Tue, 15 May 2007
12:00
DH 1st floor SR

OCIAM /CMB Special Seminar - Holes, Traps and Spots : The Modelling and Analysis of Two-Dimensional Localised Structures in some

Professor Michael Ward
(UBC, Vancouver)
Abstract

A singular perturbation analysis is presented to analyze various PDE models in a
two-dimensional domain that contain localized regions of non-uniform behavior. A
key theme of this talk is to present a unified mathematical approach, based on
an asymptotic analysis involving logarithmic series and certain Green's function
techniques, that can be used to treat a variety of PDE models such as diffusion
or eigenvalue problems in perforated domains or reaction-diffusion models with
spot-type behavior.

Tue, 15 May 2007
12:00
L3

Polarized and half polarized U(1) symmetric vacuum spacetimes with AVTD behaviour.

Yvonne Choquet Bruhat
(Universite Pierre & Marie Curie)
Abstract
    I sketch, using Kichenassamy - Rendall ideas, a simplified and generalized proof of the Fuchs theorem for differential equations with a singularity. I use the theorem to construct solutions of polarized and half polarized U(1) symmetric vacuum spacetimes with "Asymptotically Velocity Terms Dominated" (AVTD) behaviour near the singularity. I show that the definition I give of half polarization for U(1) symmetric vacuum space-times is a necessary and sufficient condition for non polarized such spacetimes to have this AVTD behaviour.  
Tue, 15 May 2007
10:00
DH 2nd floor SR

Discussion Meeting 1

Abstract

There will be three discussion meetings based on aspects of the

programme open to all internal project members. Others interested in

attending should contact Carlos Mora-Corral.

Mon, 14 May 2007
15:45
DH 3rd floor SR

Nonlinear Filtering of Semi-Dirichlet Processes

Professor Zhi-Ming Ma
(Chinese Academy of Sciences, Beijing)
Abstract
  The talk is based on my recent joint work with Zhechun Hu and Wei Sun. We consider a nonlinear filtering problem for general right continuous Markov processes associated with semi-Dirichlet forms. We show that in our general setting the filtering processes satisfy also DMZ (Duncan-Mortensen-Zakai) equation. The uniqueness of the solutions of the filtering equations are verified through their Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. We investigate further the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes.
Mon, 14 May 2007
14:15
DH 3rd floor SR

The diameter of G (n,c/n)

Dr Oliver Riordan
(University of Cambridge (DPMS))
Abstract
  Recently, comparison with branching processes has been used to determine the asymptotic behaviour of the diameter (largest graph distance between two points that are in the same component) of various sparse random graph models, giving results for $G(n,c/n)$ as special cases. In ongoing work with Nick Wormald, we have studied $G(n,c/n)$ directly, obtaining much stronger results for this simpler model.  
Mon, 14 May 2007
12:00
L3

Self-dual supergravity and twistor theory

Martin Wolf
(Imperial College, London)
Abstract
 
By generalizing and extending some of the earlier results derived by Manin and by Merkulov, a twistor description is given of four-dimensional N-extended (gauged) self-dual supergravity with and without cosmological constant. In particular, superconformal structures are introduced and used as a starting point to define complex quaternionic, quaternionic Kaehler and hyper-Kaehler supermanifolds. A supersymmetry generalization of the Penrose and Ward constructions are presented.
 
Fri, 11 May 2007
15:15
L3

TBA

Thu, 10 May 2007

14:00 - 15:00
Comlab

Wave propagation in 1-d flexible multi-structures

Prof Enrique Zuazua
(Universidad Autonoma de Madrid)
Abstract

In this talk we will mainly analyze the vibrations of a simplified 1-d model for a multi-body structure consisting of a finite number of flexible strings distributed along a planar graph. In particular we shall analyze how solutions propagate along the graph as time evolves. The problem of the observation of waves is a natural framework to analyze this issue. Roughly, the question can be formulated as follows: Can we obtain complete information on the vibrations by making measurements in one single extreme of the network? This formulation is relevant both in the context of control and inverse problems.

Using the Fourier development of solutions and techniques of Nonharmonic Fourier Analysis, we give spectral conditions that guarantee the observability property to hold in any time larger than twice the total lengths of the network in a suitable Hilbert that can be characterized in terms of Fourier series by means of properly chosen weights. When the network graph is a tree these weights can be identified.

Once this is done these results can be transferred to other models as the Schroedinger, heat or beam-type equations.

This lecture is based on results obtained in collaboration with Rene Dager.

Tue, 08 May 2007
17:00
L1

Cluster algebra structures on co-ordinate ring of flag varieties

Prof. Bernard Leclerc
(Caen)
Abstract
  Let G be a complex semisimple algebraic group of type A,D,E. Fomin and Zelevinsky conjecture that the coordinate rings of many interesting varieties attached to G have a natural cluster algebra structure. In a joint work with C. Geiss and J. Schroer we realize part of this program by introducing a cluster structure on the multi-homogeneous coordinate ring of G/P for any parabolic subgroup P of G. This was previously known only for P = B a Borel (Berenstein-Fomin-Zelevinsky) and when G/P is a grassmannian Gr(k,n) (J. Scott). We give a classification of all pairs (G,P) for which this cluster algebra has finite type. Our construction relies on a finite-dimensional algebra attached to G, the preprojective algebra introduced in 1979 by Gelfand and Ponomarev. We use the fact that the coordinate ring of the unipotent radical of P is "categorified" in a natural way by a certain subcategory of the module category of the preprojective algebra.