DOUBLE HEADER, PART II, 1:45 - 2:30 pm

Speaker: Yannic Vargas, TU Graz

Title: Hopf algebras, species and free probability

Abstract:

Free probability theory, introduced by Voiculescu, is a non-commutative probability theory where the classical notion of independence is replaced by a non-commutative analogue ("freeness"). Originally introduced in an operator-algebraic context to solve problems related to von Neumann algebras, several aspects of free probability are combinatorial in nature. For instance, it has been shown by Speicher that the relations between moments and cumulants related to non-commutative independences involve the study of non-crossing partitions. More recently, the work of Ebrahimi-Fard and Patras has provided a way to use the group of characters on a Hopf algebra of "words on words", and its corresponding Lie algebra of infinitesimal characters, to study cumulants corresponding to different types of independences (free, boolean and monotone). In this talk we will give a survey of this last construction, and present an alternative description using the notion of series of a species.

Yannic Vargas is visiting Martha Yip.