Forthcoming events in this series


Fri, 17 Feb 2012

16:00 - 17:15
Gibson 1st Floor SR

Image Segmentation: Diffusive or Sharp Interfaces and Some Global Minimization Techniques

Xue-Cheng Tai
(University of Bergen)
Abstract

Image segmentation and a number of other problems from image processing and computer vision can be regarded

as interface problems. Recently, diffusive and sharp interface techniques have been used for these problems.

In this talk, we will first briefly explain these models and compare the advantages and disadvantages of these models. Numerically, these models can be solved through some PDEs. In the end, we will show some recent results on how to use graph cut to solve these interface problems. Moreover, the global minimizer can be guaranteed even the problem is nonconex and nonlinear. The use of max-flow in a network setting and also in an infinite dimensional setting will be explained.

Thu, 01 Dec 2011

15:00 - 17:00
Gibson 1st Floor SR

Lectures on: Bifurcation Theory and Applications to Elliptic Boundary-Value Problems

Professor Charles A Stuart
Abstract

• Sufficient conditions for bifurcation from points that are not isolated eigenvalues of the linearisation.

• Odd potential operators.

• Defining min-max critical values using sets of finite genus.

• Formulating some necessary conditions for bifurcation.

Thu, 24 Nov 2011

15:00 - 17:00
Gibson 1st Floor SR

Lectures on: Bifurcation Theory and Applications to Elliptic Boundary-Value Problems

Professor Charles A Stuart
Abstract

• Bifurcation from isolated eigenvalues of finite multiplicity of the linearisation.

• Pseudo-inverses and parametrices for paths of Fredholm operators of index zero.

• Detecting a change of orientation along such a path.

• Lyapunov-Schmidt reduction

Thu, 17 Nov 2011

15:00 - 17:00
Gibson 1st Floor SR

Lectures on: Bifurcation Theory and Applications to Elliptic Boundary-Value Problems

Professor Charles A Stuart
Abstract

• Review of the basic notions concerning bifurcation and asymptotic linearity.

• Review of differentiability in the sense of Gˆateaux, Fréchet, Hadamard.

• Examples which are Hadamard but not Fréchet differentiable.  The Dirichlet problem for a degenerate elliptic equation on a bounded domain. The stationary nonlinear Schrödinger equation on RN

Wed, 15 Jun 2011

13:30 - 14:30
Gibson 1st Floor SR

Entropy regularization for weak KAM theory

Lawrence C Evans
(University of California)
Abstract

I will discuss two of my papers that develop PDE methods for weak KAM theory, in the context of a singular variational problem that can be interpreted as a regularization of Mather's variational principle by an entropy term. This is, sort of, a statistical mechanics approach to the problem. I will show how the Euler-Lagrange PDE yield approximate changes to action-angle variables for the corresponding Hamiltonian dynamics.

Wed, 15 Jun 2011

11:00 - 12:00
Gibson 1st Floor SR

Wigner-Dyson conjecture on random matrices and Erdos-Renyi graphs

Horng-Tzer Yau
(Harvard, USA)
Abstract

Random matrices were introduced by E. Wigner to model the excitation spectrum of large nuclei. The central idea is based on the hypothesis that the local statistics of the excitation spectrum for a large complicated system is universal. Dyson Brownian motion is the flow of eigenvalues of random matrices when each matrix element performs independent Brownian motions. In this lecture, we will explain the connection between the universality of random matrices and the approach to local equilibrium of Dyson Brownian motion. The main tools in our approach are the logarithmic Sobolev inequality and entropy flow. The method will be applied to the adjacency matrices of Erdos-Renyi graphs.

Tue, 14 Jun 2011

12:30 - 13:30
Gibson 1st Floor SR

Entropy and isometric embedding

Marshall Slemrod
(University of Wisconsin)
Abstract

The problem of isometric embedding of a Riemannian Manifold into

Euclidean space is a classical issue in differential geometry and

nonlinear PDE. In this talk, I will outline recent work my

co-workers and I have done, using ideas from continuum mechanics as a guide,

formulating the problem, and giving (we hope) some new insight

into the role of " entropy".