Grâce au soutien du GDR EFI, de l'IRMAR et du LMV, une rencontre d'une journée avec 4 exposés aura lieu le mercredi 28 août 2019 à **l'Institut Henri Poincaré, salle 201 ****(ATTENTION AU CHANGEMENT DE SALLE!)****. **

**IMPORTANT **

** Si vous souhaitez déjeuner avec les orateurs et les autres participants, **

**merci d'envoyer un mail à divizio[at]math.cnrs.fr**

**Organisateurs : **Lucia Di Vizio et Frank Loray

**Programme : **

**10h00-11h00 : ****Yousuke Ohyama (Tokushima University)**

**Title**: q-Stokes phenomenon of basic hypergeometric equations

**Abstract**: We study connection formula on basic hypergeometric equations. Some solutions are represented by divergent power series. Some are divergent basic hypergeometric series, and others are non-hypergeometric type series. We need several q-analogues of the Laplace transformation for different types of divergent power series. This is a jointed work with Changgui Zhang.

**11h15-12h15 : Arame Diaw (IRMAR, Univ Rennes)**

**Title**: Local classification of pairs of singular holomorphic foliations

**Abstract**: In 1980, Mattei and Moussu showed a holomorphic classification of foliations in Siegel domain in terms of the holonomy. They state that two foliations in Siegel domain are analytically conjugated if and only if their holonomies are analytically conjugated.

In this presentation, I will try to generalize the Mattei-Moussu's theorem to classify the pairs of holomorphic folations in Siegel Domain.

More precisely, if we consider two pairs of foliations (F,G) and (F',G') in the Siegel domain such that their pairs of holomonies (hol(F),hol(G)) and (hol(F'),hol(G')) along the horizontal separatrix are analytically conjugated, then under some hypothesis, we can define a germ of biholomorphism which conjugates the pair of foliations (F,G) to the pair of foliations (F',G').

**14h30-15h30 : Pierre Lairez (Inria, équipe Specfun) **

**Title**: Numerical periods in effective algebraic geometry (Joint work with Emre Sertöz)

**Abstract**: Building upon Mezzarobba's library for numerical analytic continuation and Sertöz's work on Fermat hypersurfaces, we can now compute the periods of quartic surfaces to arbitrary precision, and consequently many algebraic invariants: Picard group, endomorphism ring, number of embedded smooth rational curve of a given degree, etc. We start compiling a database of K3 surfaces with their invariants. This talk will aim at a hands-on presentation of the tools involved and a presentation of several examples of the database.

**15h45-16h45 : Arata Komyo (Osaka University)**

**Title**: A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions

**Abstract**: Algebraic solutions of the Painlev\'e VI equation and the Garnier systems have been studied. For example, Girand constructed an explicit two-parameter family of flat connections over the projective plane. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. By restricting them to generic lines, we get an algebraic family of isomonodromic deformations of the five-punctured sphere. This yields algebraic solutions of a Garnier system. In this talk, we give a generalization of this construction. That is, we construct an explicit n-parameter family of flat connections over the projective space of dimension n.