OxPDE Special Seminar
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Tue, 14/06/2011 12:30 |
Marshall Slemrod (University of Wisconsin) |
OxPDE Special Seminar  |
Gibson 1st Floor SR |
| 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". | |||
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Wed, 15/06/2011 11:00 |
Horng-Tzer Yau (Harvard, USA) |
OxPDE Special Seminar |
Gibson 1st Floor SR |
| 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. | |||
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Wed, 15/06/2011 13:30 |
Lawrence C Evans (University of California) |
OxPDE Special Seminar |
Gibson 1st Floor SR |
| 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. | |||
