Béranger Seguin

Institut für Mathematik - Universität Paderborn

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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 extensions. Something I love about these questions is the diversity of the methods we can use to study them:

  • Algebraic/combinatorial descriptions or parametrizations (e.g. class field theory in the abelian case)
  • Methods from analytic number theory to relate asymptotics to convergence properties of Dirichlet series
  • Methods from algebraic geometry (e.g. moduli spaces), to deduce estimates for the number of points of varieties from geometric invariants (in the spirit of Diophantine geometry).

I’m also interested in absolute Galois groups of local fields and their ramification filtration (as a description of these leads to a parametrization of local extensions with bounded discriminant), and for this reason I am interested 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 interactions between the combinatorics, topology, and arithmetic which these questions reveal are, in my eyes, as mysterious as they are fascinating.

I also like to secretly travel to other mathematical landscapes:

  • Grothendieck-Teichmüller theory, dessins d’enfants
  • logic (especially model theory) 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.

news

Nov 16, 2024 I will be giving seminar talks in Université Sorbonne Paris Nord (Villetaneuse) on November 29th and at ISTA Klosterneuburg (near Vienna) on December 5th. I’m excited to talk about my recent work!
Oct 20, 2024 I wrote a short introduction to Abrashkin’s nilpotent Artin-Schreier theory.
Oct 02, 2024 I have taken some time to rewrite parts of my thesis that I was unhappy with (mostly due to my bad writing style at the time). My first preprint (from 2022!) has been completely reworked and split into two parts ([part 1], [part 2]). Rewriting everything was obviously a lot of work, especially since I’m less invested in these topics now, but I was pleased to see that I was able to simplify many proofs — though it was daunting to realize how much easier some overcomplicated arguments (which took months for my graduate self to find) could have been!
Aug 05, 2024 Phillipe Caldero a mis en ligne une vidéo dans laquelle il explique (brillamment) la preuve d’un résultat d’un de mes articles. Merci à lui !
(click here to read older news)

  1. preprint
    The Geometry of Rings of Components of Hurwitz Spaces
    Béranger Seguin
    Oct 2024
    25 pages.
  2. article
    Counting Components of Hurwitz Spaces
    Béranger Seguin
    Sep 2024
    Accepted for publication in the Israel Journal of Mathematics. 22 pages.
  3. preprint
    Symmetries of various sets of polynomials
    Béranger Seguin
    Jul 2024
    17 pages.
  4. preprint
    Asymptotics of extensions of simple ℚ-algebras
    Fabian Gundlach, and Béranger Seguin
    May 2024
    32 pages.
  5. article
    Study of a division-like property
    Robin Khanfir, and Béranger Seguin
    Journal of Algebra and its Applications, Apr 2024
  6. PhD thesis
    Geometry and Arithmetic of Components of Hurwitz Spaces
    Béranger Seguin
    Jul 2023
  7. preprint
    Fields of Definition of Components of Hurwitz Spaces
    Béranger Seguin
    Mar 2023
    28 pages.