## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Spring 2004 -Hans Rademacher Lectures in Mathematics## Department of Mathematics, University of California, Berkeley

Dan-Virgil Voiculescu

will deliver four lectures on

## Aspects of Free Probability

The Free Parallel to Classical Probability

Monday....February 23, 2004....4:00pmAbstract:We shall discuss a probabilistic framework for quantities with the highest degree of noncommutativity. Unexpectedly many concepts in classical probability theory have counterparts in this context.

Random Matrices and von Neumann Algebras

Tuesday....February 24, 2004....4:00pmAbstract:Von Neumann algebras and the large N limit of random matrices provide basic models of free probability. Equating the two has led to new insights in both subjects.

Free Entropy

Wednesday....February 25, 2004....4:00pmAbstract:There is a free analogue to Shannon's information-theoretic entropy for continuous random variables. The subject has connections with problems on II_1 factors, large deviations for random matrices and L^2 - Betti numbers.

Free Analysis Questions

Thursday....February 26, 2004....4:00pm

Abstract:Analysis questions around cyclic derivatives and free difference quotients appear naturally in free probability. Their study involves a large Lie algebra of infinitesimal symmetries of von Neumann algebras of free groups and respectively the coalgebra duality for the free difference quotient.

Previous Rademacher Lecturers

All lectures will be held in room A-6 of the David Rittenhouse Laboratory, corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 David Rittenhouse Laboratory, preceding the lectures at 3:30pm.For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.