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 ktuples 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 Stransform, 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. 

