Singular traces and the density of states

Abstract: 

The density of states is a non-negative measure associated to a Schrodinger operator which is supported on its essential spectrum. Theoretical questions concerning the existence and properties of the density of states are of interest in solid state physics. We have recently found that quite generally the density of states measure can be computed by a formula involving a Dixmier trace. This is a surprising new application of singular traces to mathematical physics which uses recently developed techniques in operator integration theory. Joint work with N. Azamov, F. Sukochev and D. Zanin.