Past Forthcoming Seminars

26 January 2004
17:00
Jonathan Bevan
Abstract
Using a technique explored in unpublished work of Ball and Mizel I shall show that already in 2 and 3 dimensions there are vectorfields which are singular minimizers of integral functionals whose integrand is strictly polyconvex and depends on the gradient of the map only. The analysis behind these results gives rise to an interesting question about the relationship between the regularity of a polyconvex function and that of its possible convex representatives. I shall indicate why this question is interesting in the context of the regularity results above and I shall answer it in certain cases.
  • Applied Analysis and Mechanics Seminar
26 January 2004
15:45
Mathew Penrose
Abstract
Consider a graph with n vertices placed randomly in the unit square, each connected by an edge to its nearest neighbour in a south-westerly direction. For many graphs of this type, the centred total length is asymptotically normal for n large, but in the present case the limit distribution is not normal, being defined in terms of fixed-point distributions of a type seen more commonly in the analysis of algorithms. We discuss related results. This is joint work with Andrew Wade.
  • Stochastic Analysis Seminar
26 January 2004
14:15
Anita Wilson
Abstract
We consider a system of interacting Fisher-Wright diffusions which arise in population genetics as the diffusion limit of a spatial particle model in which frequencies of genetic types are changing due to migration and reproduction. For both models the historical processes are constructed, which record the family structure and the paths of descent through space. For any fixed time, particle representations for the historical process of a collection of Moran models with increasing particle intensity and of the limiting interacting Fisher-Wright diffusions are provided on one and the same probability space by means of Donnelly and Kurtz's look-down construction. It will be discussed how this can be used to obtain new results on the long term behaviour. In particular, we give representations for the equilibrium historical processes. Based on the latter the behaviour of large finite systems in comparison with the infinite system is described on the level of the historical processes. The talk is based on joint work with Andreas Greven and Vlada Limic.
  • Stochastic Analysis Seminar

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