Past

TBA

 Abstract.  Even in simple models in which thevolatility is only known to stay in two bounds, it is quite hard to price andhedge derivatives which are not Markovian.  The main reason for thisdifficulty emanates from the fact that the probability measures are singular toeach other.  In this talk we will prove a martingale representation theoremfor this market.  This result provides a complete answer to the questionsof hedging and pricing.  The main tools are the theory of nonlinearG-expectations as developed by Peng, the quasi-sure sto chastic artini and thesecond order backward stochastic differential equations.

 This is jointwork with Nizar Touzi from Ecole Polytechnique and Jianfeng Zhang fromUniversity of Southern California.

• Amy Smith presents: “Multiscale modelling of coronary blood flow derived from the microstructure”

• Laura Gallimore presents: “Modelling Cell Motility”

• Jean-Charles Seguis presents: “Coupling the membrane with the cytosol: a first encounter”

This will not be a normal workshop with a single scientist presenting an unsolved problem where mathematics may help. Instead it is more of a discussion meeting with a few speakers all interested in a single theme. So far we have:

Lenny Smith (LSE) on Using Empirically Inadequate Models to inform Your Subjective Probabilities: How might Solvency II inform climate change decisions?

Dan Rowlands (AOPP, Oxford) on "objective" climate forecasting;

Tim Palmer (ECMWF and AOPP, Oxford) on Constraining predictions of climate change using methods of data assimilation;

Chris Farmer (Oxford) about the problem of how to ascertain the error in the equations of a model when in the midst of probabilistic forecasting and prediction.

We study dynamics from models for the human tear film in one and two dimensional domains.

The tear film is roughly a few microns thick over a domain on a centimeter scale; this separation of scales makes lubrication models desirable. Results on one-dimensional blinking domains are presented for multiple blink cycles. Results on two-dimensional stationary domains are presented for different boundary conditions. In all cases, the results are sensitive to the boundary conditions; this is intuitively satisfying since the tear film seems to be controlled primarily from the boundary and its motion. Quantitative comparison with in vivo measurement will be given in some cases. Some discussion of tear film properties will also be given, and results for non-Newtonian models will be given as available, as well as some future directions.

tba

The aim of this talk is to analyze energy functionals concentrated on the jump set of 2D vector fields of unit length and of vanishing divergence.

The motivation of this study comes from thin-film micromagnetics where these functionals correspond to limiting wall-energies. The main issue consists in characterizing the wall-energy density (the cost function) so that the energy functional is lower semicontinuous (l.s.c.). The key point resides in the concept of entropies due to the scalar conservation law implied by our vector fields. Our main result identifies appropriate cost functions

associated to certain sets of entropies. In particular, certain power cost functions lead to l.s.c. energy functionals.

A second issue concerns the existence of minimizers of such energy functionals that we prove via a compactness result. A natural question is whether the viscosity solution is a minimizing configuration. We show that in general it is not the case for nonconvex domains.

However, the case of convex domains is still open. It is a joint work with Benoit Merlet, Ecole Polytechnique (Paris).

Nonlinear eigenvalue problem (NEP) is a class of eigenvalue problems where the matrix depends on the eigenvalue. We will first introduce some NEPs in real applications and some algorithms for general NEPs. Then we introduce our recent advances in NEPs, including second order Arnoldi algorithms for large scale quadratic eigenvalue problem (QEP), analysis and algorithms for symmetric eigenvalue problem with nonlinear rank-one updating, a new linearization for rational eigenvalue problem (REP).

TBA

The first part of Galois' Second Mémoire, less than three pages of manuscript written in 1830, is devoted to an amazing insight, far ahead of its time. Translated into modern mathematical language (and out of French), it is the theorem that a primitive soluble finite permutation group has prime-power degree. This, and Galois' ideas, and counterexamples to some of

them, will be my theme.