Hi, I am João Vitor, also known as JV. I am currently based at the University of Newcastle (the Aussie one), where I do a casual teaching job. I did my PhD at the University of Newcastle under the supervision of George Willis and co-supervision of Colin Reid and Stephan Tornier, where I studied the class of elementary tdlc (totally disconnected, locally compact) groups that not only is quite interesting in many ways but is also quite important for the understanding of topological groups, being necessary on the classification of chief factors of tdlc groups for instance.

My interest in Mathematics includes mostly topics in algebra, topology and logic. Mainly I am working now in the decomposition rank, a rank in the class of elementary tdlc groups that assigns to each group a countable ordinal that describes, in some way, their complexity. I already have a work on such a rank, but I hope to get a better (countable) upper bound for it by adapting some work on elementary amenable groups. I also have some work on incidence rings and their groups of units, generalizing a construction of simple tdlc groups from a previous article (Topologically simple, totally disconnected, locally compact infinite matrix groups). At the moment I am also trying to learn more about computability of topological groups, planning to publish until soon an article that gives conditions for incidence groups to be computable.

Links for the arXiv version of the articles can be found on the “Publications” page. My CV can be found on the “CV” page, which gives my Currículo Lattes, a quite useful research CV (there is a button on the top-right corner for the English version).

Tem uma versão para esse site em Português na aba “PT-BR”.