I am primarily focused on exploring mathematical structures that arise from the topological phases of quantum many-body systems, specifically higher fusion categories. These categories play a fundamental role in understanding the intricate connections between topological quantum field theories (TQFTs), homotopy theory, representation theory and related areas of study. Additionally, I am particularly intrigued by the phenomenon of condensation, symmetry gauging, and phase transitions within these topological phases, as they give rise to an exceptionally diverse and intricate structures and problems in the fundamental study of higher category theory.
Educational backgrounds
Doctor of Philosophy
2021 - Present
Georg-August-Universität Göttingen
Master of Mathematics
2017 - 2021
Jesus College, University of Oxford
ORCID [orcid.org/0009-0004-4693-8739]
Get in touch at [hao.xu@mathematik.uni-goettingen.de]