Mathematicians meet Fermi surfaces: a semiclassical approach to the dynamics of Bloch electrons
The Fermi surface is an important concept in solid state physics and in the theory of transport of electron in metals. While physically this has been thoroughly investigated in decades of experiments, the mathematics has lagged behind. Only one class of examples has been thoroughly studied as part of a program started by Novikov and developed by his topological school. In this talk I will start from the physical definition of Fermi surface and a review of recent results by Novikov and Maltsev to justify the need for a new approach. I will then suggest a rigorous definition of the physical Fermi surface in presence of perturbations in the semiclassical regime inspired by recent development in the mathematics of topological insulators. The talk is based on a joint work with Max Lein and Giuseppe De Nittis.