I am a PhD candidate in mathematics at Leiden University, studying noncommutative geometry (NCG) and its applications in index theory and mathematical physics. 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.
Besides mathematics, I am also an enthusiastic long-distance runner.
Research. The "noncommutative essence" of the real world suggests the possibility of NCG being a language of physics. One of the most successful attempts was provided by the seminal work of Jean Bellissard and his collaborators on the integer quantum Hall effect. Since then, C*-algebras and K-theory are prominent in understanding solid state systems, in particular, topological insulators. Motivated by the work of Bourne and Mesland on index theory of aperiodic topological insulators, and Meyer's work on groupoid correspondences, I am reconsidering the structure of C*-algebras modelling topological insulators, and attempting to provide a novel approach with techniques of groupoids correspondences and partial dynamical systems.
Recent focus of my research is about index theory of finite spectral truncations, namely, how to obtain numerical index pairings using only finite-dimensional spectral data that come from a finite energy cut-off of an infinite dimensional spectral triple. There have been several successful attempts, among which there is Schulz-Baldes and Loring's spectral localisers. Ongoing work of mine will provide a systematic understanding of this and similar techniques in literature.