Analysis Seminar: Double Haar Systems on Double Lie Groupoids

Abstract: A Lie groupoid is a generalization of a Lie group in which multiplication is not always defined for all pairs of elements. Thus, a double groupoid is a type of higher groupoid structure in which there are two groupoid products on the same underlying set and the two products must satisfy a certain compatibility law. An example we will consider in this talk is that of an irrational torus. Groupoid structures give rise to convolution algebras, therefore a double groupoid induces two convolution products. An interesting question to ask is, in what sense are the two products compatible? To formulate this question, we introduce  ``double Haar system." Here, a Haar system is a generalization of the familiar Haar measure for a groupoid. This is based on joint work with Joel Villatoro.

Host: Alan Chang