# Talk

Modul:   MAT675  PDE and Mathematical Physics

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

Prof. Dr. Guy David talk

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.