Mathematicians meet Fermi surfaces: a semiclassical approach to the dynamics of Bloch electrons
Marcello Seri (Groningen)
Abstract:
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.