Algebra & Combinatorics Research Group  |  Texas A&M University





A&C Seminar

Working Seminar
   in Algebra

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A&C Seminar:  Fall 2008, Fridays, Milner 317, 3:00–3:50 p.m.

November 19 Mitja Mastnak (Saint Mary's University)
2:00–2:55 Hopf algebraic approach to the combinatorics of free probability
Abstract:   In the talk I will try to explain how combinatorial Hopf algebras can be used to study joint distributions of k-tuples in a noncommutative probability space. In recent joint work with A. Nica we have constructed a Hopf algebra whose multiplication of characters corresponds to free multiplicative convolution of joint distributions. I will highlight the case k=1 when the combinatorial Hopf algebra in question is the well known Hopf algebra of symmetric functions. In this case several notions in free probability, such as the S-transform, its reciprocal 1/S, and its logarithm log S, relate in a natural sense to the sequences of complete, elementary and power sum symmetric functions.