Fabrizio Genovese

Fabrizio Genovese
Research Scholar
Applied Category Theory
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Category Theory is a branch of mathematics invented in the second half of the last century, that had huge applications in algebraic topology and geometry and allowed to solve many open conjectures. Applied Category Theory (ACT) refers to the applications of categorical techniques outside of the realm of pure mathematics. The idea of applying category theory outside of mathematics can be traced back to the seventies, but early work in this direction was scarce and scattered.

In the last five years or so, domains to which categorical techniques were applied have been multiplying exponentially, and I am among the people that witnessed this process and contributed in founding ACT as a research field of its own. In particular, I became acquainted with ACT through the study of Categorical Quantum Mechanics and Categorical Models of Natural Language during my PhD years, under the supervision of Bob Coecke and Dan Marsden. Since then, my interests have shifted towards investigating concurrency and cryptography. With respect to concurrency, I started by applying category theory to describe ways of composing Petri Nets and extending them with new features, building on the work of Montanari, Meseguer, Sassone and others. In particular, I am trying to put together two approaches: On one hand the one of Bonchi, Sobocinski, Gadducci et al, which composes nets from an observational perspective, and on the other the one of John Baez and his students, which look at them from a more resource-oriented perspective.

This work is now the foundation of the Statebox programming language, of which I directed research since its foundation, leading core devs in implementing it in a formally verified setting (Idris). Recently, I also took interest in studying message broadcasting consensus protocols categorically. This fundamentally means putting together the recent work on categories of profunctor optics, which is receiving a great deal of interest right now, with the not-so-recent work on sheaf theory, which goes all the way back to the French school of Algebraic Geometry.

With respect to cryptography, I am building on the work of Dusko Pavlovic and others, by applying tools such as graphical languages for high-dimentional PROPs. The aim is to describe cryptographic protocols in a way that accounts for resource ownership and different security levels in the protocol.

I strongly believe in open access to research, and recently I have started refusing to publish in non-open source proceedings. One of the consequences of this is that nearly all of my papers have a version on the arXiv, which you can freely access.

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