Bonjour, ce mardi 15 novembre 2016 auront lieu 3 seminaires ! ---- À 10h30 en B107, Suzy Maddah nous parlera de : On Generalized Hypergeometric Solutions of Linear Differential Systems of First Order. Résumé : In this talk, we consider linear differential systems of first order (equivalently linear differential equations of arbitrary order), and we question whether they can be solved in terms of generalized hypergeometric functions. This question is motivated by the many properties of the latter which arise in physics and combinatorics. It has been tackled in the literature for second-order differential equations, namely Bessel's, Whittaker's, Kummer's, and Gauss's. We propose a new algorithm which surpasses the restrictions on the dimension of the system, and equivalently on the order of the equation. This is a joint work with Frédéric Chyzak. ---- À 14h00 en B107, Samuel Petite nous parlera de : Restrictions sur le groupe d'automates cellulaires préservant un sous-shift fixé. Résumé : Un sous shift est un ensemble fermé de suites sur un alphabet fini, invariant par décalage (le shift). L'ensemble des automates cellulaires préservant ce sous shift est en général un groupe dénombrable compliqué. Nous présenterons dans cet exposé un survol des différentes restrictions sur ces groupes pour les sous-shift d'entropie nulle. ---- À 15h15 en B107, Quoc Hoan Ngo nous parlera de : An interface between physics and number theory. Résumé : In this talk are studied the polylogarithms and the harmonic sums at non-positive (i.e. weakly negative) indices. General results about these objects in relation with Hopf algebras are provided. The technics are based on the combinatorics of noncommmutative generating series relative to the Hopf φ-shuffle algebra. Our work here will also propose a global process to renormalize the divergent polyzetas. Finally, we will apply these ideas to non-linear dynamical systems with singular inputs. ---- A mardi, Thierry