Thu, 03 Mar 2016

16:00 - 17:00
L2

Hecke eigenvalue congruences and experiments with degree-8 L-functions

Neil Dummigan
(University of Sheffield)
Abstract

I will describe how the moduli of various congruences between Hecke eigenvalues of automorphic forms ought to show up in ratios of critical values of $\text{GSP}_2 \times \text{GL}_2$ L-functions. To test this experimentally requires the full force of Farmer and Ryan's technique for approximating L-values given few coefficients in the Dirichlet series.

Thu, 25 Feb 2016

16:00 - 17:00
L2

Badly approximable points

Victor Beresnevich
(University of York)
Abstract

I will discuss the notion of badly approximable points and recent progress and problems in this area, including Schmidt's conjecture, badly approximable points on manifolds and real numbers badly approximable by algebraic numbers.

Mon, 16 Nov 2015

15:00 - 16:00
L2

Magnitudes of compact sets in euclidean spaces: an application of analysis to the theory of enriched categories

Tony Carbery
(University of Edinburgh)
Abstract

Leinster and Willerton have introduced the concept of the magnitude of a metric space, as a special case as that of an enriched category. It is a numerical invariant which is designed to capture the important geometric information about the space, but concrete examples of ts values on compact sets in euclidean space have hitherto been lacking. We discuss progress in some conjectures of Leinster and Willerton.

Mon, 16 Nov 2015

16:00 - 17:00
L2

The Stokes-Fourier equations as scaling limit of the hard sphere dynamics

Laure Saint-Raymond
(Ecole Normale Superieure)
Abstract
In his sixth problem, Hilbert asked for an axiomatization of gas dynamics, and he suggested to use the Boltzmann equation as an intermediate description between the (microscopic) atomic dynamics and (macroscopic) fluid models. The main difficulty to achieve this program is to prove the asymptotic decorrelation between the local microscopic interactions, referred to as propagation of chaos, on a time scale much larger than the mean free time. This is indeed the key property to observe some relaxation towards local thermodynamic equilibrium.

 

This control of the collision process can be obtained in fluctuation regimes. In a recent work with I. Gallagher and T. Bodineau, we have established a long time convergence result to the linearized Boltzmann equation, and eventually derived the acoustic and incompressible Stokes equations in dimension 2. The proof relies crucially on symmetry arguments, combined with a suitable pruning procedure to discard super exponential collision trees.
Wed, 18 Nov 2015
15:00
L2

Algebraic Codes for Public Key Cryptography

Alain Couvreur
(Ecole Polytechnique)
Abstract

We present McEliece encryption scheme and some well-known proposals based on various families of error correcting codes. We introduce several methods for cryptanalysis in order to study the security of the presented proposals.

Thu, 18 Jun 2015

17:00 - 18:00
L2

TheLMS Hardy Lecture: The famous inverse scattering transform method and its less famous discrete version

Prof Nalini Joshi
(University of Sydney)
Abstract

Abstract: The simplest solutions of integrable systems are special functions that have been known since the time of Newton, Gauss and Euler. These functions satisfy not only differential equations as functions of their independent variable but also difference equations as functions of their parameter(s).  We show how the inverse scattering transform method, which was invented to solve the Korteweg-de Vries equation, can be extended to its discrete version.

S.Butler and N.Joshi, An inverse scattering transform for the lattice potential KdV equation, Inverse Problems 26 (2010) 115012 (28pp)

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