# Béranger Seguin

**Contact me:**math[at]beranger-seguin[dot]fr

Since September 2023, I am employed as a postdoctoral researcher in the Arbeitsgruppe Computeralgebra und Zahlentheorie at the University of Paderborn (Germany). My work there is centered around the topic of arithmetic statistics, and more precisely around the problem of the description of the asymptotic distribution of field extensions. Something I love about these questions is the diversity of the methods we can use to study them:

- Using algebraic (or combinatorial) descriptions/parametrizations of these extensions (e.g. class field theory in the abelian case)
- Using methods from analytic number theory to relate asymptotics to convergence properties of Dirichlet series
- Using methods from algebraic geometry (e.g. moduli spaces) to reduce to point-counting problems for varieties over finite fields.

I’m also interested in the description of absolute Galois groups and their ramification filtration (as such a description leads to a parametrization of extensions with bounded discriminant), and for this reason I have some interest in the theory of Galois representations, \(\varphi\)-modules, etc.

In July 2023, I 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.

I also like to secretly travel to other mathematical landscapes:

- Grothendieck-Teichmüller theory and dessins d’enfants
- logic and proof theory, formalization
- non-commutative algebra, skew fields

I love music — especially jazz — a lot, and I’m always glad to discuss music or jam around with people.