Ph. Boalch	Dynkin diagrams for some moduli spaces of meromorphic differential equations Abstract: I will explain how one may associate some moduli spaces of meromorphic differential equations to certain (special) finite graphs. In a sense (that will be explained) this extends some work of Okamoto (computing symmetry groups of Painleve equations) in the case when the moduli spaces are two-dimensional, and work of Crawley-Boevey and others in the case when the differential equations only have regular singularities (and the graph is star-shaped).
A. Granier	A Galois D-groupoid for q-difference equations Abstract: In his paper "Le groupoide de Galois d'un feuilletage" (2001), B. Malgrange introduces a notion of D-groupoid in order to define, for non linear differential equations, an object which generalizes the differential Galois group of linear differential equations. In fact, his construction can be adapted to other dynamical systems. In the talk, we define a Galois D-groupoid for non linear q-difference equations and we show that the definition is legitimate proving that, for some classes of linear q-difference systems, the linear Galois group can be recovered from the Galois D-groupoid.
C. Hardouin	Théorie de Galois différentielle des équations aux différences
C. Krattenthaler	Sur l'intégralité des coefficients de Taylor des applications de miroir Résumé: Dans cet exposé, j'expliquerai comment on peut démontrer que les coefficients de Taylor de certaines séries associées aux solutions de certaines équations différentielles hypérgéométriques avec monodromie unipotente maximale sont des entiers. Comme conséquences, on peut démontrer de nombreux résultats d'intégralité sur les coefficients de Taylor des applications de miroir, qui améliorent et raffinent des résultats antérieurs de Lian et Yau, et de Zudilin. C'est un travail commun avec Tanguy Rivoal.
F. Pellarin	A-formes modulaires Résumé : La lettre $A$ du titre désigne l'anneau $\bf{F}_q[\theta]$ avec $\theta$ indéterminée et $\bf{F}_q$ corps fini à $q$ éléments. Soit $C$ le complété d'une clôture algébrique de $\mathbf{F}_q((1/\theta))$ pou l'unique extension de la valuation $\theta^{-1}$-adique. Sur l'espace $\Omega:=C\setminus \bf{F}_q((1/\theta))$ agit le groupe $\mathbf{GL}_2(A)$ par homographies. L'alg\`ebre des $A$-formes modulaires est une alg\`ebre sur $C[[t]]$ de fonctions automorphes $\Omega\rightarrow C[[t]]$ ($t$ nouvelle indéterminée) généralisant les formes modulaires de Drinfeld, et munie d'une ``structure de Frobenius". Le but de cet exposé est de faire un survol de la théorie de ces formes, et d'en donner quelques applications.
A. Pulita	Differential and difference equations Abstract: The object of the talk is to explain the André-Di Vizio deformation functor in the p-adic framework. We present a general method permitting to deform a differential equation into a q-difference equation. The method works as well in the complex case, but is not an equivalence. In order to to this we recall an equivalent presentation of the notion of linear differential equation due (essentially) to Grothendieck, permitting to perform the deformation almost easily.
J. Roques	Equations hypergéométriques basiques généralisées Résumé: L'étude des équations hypergéométriques basiques généralisées ayant un "gros" ou un "petit" groupe de Galois sera le fil conducteur de cet exposé à teneur Galoisienne.
V. Spiridonov	Elliptic hypergeometric terms Abstract: General elliptic hypergeometric functions are defined as (multiple) series or integrals whose terms satisfy linear first order finite difference equations in summation or integration variables with elliptic coefficients. We discuss general structure of such terms in the univariate case and present some examples of multivariate terms attached to classical root systems. We describe also relevant difference equations for particular examples of elliptic hypergeometric functions themselves.
S. Zhou.	Formal Solution of a Cauchy Problem with Singular Initial Condition and Mordell's Integral Abstract: We begin this talk with considering the heat equation with a initial condition f'(z) = 1/(1-exp(z); z\neq 2\pi Zi. The problem has a formal power series solution, which is related to f'(z). By means of known results of Lutz, Miyake and Schafke, we get its Borel-sum. Then after a variable transformation, the formal solution can be treated as a q-series, also a formal solution of a associated q-difference equation. So two sums are given by means of heat kernel and Theta function respectively. Finally, with the analytic theory of q-difference equations, we can generalize the Mordell's Theorem when calculating the difference between the two sums.