# Béranger Seguin

`Laboratoire Paul Painlevé / Département de Mathématiques et Applications`

**Contact me:**beranger[dot]seguin[at]ens[dot]fr

I am a third year PhD student supervised by Pierre Dèbes and Ariane Mézard.

My current work is centered around the use of geometric methods for number-theoretical purposes. I have spent the last few years working on the regular inverse Galois problem and, to this end, on the geometry and arithmetic of Hurwitz spaces, which are moduli spaces of branched covers of \(\mathbb{P}^1\).

More precisely, I study the irreducible components of these spaces using combinatorial, topological and arithmetical approaches. The links between these points of view 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:

- logic and proof theory (I am interested in formalization programs)
- higher category theory
- non-commutative algebra.

I also happen to like music (especially jazz) a lot, and I’m always glad to discuss music or play with people.