Félix Parraud: The spectrum of tensor of random and deterministic matrices

Abstract:

 This talk will be focused on introducing basics of free probability, and in particular the notion of strong convergence which can be summarized as such: given a family of random matrices, how does the norm of any functions evaluated in them behave? This type of results have important application in operator algebra. In particular, recently the community has been focused on studying tensor of matrices due to a result of Ben Hayes stating that the so-called Peterson-Thom conjecture could be proved by showing the strong convergence of a specific family of tensor of random matrices. In this talk I will give a history of the problem, present a strategy to prove it, and explain the tools necessary to do so.