Programme:
Friday 15^{th} April
Location:
Room 214, Department of Mathematics.
Time 
Speaker 
Title 
2:003:00 

Integrability in submanifold
geometry 
3:004:00 

New explicit reductions for
DKP, BoyerFinley equation and dispersionless limit of (2+1) dimensional
Harry Dym 
4:004:30 Tea 

4:305:30 

Asymptotic monopole metrics 
Saturday
16^{th} April
Location:
Room 214, Department of Mathematics.
Time 
Speaker 
Title 
9:3010:30 

SchrödingerChernSimons
Vortex Dynamics 
10:3011:00
Coffee 


11:0012:00 

Geodesic
approximation of time dependent unitons 
12:001:00 

Darboux
Related Quantum Integrable Systems on a Space of Constant Curvature

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 kmonopole. 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.
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.
Abstract:
The slow moving solitons in the modified chiral model can be regarded as
a finitedimensional dynamical system, thus giving the first example of a
model where exact solutions can be compared with the dynamics on their moduli
space.
Abstract We consider integrable
deformations of the LaplaceBeltrami 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.
Abstract SchrödingerChernSimons 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.
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
12^{th} April^{ } 2005