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Speaker: Amaury Freslon, U. Paris VII
Title: Invariant theory, quantum groups and free probability
Abstract: Partitions of finite sets are very rich objects which can be used in several areas of mathematics to deal with combinatorial problems. One application was designed by R. Brauer in the 1930s to study the invariant theory of the orthogonal group and led to several developements until recent years. Another application was developped by R. Speicher to give a purely combinatorial approach to free probability. Building on the latter, T. Banica and R. Speicher gave in 2009 a «partition» approach to compact quantum groups (easy quantum groups) suitable for free probabilistic applications. We will show that, generalizing their work to the notion of «partition quantum groups», one can also deal with invariant theoretic problems both for groups and quantum groups and recover many results from both fields, as well as new ones.
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