Topology Seminar: Daniel Sheinbaum

We will introduce basic notions of quantum mechanics, mostly employed in condensed matter physics, such as a separable Hilbert space, Bloch's theorem and Fermi surfaces. Then we will describe the problem of stability of Fermi surfaces and relate it to the mathematical concepts of Fredholm operators and homotopy classes. Equipped with these concepts we show that our proposed scheme yields a classification of topologically stable Fermi surfaces by K-1(X), where X is the Brillouin zone and K-1 is a well known functor in K-theory. We will show an explicit example when X = S1, known as the spectral flow and its relation to quantum anomalies. This is work in progress joint with Alejandro Adem and Gordon W. Semenoff.