# Current

Unless stated otherwise, the seminar takes place on Tuesdays, from 10 to 11, in room 385 at IMB. To get announcements, you can subscribe to the mailing-list.
• 2017-11-14
10:00
Salle 385
Jean Kieffer (ENS Paris)
Accélération du protocole d'échange de clés de Couveignes-Rostovtsev-Stolbunov
Ce protocole d’échange de clés est fondé sur la théorie de la multiplication complexe: un ordre dans un corps quadratique imaginaire agit sur un ensemble de courbes elliptiques ordinaires isogènes définies sur un corps fini. Pour instancier le protocole, on est amené à calculer des isogénies de différents degrés entre ces courbes à l’aide des algorithmes développés pour le comptage de points. Ce cryptosystème peut être accéléré par un bon choix de courbe elliptique initiale, notamment par la présence de points de torsion rationnels, et l’on présente une méthode de recherche de telles courbes.
• 2017-11-20
14:00
Salle 385
Christian Klein
Computational approach to compact Riemann surfaces
A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the de ning equation of the algebraic curve on collocation points along these contours and by analytically continuing the roots. The collocation points are chosen to correspond to Chebychev collocation points for an ensuing Clenshaw–Curtis integration of the holomorphic differentials which gives the periods of the Riemann surface with spectral accuracy. At the singularities of the algebraic curve, Puiseux expansions computed by contour integration on the circles around the singularities are used to identify the holomorphic differentials. The Abel map is also computed with the Clenshaw–Curtis algorithm and contour integrals. As an application of the code, solutions to the Kadomtsev–Petviashvili equation are computed on non-hyperelliptic Riemann surfaces.
• 2017-11-28
10:00
Salle 385
Frank Vallentin
Coloring the Voronoi tessellation of lattices
We define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tesselation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the irreducible root lattices and for this we apply a generalization of the Hoffman bound.