Colloquium Mathematics - Dr. M. Kool (UU)

Title:

Discovering new geometry from physics

Abstract:

Physics often leads to the development of new mathematics (and vice versa). I will discuss a mysterious symmetry of a quantum field theory, known as S-duality. Roughly speaking, S-duality says that the theory at strong interactions g is equivalent to a dual theory at weak interactions 1/g. In 1994, Vafa-Witten argued that this symmetry manifests itself in a beautiful transformation property of the "partition function", which ought to be a "modular form"; a type of functions which plays an important role in number theory. In 2017, geometers were able to define Vafa-Witten's partition function mathematically and test the predictions of the physicists. I give a non-technical overview of these developments.