Past Forthcoming Seminars

18 October 2004
15:45
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.
  • Stochastic Analysis Seminar
18 October 2004
14:15
Dr J Trashorras
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.
  • Stochastic Analysis Seminar
15 October 2004
15:15
Alex Wilkie
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.

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