Lecture 1: 10 October 2022 at 3:30 pm
Lecture 2: 11 October 2022 at 2:30 pm
Lecture 3: 12 October 2022 at 3:00 pm
Abstract: Quantum field theory is witnessing a symmetry revolution with the discovery of various novel forms of global symmetries: higher-form symmetries, higher-group symmetries, sub-system symmetries, non-invertible symmetries etc. These symmetries are expected to have profound implications for the understanding of quantum field theories relevant in high-energy physics and condensed matter physics. In these lectures, I will focus on non-invertible symmetries, which is the most general form of symmetries in relativistic quantum field theories. The mathematical structure describing such symmetries is that of category theory. I will describe the dictionary between the physical and mathematical concepts in detail. I will also describe the current state of the art in the study of such symmetries and we will see that natural physical questions in this context lead us to the cutting edge of research in higher-category theory.