Combinatorics of partitions and the geometry of sheaves

Abstract: 

This will be a whirlwind tour of some topics of current interest in higher dimensional geometry and its interface with some aspects of theoretical physics. I will start with elementary properties of the generating function of partitions, well known since Euler, and discuss how this series as well as various relatives arise in modern geometry via sheaf theory. There will be a passing mention of modularity, the electromagnetic duality of gauge theories, the classification of Platonic solids and infinite-dimensional Lie algebras; I will aim to demostrate how all these topics fit together via geometry and gauge theory.