At the Perimeter
Graham spent the past week at the Perimeter Institute for Theoretical Physics in Canada, as a guest of its Director Neil Turok, talking with several of its leading theoreticians. This was part of Graham’s research for his forthcoming book on the relationship between mathematics and fundamental physics, which Einstein called ‘miraculous’. For Paul Dirac, theoreticians who work on fundamental physics should regard mathematical beauty as their lodestar.
In Graham’s first stay at the Perimeter Institute, in 2012, he gave a public lecture on ‘Paul Dirac and Mathematical Beauty’, now available on Youtube. As Graham saw, the Institute is a unique place with a carefully engineered environment that encourages discussion and collaboration. Over lunch, Turok told Graham that he wants the Institute to be the best possible place to conceive and incubate new ideas’, adding that ‘there are no groups here, only creative individuals who are free to pursue their curiosity and are able to cross boundaries between different disciplines’.
Graham’s next book will look at the history of the subject, as well its developing relationship. This is why Graham wanted to revisit the Institute, now one of the world’s leading centres of research into quantum field theory, a source of great interest to both physicists and mathematicians. The importance of mathematics to modern theoretical physics was highlighted by the Institute’s recent hiring of the Irish mathematician Kevin Costello, whose innovative research has caught the imagination of several leading theoreticians, including Edward Witten. Turok says: ‘New mathematics is now crucial to many areas of contemporary theoretical physics and it’s great to see mathematicians working so closely here with physicists.’
One of the most productive areas of mathematics-physics collaboration in the past few years has been the theoretical study of scattering of fundamental particles. Institute’s leading theoreticians, the Venezuelan physicist Freddy Cazacho, is one of the leaders in this field, following his collaboration with Nima Arkani-Hamed, of the Institute for Advanced Study in Princeton. Graham spoke to the two of them, and learned how their aim of shedding light on the interactions of sub-atomic physics has led them to new areas of contemporary mathematics, especially in the field of algebraic geometry, notably in the development of so-called Positive Grassmanians.
One of the highlights of Graham’s visit was the opportunity to attend gathering of mathematicians who assembled at the Perimeter Institute to discuss the theme of ‘Symplectic Duality and Gauge Theory’. On the Saturday morning, it was ‘standing room only’ for Edward’s talk on the Geometric Langlands Programme and the light it sheds on gauge theories. Graham was struck by the atmosphere in this talk: ‘here was a great theoretician reaching out to mathematicians, bringing new insights into front-line mathematics from front-line physics, at the same time as seeking inspiration from mathematics’. It was a fitting climax to an enormously productive visit.