Probabilistic Operator Algebras Seminar

(University of Copenhagen)

We seek an analog for the quantum permutation group S+n of the normalized Hamming distance
for permutations. We define three distances on the tracial state space of C(S+n) that generalize
the L1-Wasserstein distance of probability measures on Sn equipped with the normalized Hamming
metric, for which we demonstrate basic metric properties, subadditivity under convolution, and
density of the Lipschitz elements in the C-algebra. Two of those metrics are based on a similar
construction to Biane and Voiculescu’s free Wasserstein distance.

(University Aix Marseille)

Within the framework of representation theory of Lie groups of type SU(N) we shall recall the
pictograph approach relating Littlewood-Richardson (LR) coefficients to honeycombs and other
dual presentations, in particular O-blades standing for Ocneanu blades. We shall also present a
pictographic approach of Kostka coefficients using degenerated O-blades. If time allows, we shall
see how the asymptotic behavior of LR coefficients is related to the volume function of the hive
polytope, which can be obtained in terms of the Fourier transform of a convolution product of
Harish-Chandra orbital measures, and see how such considerations can be generalized to study
intertwiners for other types of Lie groups

(KU Leuven)

Building on the classical noncommutative entropy for automorphisms of nuclear C*-algebras, I will
introduce a formally different notion of entropy which uses the more refined cpc approximations
given by finite nuclear dimension or finite decomposition rank. I will compare these formally different
notions and relate them to a measure-theoretic notion of entropy for traces. This is joint work with
Bhishan Jacelon