Mathematics Colloquium

Interactions between mathematical physics and enumerative geometry have been a very rich source of new ideas in both fields for the past quarter of a century. This talk will be about some more recent developments that link enumerative geometry with quantum groups and other objects that are really central to both representation theory and how it is applied in mathematical physics. While the overarching picture is really beautiful, thanks to many deep insights of many people, I will try to explain its main ingredients in the simplest examples.