The computation of flows of compressible fluids will be
discussed, exploiting the symmetric form of the equations describing
compressible flow.
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.
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.
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.
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.