Clay Lecture: John Morgan (Columbia University) -- Physics, Loop Groups, and Low Dimensional Topology

It has long been known that, unlike the case of higher dimensions, topology of dimensions 3 and 4 is extremely difficult to tackle in its own terms. Ideas from other parts of mathematics and from physics have played an important role in the development of the subject. In this talk, I will review two striking examples of this phenomena, emphasizing the interplay of ideas from disparate sources. The two case studies are: (i) 4 dimensional gauge theory and its descendants and (ii) the Jones polynomial with its quantum and quantum algebraic cousins. As part of the second case study, I will discuss in some detail Graeme Segal’s Loop Group approach to two-dimensional CFT.