The Generation Game

We're here with three generations of mathematicians working in conformal field theory. Nivedita, who's my grad student. I guess you started in the physics department and then transferred to maths. And Graeme Segal, who I mean, you're the founder in some sense. — three times as old as Nivedita. — So, in the '80s conformal field theory was really a thing that was done only by physicists and um Graeme Segal did this like great service to mathematicians, which is he transformed something that was completely impossible for others to mathematicians to parse into something that is now on solid mathematical grounds. I tried to understand what two-dimensional field theory was and after a lot of conversation with Witten, I hit upon a mathematical definition of the theory, which mathematicians seem to have been able to understand and that had played a role in moving the subject in from being part of physics to part of mathematics. I still, after all these years, can't really speak to a physicist unless they're sort of highly trained already in speaking to mathematicians. — So, what one thing that I really like about conformal field theory is how it has attracted um a lot of people with different backgrounds. There's mathematicians who are trained as probabilists that have started studying aspects of conformal field theory. There's mathematicians trained as algebraic geometers that have been attracted to the same area. There's mathematicians who have I myself uh started in operator algebras, which is yet another area. And these areas of math don't have much overlap. But, they can all be used as a particular way of attacking the same conformal field theory problems. I I think mathematics is a subject that is transmitted person to person and that I don't think that's recent. I think that goes back a long way. The paper Graham wrote the definition of conformal field theory is something I still go back to maybe every two weeks because there are some nuggets of wisdom here and there. There always things that I don't understand and then I either email Graham or email Andre and then they once I distinctly remember I asked Andre some question about obviously like an open problem that I like could not understand and he said "Maths is full of mysteries. " —