Teaching

Lectures on 'Extended Operators in QFTs and Tensor Categories' at Indian Insitute of Technology (IIT) Madras.

I gave a set of four lectures on extended operators in QFTs and their relation to tensor categories at IIT Madras. The lecture notes and videos of the series will be available soon. The abstract of the series is given below.

Quantum field theories (QFTs) contain not only point operators inserted at specific spacetime points, but also extended operators supported on lines, surfaces, and other higher-dimensional submanifolds. These extended operators encode information that is invisible to the spectrum of local operators alone. A complete description of a QFT, therefore, requires understanding its full set of extended operators and their correlation functions. In this series of talks, I will explain how extended operators naturally organize into mathematical structures known as higher categories. I will illustrate this in explicit examples of quantum field theories in various dimensions. I will explain how this framework has been especially powerful in describing topological operators and has driven the recent study of generalized symmetries. The overarching goal is to provide a physicist-friendly introduction to tensor categories and to motivate their central role in modern approaches to QFT. No prior background in category theory will be assumed.

Teaching Assistant

• Quantum Field Theory 1 at International Centre for Theoretical Physics

• Classical Mechanics 1 at Queen Mary University of London

• Supersymmetric Methods in Physics at Queen Mary University of London