Antonio Lorenzin

I am a category theorist interested in classical and quantum probability, living in a superposition between being a mathematician and a theoretical computer scientist. For me, math is most fun when it has a pure soul, and yet enjoys being applied.

After my bachelor's and master's studies in Trento, I moved to Pavia for my PhD, where I worked on triangulated categories. These show up a lot in representation theory and algebraic geometry because of their homological flavour.

When I finished my PhD, I decided to switch directions and focus on category-theoretic approaches to probability, especially Markov categories. What I like about this perspective is that you can actually draw things like complex integrals using string diagrams, little networks of wires and boxes (you can think of them as special bipartite graphs). On top of that, the categorical viewpoint naturally highlights compositional structure and modularity, a bit like the way programming languages are built. This is more than just a simple analogy: it's one of the reasons why theoretical computer science is interested in this approach (see here).

Since my master's, I've also being fascinated by quantum mechanics. That's why I've been exploring quantum probability theory through the same categorical lens. In the long run, my dream is to build a common categorical framework that brings together classical and quantum probability, powerful enough to recover important theorems just from categorical properties.