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.

• 2026-05-19
  11:00
  Salle 2
  Razvan Barbulescu (CANARI)
  Logarithmic density of rank ≥ 1 and rank ≥ 2 genus-2 Jacobians and applications to hyperelliptic curve cryptography
  In this talk we present quantitative existence results for genus-2 curves over $\mathbb Q$ whose Jacobians have Mordell–Weil rank at least 1 or 2, ordering the curves by the naive height of their integral Weierstrass models. If the number of curves of a given height is $X$ and the number of curves having a given rank $r$ is $Xc$ we say that the logarithmic density of rank $r$ curves is $c$. Using a geometric argument we show that the rank-2 genus-2 curves have logarithmic density ≥5/7. For comparison the conjectured logarithmic density of rank-2 elliptic curves is 19/24, which is less than 5/7. We continue with results about the logarithmic densities of the quadratic twists of a genus-2 curve, which has consequences in a new line of quantum algorithms for the discrete logarithm problem, which was initiated by Regev. Based on joint work with M. Barcau, V. Pasol and G. Turcas.
• 2026-05-26
  11:00
  Salle 2
  Katherine Stange (University of Colorado, Boulder)
  The arithmetic of thin orbits
  We consider the local-to-global question for orbits of thin groups/semigroups. We will discuss Apollonian circle packings, continued fractions, and some related problems. In the Apollonian case, we ask about the integers which occur as curvatures in a packing. We observe that they satisfy certain congruence restrictions, and ask whether all sufficiently large integers otherwise occur. In the case of continued fractions, we consider variants of Zaremba's conjecture on the rationals with bounded continued fractions. Joint work includes work with Haag, Kertzer, and Rickards.