Groups and Operator Algebras Seminar

Speaker: Ian Thompson (University of Copenhagen)

Title: Dilation distance for tuples of operators

Abstract: Over the past decade, there has been a great amount of focus in relaxed interpolation problems for tuples of operators by completely positive maps, where one only asks for interpolation up to some constant. Both the existence of such constants, as well as their optimal value, have been a guiding problem that underlies many modern questions in matrix convexity, for instance. In particular, within a program of Gerhold, Shalit, and collaborators, they have calculated such optimal constants in a variety of circumstances, and this has led to connections and techniques ranging from stability properties for operators, quantum information theory, and free probability. In this talk, we will give a history of this program as well as talk about some new/upcoming work.