Mon, 25 Jan 2016

14:15 - 15:45
L5

Propagation in a non-local reaction-diffusion equation

Christopher Henderson
(ENS Lyon)
Abstract

The first reaction-diffusion equation developed and studied is the Fisher-KPP equation.  Introduced in 1937, it accounts for the spatial spreading and growth of a species.  Understanding this population-dynamics model is equivalent to understanding the distribution of the maximum particle in a branching Brownian motion.  Various generalizations of this model have been studied in the eighty years since its introduction, including a model with non-local reaction for the cane toads of Australia introduced by Benichou et. al.  I will begin the talk by giving an extended introduction on the Fisher-KPP equation and the typical behavior of its solutions.  Afterwards, I will describe the model for the cane toads equations and give new results regarding this model.  In particular, I will show how the model may be viewed as a perturbation of a local equation using a new Harnack-type inequality and I will discuss the super-linear in time propagation of the toads.  The talk is based on a joint work with Bouin and Ryzhik.

 

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Thu, 26 Feb 2015

16:00 - 17:00
L5

Restriction of Banach representations of GL_2(Q_p) to GL_2(Z_p)

Gabriel Dospinescu
(ENS Lyon)
Abstract

Thanks to the p-adic local Langlands correspondence for GL_2(Q_p), one "knows" all admissible unitary topologically irreducible representations of GL_2(Z_p). In this talk I will focus on some elementary properties of their restriction to GL_2(Z_p): for instance, to what extent does the restriction to GL_2(Z_p) allow one to recover the original representation, when is the restriction of finite length, etc.

Mon, 20 May 2013

14:15 - 15:15
Oxford-Man Institute

Eigenvalues of large random matrices, free probability and beyond.

CAMILLE MALE
(ENS Lyon)
Abstract
Free probability theory has been introduced by Voiculescu in the 80's for the study of the von Neumann algebras of the free groups. It consists in an algebraic setting of non commutative probability, where one encodes "non commutative random variables" in abstract (non commutative) algebras endowed with linear forms (which satisfies properties in order to play the role of the expectation). In this context, Voiculescu introduce the notion of freeness which is the analogue of the classical independence.

A decade later, he realized that a family of independent random matrices invariant in law by conjugation by unitary matrices are asymptotically free. This phenomenon is called asymptotic freeness. It had a deep impact in operator algebra and probability and has been generalized in many directions. A simple particular case of Voiculescu's theorem gives an estimate, for N large, of the spectrum of an N by N Hermitian matrix H_N = A_N + 1/\sqrt N X_N, where A_N is a given deterministic Hermitian matrix and X_N has independent gaussian standard sub-diagonal entries.

Nevertheless, it turns out that asymptotic freeness does not hold in certain situations, e.g. when the entries of X_N as above have heavy-tails. To infer the spectrum of a larger class of matrices, we go further into Voiculescu's approach and introduce the distributions of traffics and their free product. This notion of distribution is richer than Voiculescu's notion of distribution of non commutative random variables and it generalizes the notion of law of a random graph. The notion of freeness for traffics is an intriguing mixing between the classical independence and Voiculescu's notion of freeness. We prove an asymptotic freeness theorem in that context for independent random matrices invariant in law by conjugation by permutation matrices.

The purpose of this talk is to give an introductory presentation of these notions.

Mon, 28 Jan 2013

15:45 - 16:45
Oxford-Man Institute

Near-critical Ising mode.

CHRISTOPHE GARBAN
(ENS Lyon)
Abstract
In this talk, I will present two results on the behavior of the Ising model on the planar lattice near its critical point: (i) In the first result (joint work with F.Camia and C. Newman), we will fix the temperature to be the critical temperature T_c and we will vary the magnetic field h \geq 0. Our main result states that in the plane Z^2, the average magnetization at the origin behaves up to constants like h^{1/15}. This result is interesting since the classical computa- tion of the average magnetization by Onsager requires the external magnetic field h to be exactly 0 . (ii) In the second result (joint work with H. Duminil-Copin and G. Pete), we focus on the correlation length of the Ising model when h is now fixed to be zero and one varies instead the temperature T around T_c. In rough terms, if T
Thu, 03 Nov 2011

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

On hypergraph partitioning based ordering methods for sparse matrix factorization

Dr Bora Ucar
(ENS Lyon)
Abstract
We will discuss the use of hypergraph-based methods for orderings of sparse matrices in Cholesky, LU and QR factorizations. For the Cholesky factorization case, we will investigate a recent result on pattern-wise decomposition of sparse matrices, generalize the result and develop algorithmic tools to obtain effective ordering methods. We will also see that the generalized results help us formulate the ordering problem in LU much like we do for the Cholesky case, without ever symmetrizing the given matrix $A$ as $A+A^{T}$ or $A^{T}A$. For the QR factorization case, the use of hypergraph models is fairly standard. We will nonetheless highlight the fact that the method again does not form the possibly much denser matrix $A^{T}A$. We will see comparisons of the hypergraph-based methods with the most common alternatives in all three cases.

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This is joint work with Iain S. Duff.

Thu, 01 Dec 2005

14:00 - 15:00
Rutherford Appleton Laboratory, nr Didcot

Dynamic-load balancing issues and preliminary out-of-core experiments in a parallel sparse solver

Dr Jean-Yves L'Excellent
(ENS Lyon)
Abstract

Parallel sparse direct solvers are an interesting alternative to iterative methods for some classes of large sparse systems of linear equations. In the context of a parallel sparse multifrontal solver (MUMPS), we describe a new dynamic scheduling strategy aiming at balancing both the workload and the memory usage. More precisely, this hybrid approach balances the workload under memory constraints. We show that the peak of memory can be significantly reduced, while we have also improved the performance of the solver.

Then, we present preliminary work concerning a parallel out-of-core extension of the solver MUMPS, enabling to solve increasingly large simulation problems.

This is joint work with P.Amestoy, A.Guermouche, S.Pralet and E.Agullo.

Fri, 29 Feb 2008
15:30
L2

The Modular Flow

Professor Etienne Ghys
(ENS Lyon)
Abstract
A lattice in the plane is a discrete subgroup in R^2 isomorphic to Z^2 ; it is unimodular if the area of the quotient is 1. The space of unimodular lattices is a venerable object in mathematics related to topology, dynamics and number theory. In this talk, I'd like to present a guided tour of this space, focusing on its topological aspect. I will describe in particular the periodic orbits of the modular flow, giving rise to beautiful "modular knots". I will show some animations
Mon, 14 Jan 2008
13:15
Oxford-Man Institute

Optimal transport and curvature (monge meets Riemann)

Prof. Cedric Villani
(ENS Lyon)
Abstract
Born in France around 1780, the optimal transport problem has known a scientific explosion in the past two decades, in relation with dynamical systems and partial differential equations. Recently it has found unexpected applications in Riemannian geometry, in particular the encoding of Ricci curvature bounds
Mon, 05 Mar 2007
14:15
DH 3rd floor SR

Pinning of a polymer in a random medium and interacting particle system.

Dr Vincent Beffara
(ENS Lyon)
Abstract
  We present a link between polymer pinning by a columnar defect in a random medium and a particular model of interacting particles on the line, related to polynuclear growth. While the question of whether an arbitrarily small intensity for the defect always results in pinning is still open, in a 'randomized' version of the model, which is closely related to the zero-temperature Glauber dynamics of the Ising model, we are able to obtain explicit results and a complete understanding of the process. This is joint work with Vladas Sidoravicius and Maria Eulalia Vares.  
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