Title: Basic structure theoretic results for crossed products

Abstract: The theory of operator algebras was started in the 1930s by Murray and von Neumann in order to form a rigorous mathematical framework for quantum mechanics. Roughly speaking, they can be thought of as an infinite-dimensional analogue of matrix algebras, but with additional analytic structure that gives them far nicer properties than typical algebraic rings.

In this talk, we give a brief overview of some results relating to operator algebras arising out of dynamics, known as crossed products. These objects take as input data a group acting on a topological or measurable space (or a noncommutative analogue), and form an operator algebra that encodes the given dynamical structure. One can then ask about characterizing basic results about crossed products in terms of the original dynamical system (or vice versa).

In particular, this talk will give a brief overview of some recent results that completely characterize when various crossed products are simple, and also when they have a very limited, "canonical" set of subalgebras.

In conjunction with the colloquium he is giving a special lecture (hyper link here) the same day at 12:30 in Muhly Lounge on introductory materials related with this colloquium.

Short Bio of the speaker: Dan Ursu is a Postdoctoral researcher of York University and he got his Ph. D. from the University of Waterloo in 2022.