Current

The seminar is held on Tuesdays from 11 to 12 and is organised by Sabrina Kunzweiler and Maxime Bombar. Unless stated otherwise it takes place in room 2 of IMB. To get announcements, you can subscribe to the mailing list of the Bordeaux number theory seminars. Last minute changes may appear first on the IMB website.

• 2026-06-02
  11:00
  Salle 2
  Marc Houben (CANARI)
  Arithmetic dynamics of algebraic groups
  The Artin-Mazur zeta function is a formal power series that counts the periodic points of a discrete dynamical system. Hinkannen established its rationality for any rational map on the projective line over an algebraically closed field of characteristic zero. The situation in positive characteristic is more delicate, and much less is known. We consider particular classes of discrete dynamical systems arising from endomorphisms of algebraic groups in characteristic $p$. By studying complex analytic properties of the zeta function, we show that, in some cases, rationality is rather the exceptional case.
• 2026-06-09
  11:00
  Salle 2
  Mickaël Montessinos (Eötvös Loránd University)
  Computing isomorphisms to matrix algebras using Amitsur cohomology
  Computing isomorphisms to matrix algebras has become an essential tool in conversions between representations of endomorphism rings of abelian varieties over finite fields. We present an approach relying on Amitsur cohomology, which yields a polynomial reduction to the computation of S-units in number fields.
• 2026-06-16
  11:00
  Salle 2
  Péter Kutas (Eötvös Loránd University)
  Algebraic aspects of superspecial abelian surfaces with RM and CM
  The Ibukiyama-Katsura-Oort correspondence establishes an algebraic framework for principally polarized superspecial abelian surfaces. This framework is powerful enough such that surfaces with extra structures can also be incorporated. We will discuss abelian varieties with real multiplication (an embedding of a totally real quadratic order into the endomorphism ring in a way that the image is symmetric with respect to the Rosati involution) and complex multiplication (an embedding of a quartic CM order which is stable under Rosati). Surfaces with RM admit a Deuring-like correspondence and we show how this can be used to solve algebraic pathfinding for surfaces with RM that have strict class number 1. Surfaces with CM give rise to the Shimura class group action that can be defined even in characteristic $p$ and we provide some cryptographic and number theoretic applications of it.