There has long been a close relationship between pure mathematics and theoretical physics. Many subfields of mathematics began with attempts to address problems from theoretical physics. A famous example is Newton's development of calculus, which he applied to understand the motion of the planets. On the other hand mathematics provides an essential language for physicists to describe their theories, and calculational tools to allow them to make precise predictions.
In the last few decades this relationship between maths and physics has become extremely strong. The present-day interaction revolves around a subject called quantum field theory, which forms an incredibly powerful calculational tool in theoretical physics, but which has not yet been understood in precise mathematical terms. Quantum field theory has been described as being the calculus of infinite dimensions.
This work is exploring a class of problems in pure mathematics which are closely related to important ideas in quantum field theory. The ultimate goal is to prove a general result showing they can always be solved – bringing us a little closer to a mathematical understanding of quantum field theory.
Professor Tom Bridgeland
The Royal Society Professorships are prestigious appointments that provide long-term support for internationally recognised scientists of exceptional accomplishments from a range of diverse fields, including biochemistry, genetics, mathematics, chemistry, computer science, developmental biology and physics.