This will be a talk on how models of group algebras (quan-tum groups) with von Neumann trace (Haar measure), free product groups and natural positive definite functions like Haagerup functions, regular free product functions (now called Boolean product) give contruction of conditional free probability, which, as a special case, get contruction of the free probability, Boolean probility and monotonic (antimo-notone) probability of Muraki. Also classical (commutative) modelling of probability will be done. Also central limit theorems will be presented with some applications to Harmonic Analysis on free groups.
Marek Bozejko (*1946) received his doctoral degree in Mathematics at the Wroclaw University in 1973. In the following years he worked as an assistant professor at the Institute of Mathmatics at Wroclaw University where he also handed in his habilitation in 1980. Afer working as an associate professor he became full professor in 1990. Marek Bozejko has furthermore been visting professor at the Uni-versity of Milan, the University of Heidelberg and the University of Vancouver. He has received many awards such as the Prize of the Polish Ministry of Science and Higher Education or the Humboldt Research Award.
Moderation: Professor Dr. Volkmar Liebscher