https://www.fields.utoronto.ca/programs/scientific/07-08/operator_algebr...

The second last lecture in the graduate course on free probability will be given by Uffe Haagerup

UFFE HAAGERUP

Brown's spectral distribution measure for operators in finite factor.

Brown's spectral distribution measure was introduced by L. G. Brown in 1983 based on the Fuglede-Kadison determinant in a finite factor and the theory of subharmonic functions in two real variables. The Brown measure has been computed for a number of (non-normal) operators that occur naturally in free probability: Voiculescu's circular operator and more generally R-diagonal operators and elliptic operators. We will discuss the various methods, that have been used for such computations, and also briefly discuss the applications of the Brown measure to construction of invariant subspaces.