Colloquium: Tuesday, April 10, 2 pm. Speaker: Adam Skalski, (Polish Academy of Sciences). Title: “On new constructions of compact quantum groups”.
Initial developments in the theory of (topological) quantum groups were motivated on one hand by the desire to extend the classical Pontryagin duality for locally compact abelian groups to a wider class of objects and on the other by the idea of replacing the study of a space by the investigation of the algebra of functions on it. In 1980s the theory was given a big boost by the discovery of a big class of examples arising as deformations of classical compact Lie groups and the resulting conceptual progress, mainly due to Woronowicz. In this talk we will describe this background and present two approaches to constructions of quantum groups developed in the last decade, leading to so-called quantum symmetry groups and liberated quantum groups. They turn out to produce very interesting examples and offer connections to noncommutative geometry and free probability.