Classification of low-rank odd-dimensional modular categories

Abstract

Modular categories are important algebraic structures that appear in a diverse quantity of applications, including topological quantum field theory, representation theory of braid quantum groups, von Neumann algebras, conformal field theory, and vertex operator algebras. They also appear in the study of topological phases of matter and topological quantum computation. An important class of modular categories are those of odd dimension. In this talk, we will present a classification of low-rank odd-dimensional modular categories and the methods we used to do so, including a computer algorithm and other properties of odd-dimensional modular categories.

Reference: arXiv:2305.14542 (with Agustina Czenky and Julia Plavnik)

Speaker Intro

I am a rising high school senior at Bellevue High School in Bellevue, Washington and a participant in the MIT PRIMES-USA program, where I conducted this research. I am also interested in computer science, both algorithmically and through web development.