Speaker
Svitlana Mayboroda, ETH
Abstract
We shall discuss the Weyl law-style bounds on the integrated density states and the associated estimates on the supports of Wigner functions for the Schrodinger eigenfunctions. Contrary to the classical Weyl law, these results are not asymptotic, and not requiring traditional restrictions on the underlying potential. They are, as a natural pay-off, less precise – the absence of asymptotics necessitates covering many regimes simultaneously. We shall discuss their advantages, disadvantages, and connections with the uncertainty principle and the Anderson localization.
This is joint work with G. David, J. De Dios, M. Filoche, E. Malinnikova.