Geometric conformal field theory: what, why, and how
Since the early days of quantum field theory, mathematicians have worked to find a system axioms which describe the phenomena described by physicists. One of the most successful pieces of this endeavor was Atiyah's 1988 axiomatization of quantum field theories with topological symmetry via cobordism categories, which initiated a field of research that remains extremely active to this day. Less well known, however, is an earlier definition of Segal for a different flavor of quantum field theories, called conformal field theories, which inspired Atiyah's definition. The goal of this talk is to introduce and motivate Segal's definition of a conformal field theory, and to describe how it fits into the broader mathematical landscape. I will also discuss some of the challenges which arose during its development, along with recent and ongoing work to address them.
Dr James Tener, Australian National University