Workshop on INTEGRABLE SYSTEMS,

University of Glasgow, 23rd-24th April

Location: Room 203, Department of Mathematics.

Provisional Programme:

 

Friday 23rd April

 

Time

Speaker

Title

 

2:00-3:00

 

Johan van de Leur

 

The construction of 3-dimensional Frobenius manifolds from various KP hierarchies.

 

3:00-4:00

 

Paolo Lorenzoni

 

Deformations of bihamiltonian structures of hydrodynamic type

 

4:00-4:30 Tea

 

 

 

 

4:30-5:30

 

Liana David

 

Compatible metrics and non-local bi-Hamiltonian structures

 

 

Saturday 24th April

 

Time

Speaker

Title

 

9:30-10:30

 

Guido Carlet

 

On Toda-type hierarchies

 

10:30-11:00 Coffee

 

 

 

 

 

 

11:00-12:00

 

 

Jenya Ferapontov

 

Hydrodynamic reductions of multi-dimensional dispersionless PDEs:

the test for integrability.

 

 

12:00-1:00

 

Harry Braden

 

Beauville-Mukai, Calogero-Moser and Branes

 

 

 

Abstracts

 

Harry Braden:         Beauville-Mukai, Calogero-Moser and Branes

 

Abstract: Supersymmetric field theory suggests an ansatz for a new class of integrable
systems, generalising the Calogero-Moser model. These systems are constructed from
abelian surfaces and are analogous to those of Beauville-Mukai based on K3 surfaces.
They provide the sought after `Double Elliptic Systems'.

Guido Carlet:          On Toda-type hierarchies

 

Abstract We first describe an extended version of the Toda chain
hierarchy. Later we present the tri-Hamiltonian structure of the
two-dimensional Toda hierarchy.

Liana David:            Compatible metrics and non-local bi-Hamiltonian structures

 

Abstract:

Jenya Ferapontov: Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability.

 

Abstract  A multi-dimensional quasilinear system is said to be `integrable'
if it can be decoupled in infinitely many ways into a collection of
compatible n-component one-dimensional systems in Riemann
invariants. Exact solutions described by these reductions, known  as
nonlinear interactions of planar simple waves, can be viewed as
natural dispersionless analogs of n-gap solutions. It is
demonstrated that the requirement of the existence of `sufficiently
many' n-component reductions provides the effective classification
criterion.

Johan van de Leur: The construction of 3-dimensional Frobenius manifolds from various KP hierarchies.

Abstract. Frobenius manifolds in 3 dimensions are characterised by the time dependent
Euler top equations. Using the Grassmannian of the 3-component KP hierarchy we
construct 1-parameter families of rational solutions of this system.
Analysing these solutions, one can show that such solutions already appear in
the 1-component KP hierarchy.

Paolo Lorenzoni:    Deformations of bihamiltonian structures of hydrodynamic type

 

Abstract: We discuss a perturbative approach to the classification problem of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter.

Updated 13th April 2004