Research Interests

Two primary schools putting QFT on firm mathematical footing are Algebraic Quantum Field Theory (AQFT) and Functorial Quantum Field Theory (FQFT). These are analogous to the Heisenberg and Schrödinger pictures of quantum mechanics, where the former focuses on observables and the algebraic properties thereof, and the latter describes the (time) evolution of state spaces. These two approaches have been studied independently until very recently when attempts are being made to relate the two. My work is based on a special subclass of quantum field theories, 2 dimensional chiral conformal field theories (CFTs). Two-dimensional CFTs describe critical phenomena in various condensed matter systems, and they also form the building blocks of string theory. The aim is to give a construction of a fully extended Segal chiral CFT (a functor defined on the category of conformal manifolds) from the algebraic data of a conformal net. 

I am also working on giving a rigorous mathematical basis to the idea that a d-dimensional (T)QFT has a monoidal (d-1)-category of symmetries. Global and higher categorical symmetries are being discovered by physicists in QFTs, and my project aims to present that such structures are expected to exist where symmetries are generalised to topological interfaces between QFTs. 

In the past decade, using higher categories has proven to be an essential ingredient in studying quantum field theories from a mathematical perspective. Studying QFT in the language of higher category theory beautifully and naturally incorporates many subtle concepts like generalised symmetries, topological defects, and locality, to name a few.