Some of my research talks from conferences are collected below, with slides where available.
Workshop on Geometric Methods in Physics, Białowieza, Poland, June 2021.
Title: Crossed product operator algebras.
Abstract: To be added.
Faculty Seminar, University of Białystok, Poland, January 2021.
Title: Multipliers of operator algebras associated to groups: special cases.
Abstract: To be added.
7th Workshop on Operator Algebras and their Applications, IPM Tehran, Iran, January 2020. Conference website. Link to slides.
Title: Approximation properties for group actions via multipliers.
Abstract: Multipliers of a discrete group can be used to characterise approximation properties of the associated reduced group C*-algebra. These techniques have proved influential in the theory of approximation properties of C*-algebras: they have shed new light on some C*-algebra properties and motivated the introduction and study of others. I will begin by introducing multipliers defined on a group, and describe how they can be used to characterise approximation properties of the reduced group C*-algebra. I will then discuss some of the difficulties one encounters in trying to describe approximation properties of the reduced crossed product C*-algebra associated to a group action. To get around these difficulties I will introduce multipliers of group actions, which generalize multipliers of groups, and explain how these allow us to characterise approximation properties of reduced crossed products, as well as give new proofs of existing results on such properties.
20th Canadian Abstract Harmonic Analysis Symposium, Carleton University, Ottawa, Canada, May 2018. This was a blackboard talk.
Title: Multipliers of actions and dual coactions.
Abstract: (To be added)
Operator algebras: subfactors and their applications, Newton Institute, Cambridge, England, April 2017. Conference website. This was a blackboard talk; a video recording is available here.
Title: Herz-Schur multipliers and approximation properties.
Abstract: Herz-Schur multipliers of a discrete group have proved useful in the study of C*-algebras, as they can be used to link properties of the group to approximation properties of the reduced group C*-algebra. The development of these ideas has shed light on some C*-algebra properties, and motivated the introduction and study of others. I will introduce Herz-Schur multipliers, and discuss some of their applications, before describing a generalisation of these functions to multipliers of a C*-dynamical system. In the final part of the talk I will show how the generalised Herz-Schur multipliers can be used to study approximation properties of the reduced crossed product formed by a group acting on a C*-algebra, paralleling the applications of Herz-Schur multipliers; these new tools allow us to study approximation properties of the reduced crossed product without requiring the group to be amenable.