An Application of Homotopy Theory to Condensed Matter Physics

The classification of phases of matter is a topic of much current interest. While descriptions of quantum mechanical systems often use discrete lattice models, one can typically approximate by continuous field theories. There is a well-developed mathematical framework for studying field theories, and this brings powerful techniques to the table. In this general talk, I will describe joint work with Mike Hopkins (Harvard) in which we carry out this scheme for invertible phases of matter and deduce the classification in terms of bordism groups of manifolds. Much of the talk will focus on general ideas at an elementary level.