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)
  Apollonian circle packings