In the quest to characterise stably-finite extensions, we developed machinery that captures the $K$-theory arising out of the Deaconu-Fletcher construction for commuting Hilbert bimodules. An application of this general machinery to rank-$2$ Deaconu-Renault groupoids with totally disconnected locally compact Hausdorff unit space gives us both a solid grasp of their $K$-theory and a stable-finiteness result about their extensions. This is joint work with Astrid an Huef and Aidan Sims.

Bio: Abraham Ng is an Australian mathematician. He did a DPhil at the University of Oxford under the supervision of Charles Batty and David Seifert, finishing in 2020. Since then, he has been postdoc-ing under Aidan Sims at the University of Wollongong. His research interests include operator semigroups (strongly continuous and discrete) and C*-algebras (related to graphs and groupoids).