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.

• 2026-10-13
  11:00
  Salle 2
  Mingjie Chen (KU Leuven)
  Reduction of Polarizations on Products of Elliptic Curves
  Let $A=E_1 \times E_2$ be a product of elliptic curves. Polarizations on $A$ can be represented by positive definite Hermitian matrices $H=\begin{pmatrix}a & h \\ \hat h & b \end{pmatrix}$, with $a, b \in \mathbb{Z}$ and $h \in \mathrm{Hom}(E_1,E_2)$. Equivalence of polarizations corresponds to the natural congruence action of $\mathrm{Aut}(A)$ on these matrices. We develop algorithms for reducing such matrix representatives within their equivalence classes. The algorithms transform a given polarization into an equivalent representative with controlled coefficients. By analyzing the reduction process, we derive explicit bounds on $a$, $b$, and $\deg(h)$ for the resulting representatives. This talk is based on ongoing joint work with Harun Kir, Eli Orvis, and Benjamin Wesolowski.