Résumé : Nous proposons deux versions équivalentes de l’hypothèse de Riemann. Je
passerai du temps sur la première dont la preuve de l’équivalence avec HR est
élémentaire. Elle concerne la probabilité que deux entiers aléatoires indépendants
de même loi géométrique soient premiers entre eux. L’autre, dont la preuve de
l’équivalence avec HR est plus sophistiquée, concerne le nombre de chemins convexes
à sommets entiers joignant l’origine au point de coordonnées (n,n).
(Travail en collaboration avec Julien Bureaux)

Résumé : I will consider the energy-critical wave maps equation with values in the two-dimensional sphere in the equivariant case, that is for symmetric initial data. It is known that if the initial data has small energy, then the corresponding solution scatters. Moreover, the initial data of any scattering solution has topological degree 0. I try to answer the following question : what are the non-scattering solutions of topological degree 0 and the least possible energy ? According to the Soliton Resolution Conjecture, such "threshold" solutions should decompose asymptotically into a superposition of two ground states at different scales, with no radiation.
It turns out that one can construct non-scattering threshold solutions. I will also describe the dynamical behavior of any threshold solution : the two ground states collide and the solution scatters in one time direction.
Joint work with Andrew Lawrie (MIT).

Lieu : Salle MIP

Résumé : _Global sensitivity analysis_ aims at measuring how the variations of one or several input factors contribute to the variation of a resulting output phenomenon, over the whole domain of possible values. In contrast, _target sensitivity analysis_ as we define it, aims at measuring the influence of the factors over the occurrence of the phenomenon in a restricted domain of values. Alternatively, _conditional sensitivity analysis_ evaluates the influence of the factors within such restricted domain only, ignoring what happens outside.
It appears that sensitivity analysis based on nonparametric _dependence measures_, recently advocated by Da Veiga (2015), is particularly adapted to our framework.
In this presentation, I will first discuss the use of nonparametric dependence measures for sensitivity analysis, before detailing how they can be tailored for target and conditional sensitivity analysis. Both aspects will be numerically illustrated.
S. Da Veiga, Global sensitivity analysis with dependence measures, Journal of Statistical Computation and Simulation, 2015, 85, 1283-1305.

Lieu : Salle 106 Bat 1R1

Résumé : Le but de l’exposé est de présenter de nouvelles méthodes pour travailler sur les localisations exactes à gauche de topos (supérieurs ou pas).
La motivation est de pallier à l’insuffisance de la notion de site pour les topos supérieurs. Une source d’application est le Calcul de Goodwillie, qui fournit des exemples de localisations « non-topologiques ».