15:15
15:15
14:00
Computational Techniques in Biomedical Engineering: From Cell to Vessel
16:30
Compact Source and Dipole Representation of Solutions of the Wave Equation in Irregular Regions
Abstract
Moving hydrodynamic boundaries (waves and bubbles, for example) produce acoustic signatures.
16:00
On p-adic L-functions and main conjectures in non-commutative Iwasawa theory
Optimization on matrix manifolds
Abstract
It is well known that the computation of a few extreme eigenvalues, and the corresponding eigenvectors, of a symmetric matrix A can be rewritten as computing extrema of the Rayleigh quotient of A. However, since the Rayleigh quotient is a homogeneous function of degree zero, its extremizers are not isolated. This difficulty can be remedied by restricting the search space to a well-chosen manifold, which brings the extreme eigenvalue problem into the realm of optimization on manifolds. In this presentation, I will show how a recently-proposed generalization of trust-region methods to Riemannian manifolds applies to this problem, and how the resulting algorithms compare with existing ones.
I will also show how the Joint Diagonalization problem (that is, approximately diagonalizing a collection of symmetric matrices via a congruence transformation) can be tackled by a differential geometric approach. This problem has an important application in Independent Component Analysis.
17:00
Gradient flows as a selection criterion for equilibria of non-convex
material models.
Abstract
For atomistic (and related) material models, global minimization
gives the wrong qualitative behaviour; a theory of equilibrium
solutions needs to be defined in different terms. In this talk, a
process based on gradient flow evolutions is presented, to describe
local minimization for simple atomistic models based on the Lennard-
Jones potential. As an application, it is shown that an atomistic
gradient flow evolution converges to a gradient flow of a continuum
energy, as the spacing between the atoms tends to zero. In addition,
the convergence of the resulting equilibria is investigated, in the
case of both elastic deformation and fracture.
15:45
Fractal Properties of Levy Trees
Abstract
Levy trees are random continuous trees that are obtained as
scaling limits of Galton-Watson trees. Continuous tree means here real tree, that is a certain class of path-connected metric spaces without cycles. This class of random trees contains in particular the continuum random tree of Aldous that is the limit of the uniform random tree with N vertices and egde length one over the square root of N when N goes to infinity. In this talk I give a precise definition of the Levy trees and I explain some interesting fractal properties of these trees. This talk is based on joint works with J-F Le Gall and M. Winkel available on arxiv : math.PR/0501079 (published in
PTRF) math.PR/0509518 (preprint)
math.PR/0509690 (preprint).
14:15
Heat kernels of Schr
Abstract
I will present two-sided estimates for the heat kernel of the elliptic
Schr
14:15
16:30
EXOTIC SYMMETRIES : NEW VIEWS ABOUT SPACE
Abstract
The dream of a "cosmic Galois group" may soon become an established reality .
15:00
14:15
10:00
Separation of Variables for PDEs. A new look at an old subject.
Abstract
Taking a view common in the finite element analysis, we interpret
the first N terms of the usual Fourier series solution as the exact
solution of an approximating problem in a subspace spanned by the
eigenfunctions of the underlying Sturm Liouville problem. This view
leads to a consistent solution technique for the heat, wave and
Poisson's equation, and allows an analysis of the error caused by
truncating the Fourier series. Applications to a variety of problems
will be discussed to demonstrate that the analytic approach remains a
valuable complement to purely numerical methods.
The talk is intended for students with an interest in actually
solving partial differential equations. It assumes a standard
background in undergraduate mathematics but not necessarily prior
exposure to the subject. The goal is to show that there is more to
separation of variables than is apparent from standard texts on
engineering mathematics.
17:00
16:30
Can one count the shape of a drum?
Abstract
It is by now well known that one cannot HEAR the shape of a
drum: There are many known examples of isospectral yet not isometric "drums". Recently we discovered that the sequences of integers formed by counting the nodal domains of successive eigenfunctions encode geometrical information, which can also be used to resolve spectral ambiguities. I shall discuss these sequences and indicate how the information stored in the nodal sequences can be deciphered.
16:00