14:15
14:15
16:30
Boundary Value Problems on Measure Chains
Abstract
When modelling a physical or biological system, it has to be decided
what framework best captures the underlying properties of the system
under investigation. Usually, either a continuous or a discrete
approach is adopted and the evolution of the system variables can then
be described by ordinary or partial differential equations or
difference equations, as appropriate. It is sometimes the case,
however, that the model variables evolve in space or time in a way
which involves both discrete and continuous elements. This is best
illustrated by a simple example. Suppose that the life span of a
species of insect is one time unit and at the end of its life span,
the insect mates, lays eggs and then dies. Suppose the eggs lie
dormant for a further 1 time unit before hatching. The `time-scale' on
which the insect population evolves is therefore best represented by a
set of continuous intervals separated by discrete gaps. This concept
of `time-scale' (or measure chain as it is referred to in a slightly
wider context) can be extended to sets consisting of almost arbitrary
combinations of intervals, discrete points and accumulation points,
and `time-scale analysis' defines a calculus, on such sets. The
standard `continuous' and `discrete' calculus then simply form special
cases of this more general time scale calculus.
In this talk, we will outline some of the basic properties of time
scales and time scale calculus before discussing some if the
technical problems that arise in deriving and analysing boundary
value problems on time scales.
14:30
Computational fluid dynamics
Abstract
The computation of flows of compressible fluids will be
discussed, exploiting the symmetric form of the equations describing
compressible flow.
17:00
15:45
Isoperimetric inequalities for independent variables
Abstract
We shall review recent progress in the understanding of
isoperimetric inequalities for product probability measures (a very tight
description of the concentration of measure phenomeonon). Several extensions
of the classical result for the Gaussian measure were recently derived by
functional analytic methods.
14:15
About the Hopfield model of spin-glasses
Abstract
The Hopfield model took his name and its popularity within the theory
of formal neural networks. It was introduced in 1982 to describe and
implement associative memories. In fact, the mathematical model was
already defined, and studied in a simple form by Pastur and Figotin in
an attempt to describe spin-glasses, which are magnetic materials with
singular behaviour at low temperature. This model indeed shows a very
complex structure if considered in a slightly different regime than
the one they studied. In the present talk we will focus on the
fluctuations of the free energy in the high-temperature phase. No
prior knowledge of Statistical mechanics is required to follow the
talk.
14:15
15:15
Bounding back and forth through the complex field
Abstract
The first seminar will be given with the new students in
mind. It will begin with a brief overview of quantifier elimination and its
relation to the back-and-forth property.I shall then discuss complexity issues
with particular reference to algebraically closed fields.In particular,how much
does the height and degree of polynomials in a formula increase when a
quantifier is eliminated? The precise answer here gave rise to the definition
of a `generic' transcendental entire function,which will also be
discussed.
14:00
A Non-Gaussian Model with Skew for the Pricing of Options and Debt
14:00
Modelling variability in fruit growth, quality development and storage: concepts and numerical methodologies
14:30
Modelling and simulation issues in computational cell biology
Abstract
A cell is a wonderously complex object. In this talk I will
give an overview of some of the mathematical frameworks that are needed
in order to make progress to understanding the complex dynamics of a
cell. The talk will consist of a directed random walk through discrete
Markov processes, stochastic differential equations, anomalous diffusion
and fractional differential equations.
14:00