I have recently obtained a PhD in mathematics supervised by Pierre Dèbes and Ariane Mézard. You can read the manuscript or see the slides for the defense. This work focuses around the geometric approach to the regular inverse Galois problem. To this end, I have been studying the geometry and arithmetic of connected components of Hurwitz spaces, which are moduli spaces of branched covers of the projective line. The links between the combinatorial, topological, and arithmetic points of view on this question are, in my eyes, as mysterious as they are fascinating, and it is with joy that I humbly try to contribute to their elucidation.
In parallel, I like to secretly travel to other mathematical landscapes:
- Grothendieck-Teichmüller theory and dessins d’enfants
- logic and proof theory (I am interested in formalization programs)
- non-commutative algebra.
I also maintain, on this very website, a small mathematical blog named Maths from Tlön. It has no definite editorial scope: it’s just me nerding about the things I have in mind at the moment. Unfortunately, it has no comment section at the time — do not hesitate to send me feedbacks via email.
I love music - especially jazz - a lot, and I’m always glad to discuss music or jam around with people.
Geometry and Arithmetic of Components of Hurwitz Spaces2023PhD thesis. 253 pages.
Fields of Definition of Components of Hurwitz Spaces (preprint)202328 pages, 3 figures.
The Geometry of Rings of Components of Hurwitz Spaces (preprint)202252 pages.