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.  
Mon, 07 May 2007
17:00
L1

Energy scaling and domain branching in type-I superconductors

Sergio Conti
(Duisburg)
Abstract
  The intermediate state of a type-I superconductor is a classical example of energy-driven pattern-formation, first studied by Landau in 1937. Mathematically this can be modeled by a nonconvex functional with a singular perturbation, which physically represents the surface energy. In this talk I shall discuss how a combination of interpolation inequalities and explicit constructions permits to determine the scaling of the minimal energy with respect to the relevant material parameters, and therefore to predict a phase diagram for the observed microstructure. This talk is mainly based on joint work with Rustum Choksi, Robert V. Kohn, and Felix Otto.    
Mon, 07 May 2007
15:45
L3

Local-to-global principles for classifying spaces

Jesper Grodal
(Copenhagen)
Abstract
  In this talk I will show how one can sometimes "uncomplete" the p-completed classifying space of a finite group, to obtain the original (non-completed) classifying space, and hence the original finite group. This "uncompletion" process is closely related to well-known local-to-global questions in group theory, such as the classification of finite simple groups. The approach goes via the theory of p-local finite groups. This talk is a report on joint work with Bob Oliver.  
Mon, 07 May 2007
14:15
L3

Stabilizing mapping class groups of 3-manifolds

Nathalie Wahl
(Copenhagen)
Abstract

 

Abstract:

(joint work with Allen Hatcher) Let M be a compact, connected 3-manifold with a

fixed boundary component d_0M. For each prime manifold P, we consider the

mapping class group of the manifold M_n^P obtained from M by taking a connected

sum with n copies of P. We prove that the ith homology of this mapping class

group is independent of n in the range n>2i+1. Our theorem moreover applies to

certain subgroups of the mapping class group and include, as special cases,

homological stability for the automorphism groups of free groups and of other

free products, for the symmetric groups and for wreath products with symmetric

groups.