Modul: MAT675 PDE and Mathematical Physics

## Estimates for the number of eigenvalues for a Schrödinger operator

Talk by Prof. Dr. Guy David

**Date:** 18.03.21 **Time:** 18.00 - 19.00 **Room:** Y27H28

Abstract Presentation of a joint result with M. Filoche and Svitlana Mayboroda. We estimate the number of eigenvalues (integrated density of states) for an operator $L =-\Delta + V$. Think of the Weyl formula, but we look for a uniform estimate, which is not asymptotic. The statement and proof use the so-called Landscape function(the solution of $Lu=1$). We should also mention rapidly a case of random potentials.