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Thursday, May 11, 2017

**Abstract:** Compact quantum groups are noncommutative generalizations of compact groups. A natural problem, studied by a number of people and explicitly formulated by Woronowicz already in the 80s, is how to classify quantum groups with representation theory "looking like" that of a compact connected Lie group. I will explain a classification result for a large class of such quantum groups. The main goal, however, will be to discuss noncommutative random walks and their Poisson boundaries, which played a crucial role in obtaining that classification.