Title: Homotopy theory and phases of matter
Abstract: Phases of matter are classes of quantum systems that may look different microscopically but share certain common macroscopic properties. An active problem in condensed matter physics is to classify phases of matter. In certain cases, the tools of homotopy theory provide a useful mathematical framework. Specifically, certain classes of phases of matter are expected to form a generalized cohomology theory, a point of view introduced by Kitaev. This can be accessed via quantum field theories as in the work of Freed-Hopkins. Another problem is to get at this connection directly from the point of view of lattice models, which are idealizations of materials commonly used by condensed matter physicists. In this mostly expository talk, I will discuss the latter perspective, with some results on this topic which are part of joint work with Hermele, Moreno, Pflaum, Qi, Spiegel, Vishwanath and Wen.