About me

My email address is luca.mesiti@outlook.com

I am a postdoctoral research fellow at the Mathematics division of Stellenbosch University, South Africa, working in category theory and its applications to algebra and geometry.
Before this, I was a postdoctoral fellow at the University of KwaZulu-Natal, South Africa, working in category theory and pointfree topology. I am part of the Future Mathematicians Programme, hosting mathematical structures explorations in various cities of South Africa, with the aim to expose school learners and undergraduates to abstract mathematics.

My main research interests are category theory and its applications to algebra, logic and geometry. In particular, I have a keen interest in fibrations and the Grothendieck construction,
2-categories, categorical algebra, enriched categories and topos theory.

In June 2024 I obtained my PhD in Mathematics at the University of Leeds, UK, under the supervision of Nicola Gambino. My PhD thesis contributed to expand 2-categorical elementary topos theory. In particular, I presented a novel technique of reduction of the study of 2-classifiers to dense generators. I then applied it to generalize to dimension 2 the fundamental result that Grothendieck topoi are elementary topoi. In order to reach my main theorems, I produced an original calculus of colimits in 2-dimensional slices and an indexed version of the Grothendieck construction.

My research visits include Stellenbosch University (2025), the University of Genova (2023, 2025) and the University of Manchester (2022, 2023).

I am very passionate about research and I am a positive person who always smiles. I value love, truth and communication.
In my free time, I like creating mathematical and non-mathematical board games, with the aim to help students understand mathematical concepts and develop structural thinking. You can find my board games here.