My research is in the branch of abstract discrete geometry called matroid theory. You can find an introduction to matroid theory in the survey paper by James Oxley entitled What is a matroid? For a more technical discussion, take a look at the Matroid Union blog.
I have given talks for the Matroid Union series of virtual seminars organised by the Combinatorics and Optimisation department of University of Waterloo: one on monadic definability of classes of matroids, and another on matroids that are transversal and cotransversal.
I have been visiting the programme Nights on Radio New Zealand to talk about mathematics. Here are links to our conversations.