Alina Bucur
Effective Sato-Tate under GRH abstract
Abstract:
The Sato-Tate conjecture tells us about the distribution of the coefficients of the L-function of an elliptic curve -- in which case it is a theorem -- or more generally of an abelian variety. We will talk about how to make it effective if one assumes the generalized Riemann hypothesis and present some applications of the effective version to both elliptic curves and higher dimension abelian varieties. This is joint work with Fite and Kedlaya.
11:15 • EPF Lausanne, CM1 514
Domingo Hernández Abreu (Universidad de La Laguna, Canary Islands)
Approximate Matrix Factorization and W-methods for the time integration of multidimensional parabolic problems abstract
Abstract:
This talk deals with the time-integration of space-discretised parabolic problems subject to Dirichlet boundary conditions on a rectangular m-dimensional domain.We consider the combination of linearly implicit methods (W-methods) along with Approximate Matrix Factorization based on an alternating direction implicit approach, which allows to reduce the algebra cost to the level of 1D problems. Optimal results on PDE-convergence will be presented for linear problems, the Euclidean norm and arbitrary spatial dimensions m ≥ 2. Some techniques aimed at mitigating the order reduction phenomenon due to time-dependent boundary conditions are also presented and numerically illustrated in two and three spatial dimensions.This talk is based on joint work with S. González-Pinto, E. Hairer and S. Pérez-Rodríguez.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-15 (unusual room!)
Nikolai Perry (Edinburgh)
Graded Necklace Lie Bialgebras & Batalin-Vilkovisky Formalism abstract
Abstract:
The necklace Lie bialgebra is constructed from the double of a quiver. Its Lie bracket has been related to a canonical Poisson structure on the representation variety of the double quiver via a trace map. What about the Lie cobracket? By encoding the necklace Lie bialgebra in a Batalin-Vilkovisky (BV) algebra \'B\', we show that the Lie cobracket can be viewed from the perspective of a suitable representation variety. This representation variety carries a non-degenerate pairing, inducing a canonical BV operator on a quotient of its algebra of functions \'O\' — we construct a BV algebra morphism B --> O which preserves information of both the necklace bracket and cobracket. In addition, we generalise the necklace Lie bialgebra, as well as the above construction, to the Z_2-graded setting.
15:30 • Université de Genève, Conseil Général 7-9, Room 1-07
Cedric Villani (Univ. Bernard Lyon I & IHES)
Information de Fisher et équations cinétiques abstract
Abstract:
Je passerai en revue quelques occasions où l\'information de Fisher joue un rôle clé en théorie des équations de Boltzmann, Fokker-Planck, Landau, avec un accent particulier sur les découvertes récentes en théorie cinétique collisionnelle homogène à interaction très singulière (travaux de Guillen et Silvestre, et les miens propres)
17:15 • Université de Neuchâtel, B013