Mon, 26 Nov 2018

16:00 - 17:00
L4

Models for fluid boundary layers: beyond the Prandtl equation?

Anne-Laure Dalibard
(Paris VI)
Abstract

The Prandtl equation was derived in 1904 by Ludwig Prandtl in order to describe the behavior of fluids with small viscosity around a solid obstacle. Over the past decades, several results of ill-posedness in Sobolev spaces have been proved for this equation. As a consequence, it is natural to look for more sophisticated boundary layer models, that describe the coupling with the outer Euler flow at a higher order. Unfortunately, these models do not always display better mathematical properties, as I will explain in this talk. This is a joint work with Helge Dietert, David Gérard-Varet and Frédéric Marbach.

Fri, 28 Sep 2012

11:00 - 12:00
L1

Eisenstein cocycle on ${\rm GL}_n$ and computation \\ of $p$-adic L-functions of totally real fields

Pierre Charollois
(Paris VI)
Abstract

We define an integral version of Sczech cocycle on ${\rm GL}_n(\mathbf{Z})$ by raising the level at a prime $\ell$.As a result, we obtain a new construction of the $p$-adic L-functions of Barsky/Cassou-Nogu\`es/Deligne-Ribet. This cohomological construction further allows for a study of the leading term of these L-functions at $s=0$:\\1) we obtain a new proof that the order of vanishing is at least the oneconjectured by Gross. This was already known as result of Wiles.\\2) we deduce an analog of the modular symbol algorithm for ${\rm GL}_n$ from the cocyclerelation and LLL. It enables for the efficient computation of the special values of these $p$-adic L-functions.\\When combined  with a refinement of the Gross-Stark conjecture, we obtain some examples of numerical construction of $\mathfrak p$-units in class fields of totally real (cubic) fields.This is joint work with Samit Dasgupta.

Mon, 17 Nov 2008
14:15
Oxford-Man Institute

Allelic partition of Galton-Watson trees

Prof. Jean Bertoin
(Paris VI)
Abstract

We will consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We shall specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. Some limit theorems related to the distribution of the allelic partition will be also presented.

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