LMS Workshop on INTEGRABLE SYSTEMS,

University of Glasgow, 15th –16th  April 2005

 

Programme:

 

      Friday 15th April

 

Location: Room 214, Department of Mathematics.

 

Time

Speaker

Title

 

2:00-3:00

 

David Calderbank

 

Integrability in submanifold geometry

 

3:00-4:00

 

Maxim Pavlov

 

New explicit reductions for DKP, Boyer-Finley equation and dispersionless limit of (2+1) dimensional Harry Dym

 

4:00-4:30 Tea

 

4:30-5:30

 

Roger Bielawski

 

Asymptotic monopole metrics

 

 

Saturday 16th April

 

Location: Room 214, Department of Mathematics.

 

Time

Speaker

Title

 

9:30-10:30

 

Steffen Krusch

 

Schrödinger-Chern-Simons Vortex Dynamics

 

10:30-11:00 Coffee

 

 

 

   11:00-12:00

 

Maciej Dunajski

 

Geodesic approximation of time dependent unitons

 

12:00-1:00

 

Allan Fordy

Darboux Related Quantum Integrable Systems on a Space of Constant Curvature

 

Abstracts

Roger Bielawski: Asymptotic monopole metrics

 

Abstract: The natural hyperkaehler metric on the SU(2) monopole moduli space of charge k exhibits an asymptotic behaviour respecting the cluster decomposition of a k-monopole.  I will describe the hyperkaehler metrics which 1) are exponentially close to the monopole metric in the region were monopoles separate into n clusters, and 2) admit a T^n symmetry. These metrics should be viewed as a deformation of the product of the monopole metrics of lower charges which captures the interaction of the clusters.

David Calderbank: Integrability in submanifold geometry

 

Abstract:  Submanifolds of euclidean space provide a rich and very classical source of integrable systems (e.g., pseudospherical surfaces are governed by the Sine Gordon equation). More recently there has been interest in integrable systems arising from submanifold geometry in the conformal sphere or projective space (e.g., isothermic surfaces or projectively applicable surfaces). I will discuss a systematic theory of these examples, developed in joint work with Fran Burstall, which covers old and new classes of integrable submanifold geometries, complete with their spectral deformations and Baecklund transformations.

Maciej Dunajski:  Geodesic approximation of time dependent unitons                  

 

Abstract:  The slow moving solitons in the modified chiral model can be regarded as a finite--dimensional dynamical system, thus giving the first example of a model where exact solutions can be compared with the dynamics on their moduli space.

Allan Fordy: Darboux Related Quantum Integrable Systems on a Space of Constant Curvature

Abstract We consider integrable deformations of the Laplace-Beltrami operator on a space of constant curvature, obtained through the action of first order Darboux transformations. Darboux transformations are related to the symmetries of the underlying geometric space and lead to separable potentials which are related to the KdV equation. Eigenfunctions of the corresponding operators are related to highest weight representations of the symmetry algebra of the underlying space.

Steffen Krusch: Schrödinger-Chern-Simons Vortex Dynamics

 

Abstract  Schrödinger-Chern-Simons vortex dynamics on the plane is studied numerically and compared with its moduli space approximation. I will also discuss the moduli space of hyperbolic vortices that turns out to be much simpler.

Maxim Pavlov: New explicit reductions for DKP, Boyer-Finley equation and dispersionless limit of (2+1) dimensional Harry Dym

 

Abstract We found more general reductions then given by I.K. Krichever  (rational) or waterbag reduction known in plasma physics for DKP. By reciprocal  transformations above reductions recalculated to reductions of two other dispersionless systems.

 


Updated 12th  April  2005