About

I am a professor in the Institute of Mathematics and Statistics (IME) at the University of São Paulo (USP) where I am part of the Combϴ research group. There I lead the “Categorical Understanding in Computation and Algorithms” (CUÍCA) research lab. If you are interested in computational complexity theory or graph theory and you wonder how methods from category theory, topology and geometry might be useful in these subjects, get in touch!

Prior to coming to USP, I was a Faculty Research Scientist at the University of Florida, working in the GATAS lab run by James Fairbanks. I first came to the University of Florida as a visiting postdoc (in the GATAS lab) after having done a postdoc at Eindhoven University of Technology, working with Bart Jansen. Before that I completed my PhD (you can find my PhD thesis here) supervised by Kitty Meeks at the University of Glasgow in the Formal Analysis, Theory and Algorithms group. To my simultaneous benefit and frustration, I never took graduate courses and did my PhD straight out of my bachelors degree from the University of Stirling in Scotland (B.SC. (Hons.) Mathematics and its Applications, First-Class) which is also where I worked as a summer research intern with Anthony O’Hare, Jessica Enright and Adam Kleczkowski.

I am Italian and US-American. I was born and raised in Italy (except for half a decade or so when I lived in Florida) and I moved to Scotland to pursue higher education. Since then I’ve been floating around the world and now I’m basking in the subtropical sunshine.

My first languages are Italian and English and I’m getting pretty darn good at Spanish and Portuguese (conversational). My German isn’t that bad either and I can say a few words in Yuroba, but I’ve forgotten most of it.. the point is: feel free to chat to me in whatever language you want; there’s a chance I might understand you (and, if I don’t, there’s a chance I might want to learn from you!).

Research

The stories I tell are about complexity. I mean this in the broadest sense: I am interested in classifying different kinds of complexity (structural, algorithmic, behavioral, etc.) and in understanding how it arises. The main focus of my work is the emergence of complexity and how this relates to the mathematics of compositionality (the philosophical contention that the structure or meaning of the whole depends on that of its parts). In this context, I occupy the land of computational complexity where combinatorial explosion guides and motivates deep insights in graph structure theory, parameterized complexity theory and finite model theory. I use category theory and sheaf theory to better understand how the profound tools developed in the above areas relate to each other and to understand how far they can be pushed and generalized.

Organizing Roles

I was the founder and lead organizer of the e-PCC. This is an online seminar series for PhD students across Europe in discrete mathematics and/or theoretical computer science. (2020)

I was the lead organizer of PCC2020: the Postgraduate Combinatorics Conference. (Unfortunately this was postponed due to COVID19.) (2020)

Lead organizer of the Stirling Graph Theory Spring School. The invited speakers were: Jessica Enright, Kitty Meeks, John Faben. (2016)

Awards

3.5 years EPSRC doctoral research scholarship at the Universtiy of Glasgow – value: £111000.

Best in Europe (top 4% worldwide)
at the MCM (Mathematical Modelling Competition)

Prize for “Outstanding performance in the final year of a mathematics degree” – University of Stirling, Scotland.