory of C*-algebras in solid state physics: 40 years later, in honor of Jean Bellissard’s 80th birthday. Potsdam, Germany.
7 October: Online talk at Noncommutative geometry in NYC.
24–25 October: Fourth Workshop of Young Scholars in Noncommutative Geometry and Operator Algebra. Beijing, China.

Articles and preprints

Articles are listed in reverse chronological order.

All my preprints on arXiv.

Consistent symmetry breaking and topological phases (with G. C. Thiang), arXiv:2607.28181.
The odd spectral localiser via asymptotic morphisms and quasi-projections (with B. Mesland), Ann. K-Theory 11, no. 2 (2026), 213–260.
Robustness of topological phases on aperiodic lattices, Math. Phys. Anal. Geom. 29, no. 2 (2026), Paper No. 16.

Notes and 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.

Unbounded KK-theory. The notes originate from Bram Mesland’s lecture course on unbounded KK-theory given at Hausdorff school “Noncommutative Geometry and Operator Algebras” in Bonn, in May, 2023. Unbounded KK-theory treats unbounded Kasparov modules as geometric objects and study their representing noncommutative geometries in the sense of Alain Connes. I took these notes as a first draft during the course and they were made complete by Bram Mesland.
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.
C*-algebras of Bratteli diagrams and foliations of translation surfaces. My notes of the second part of Leiden NCG reading seminar on foliations. It is mainly based on, and is an expository of the paper “Bratteli diagrams, translation flows and their C*-algebras” by Ian Putnam and Rodrigo Treviño.
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”.

LaTeX

I am keen on TeXniques, though I am not good at them. Below are some templates that I have been working on over time. They are far from being complete document preambles, but might contain some useful configuration or layout. If you find any of them interesting, feel free to use or adapt them for your own projects.

Leiden thesis template. A thesis template for Leiden University. The color theme comes from a beamer template by Tobias A. de Jong. The template also includes a titlepage that meets the layout requirement of Leiden University as of 2025.
A handout template. The source code of a handout for a previous talk of mine, which contains some designs of a few theorem-like environments using the package mdframed.

Some other thoughts of mine on LaTeX.