PROGRAM, TITLES & ABSTRACTS
Program
[All the presentations will be held in "Salle de Lecture", located at the ground floor of the Institut Fourier]
Thursday 21st december
9h30-10h20: Cristina Bertone
10h30-11h: coffee break (in front of the seminar room)
11h-11h50: Samuel Le Fourn
12h15 : Lunch at Martin's cafe (for the participants to the IEA project)
afternoon: Collaborative work
15h30-16h: coffee break (in front of the seminar room)
20h : social dinner at restaurant "L'épicurien" (for the participants to the IEA project)
Friday 22nd december
9h30-10h20: Ignazio Longhi
10h30-11h coffee break (in front of the seminar room)
11h-12h: collaborative work
12h: end of the meeting
TITLES AND ABSTRACTS
Cristina Bertone (Università di Torino)
Title : On the hyperflex locus of a hypersurface (a joint project with Martin Weimann)
Abstract : In this talk we will explore some results on the hyperflex locus of a hypersurface in P^n. Some of them are a generalization of analogous results on the flex locus of a hypersurface. We will highlight that some techniques that were successful for the flex locus cannot be used for the hyperflex locus. However, we will present an example of use of a classical tool from pure Algebraic Geometry, Chern classes, that might be helpful to study the degree of the hyperflex locus.
Samuel le Fourn (Université Grenoble-Alpes)
Title : Explicit bounds on the height of CM jacobians
ABSTRACT : The problem of singular moduli admits several generalisations to higher-dimension, for example the following one. For a real quadratic field F and K/F a CM extension which is a quartic cyclic extension of Q, consider the jacobians of curves of genus 2 with CM by $\mathcal{O}_K$ such that the curves themselves have potentially good reduction everywhere. Habegger and Pazuki proved that their height can be bounded (ineffectively) only in terms of F. In the present work (joint with Linda Frey and Elisa Lorenzo--Garcia), we provide (under GRH) an explicit bound in F. In this talk, I will explain some of the main difficulties to be overcome to obtain explicit bounds, and the somewhat surprising link with questions about Minkowski's bound that arise.
Ignazio Longhi (Università di Torino)
Title : On non-archimedean continuous fractions
ABSTRACT : I plan to give a quick introduction to non-archimedean continued fractions and describe some transcendence results in the p-adic case. In the remaining time, I will say something about a possible (and still very conjectural) link with Mumford curves. All of this is joint work N. Murru and F.M. Saettone.