Speaker: Akihiro Miyagawa (Kyoto Univ.)

Title: Rationality for operators in free semicircular elements

Time/Date: 4:45-6:15pm, January 11 (Tue.), 2022

Room: This will be an online seminar on Zoom. Please ask Kawahigashi for the Zoom link.

Abstract: Free probability is a kind of noncommutative probability, which D. Voiculescu introduced to analyze operator algebras obtained from the free product. In the last few years, Roland Speicher and his coauthors revealed a relation between this theory and noncommutative rational functions. In this talk, I will explain a characterization of rationality for operators in free semicircular elements. They are essential distributions since they are limiting objects for the free central limit theorem and empirical eigenvalue distributions of independent GUE random matrices. My result is an analog of Duchamp and Reutenauerfs result in terms of noncommutative geometry, which was extended to affiliated operators by P. Linnell.