Event № 980
NOTE: Due to the situation in the south, the seminar moved from BGU to the Technion
This year's first Joint Israeli Operator Algebras/Operator Theory seminar will take place at The Technion, Amado, room 919.
12--13 Jaydeb Sarkar (ISI Bangalore)
14--15 Serban Belinschi (Institut de Mathematiques de Toulouse)
Title: Commutant lifting theorem, Nevanlinna-Pick interpolation and Schur functions in several variables
Abstract: In this talk, we will consider the classical commutant lifting theorem (due to Sarason) and Nevanlinna-Pick interpolation in the setting of reproducing kernel Hilbert spaces over the unit ball in C^n. Along the way, we will also analyze factorizations of multipliers and Schur functions (on the unit ball and the unit polydisc).[Joint work with K. D. Deepak, D. Pradhan, D. Timotin and R. Debnath]
Title: "Regularity questions for operator-valued free random variables."
Abstract: "The notion of free independence (or freeness) was introduced by Voiculescu with the purpose of studying free group factors from a probabilistic perspective. Since its introduction, it has developed in a very powerful tool, both in operator algebras /theory / spaces, and in the study of the asymptotic behavior of $k$-tuples of large random matrices.Roughly speaking, if freeness corresponds to the study of von Neumann algebras associated to free products of groups, freeness with amalgamation corresponds to studying von Neumann algebras associatedto free products of groups with amalgamation over a subgroup. This powerful generalization of freeness, due also to Voiculescu, turns outto be a very powerful tool in the study of joint distributions of non-commuting random variables (including random matrices).After introducing the notions of noncommutative distributions and offreeness, I will show how free noncommutative functions are used to encode these notions. I will explain some notions of regularity fornoncommutative distributions, and show how one obtains a characterization of the "atomic part" of free convolutions of noncommutative distributions with the aid of free noncommutative functions. The talk will be based mostly on joint work with H. Bercovici and W. Liu, and with V. Vinnikov (both ongoing and completed)."