The Langlands-Shahidi method over function fields: the Ramanujan Conjecture and the Riemann Hypothesis for the unitary groups
Luis LOMELI - 2016-02-11 (M/16/05)
On étudie la méthode de Langlands-Shahidi sur les corps de fonctions de caractéristique p. On prouve la fonctorialité de Langlands globale et locale des groupes unitaires vers les groupes linéaires pour les représentations génériques. Supposant connue la conjecture de Shahidi pour les L-paquets modérés, on donne une extension de la définition des fonctions L et des facteurs ε. Enfin, utilisant le travail de L. Lafforgue, on établit la conjecture de Ramanujan et on prouve que les fonctions L automorphes de Langlands-Shahidi satisfont l'hypothèse de Riemann.
Class number problems and Lang conjectures
Ayberk ZEYTIN - 2016-02-01 (M/16/04)
Given a square-free integer d we introduce an affine hypersurface whose integer points are in one-to-one correspondence with ideal classes of the quadratic number field Q(\sqrt{d}). Using this we relate class number problems of Gauss to Lang conjectures.
On Emergent Geometry from Entanglement Entropy in Matrix Theory
Vatche SAHAKIAN - 2016-01-29 (P/16/03)
Using Matrix theory, we compute the entanglement entropy between a supergravity probe and modes on a spherical membrane. We demonstrate that a membrane stretched between the probe and the sphere entangles these modes and leads to an expression for the entanglement entropy that encodes information about local gravitational geometry seen by the probe. We propose in particular that this entanglement entropy measures the rate of convergence of geodesics at the location of the probe.
Perturbative quantum field theory meets number theory
Ivan TODOROV - 2016-01-27 (P/16/02)



On the conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
Thibault DAMOUR, Piotr JARANOWSKI, Gerhard SCHAEFER - 2016-01-08 (P/16/01)