Research
My research interests lie in the intersection of totally disconnected locally compact groups (TDLCGs) and harmonic analysis. A lot of group theoretic work has been done regarding totally disconnected locally compact groups and their structure. At the same time, a lot of properties of locally compact groups are reflected in its measure algebra. I am interested in how specific properties of TDLCGs are reflected in its measure algebra, and if viewing these properties in a measure algebraic way can either generalise existing results, or give rise to new results!
Master's Research Project
A research paper which was completed as part of my master's degree at the University of Waterloo. It is separated into three parts. The first part provides an exposition on the scale and tidy subgroups of a TDLCG, while the second constructs a dictionary relating properties of an arbitrary locally compact group with properties of its measure algebra. The final part gives analogues on the measure algebra to the scale of an automorphism on a TDLCG and its tidy subgroups.