My general interests are categorical methods in algebra, analysis, quantum computation and topology. My D. Phil project revolves around understanding so-called interacting algebras in a wider categorical setting. The ultimate goal is to develop a framework which allows one to define interacting algebras and study their properties. At the moment I am examining PROs, PROPs and PROBs as such a setting. In particular, I am using Lack's notion of PROP composition to define interaction algebras.
Before starting my D. Phil, I wrote a masters thesis on properties of Hausdorff and Gromov distances in the lax-algebraic setting. I am still investigating some open questions in that field.
On the categorical meaning of Hausdorff and Gromov distances‚ I
Andrei Akhvlediani‚ Maria Manuel Clementino and Walter Tholen
In Topology and its Applications. 2008.
Hausdorff and Gromov Distances in Quantale−Enriched Categories
Master's Thesis 2008.