Theoretical and Computional Physics

Past Conferences 


5.    Geometric approaches to Discrete Integrable

 Systems
Algebraic geometry has been successfully applied to the

 Painlevé equations, and to the QRT maps. Can this be 

extended to higher dimensional mappings, and to lattices?

 

The workshop aims to initiate new research and research 

collaborations, in the field of Discrete Integrable Systems, 

and in closely related areas. 

Description and aim

In the field of Discrete Integrable Systems several branches 

of mathematics and physics, that are usually distinct, come 

together: complex analysis, algebraic/symplectic geometry,

 representation theory, difference/arithmetic geometry, 

graph theory, and the theory of special functions. This 

workshop intends to exploit state of the art expertise in 

the mentioned areas to attack the most prominent and

 challenging open problems related to Discrete Integrable 

Systems. The workshop will target the following five themes.

1.    Multi-dimensional Consistency, Lagrangian 

Forms
Can we extend the classification with respect to multi-

dimensional consistency, to include non-scalar cases. What

 is the significance of the new variational principle connected 

to Lagrangianforms, e.g. in physics applications.

2.    Symmetries, Integrals, Conservation laws, 

and Symplectic structures
What are the relations between (the number of) 

symmetries, integrals and conservation laws? Can one 

decide on symplectivity without deriving a symplectic 

structure? How to systematically construct symplectic

 structures.


3.    Reductions and Solutions
How to construct (explicit) solutions for periodic

 reductions, Painlevé reductions, or solutions of other type, 

i.e. finite gap, rational solutions.


4.    Detection and testing of Discrete Integrable 

Systems

What are currently the most effective methods? Can we

identify relations between different notions of integrability,

e.g. growth versus consistency?

 

Forthcoming Conferences 

       SIDE 10 is the tenth in a series of biennial conferences devoted to Symmetries and Integrability of Difference Equations and related topics: ordinary and partial difference equations, analytic difference equations, orthogonal polynomials and special functions, symmetries and reductions, difference geometry, integrable discrete systems on graphs, integrable dynamical mappings, discrete Painlevé equations, singularity confinement, algebraic entropy, complexity and growth of multivalued mapping, representations of affine Weyl groups, quantum mappings and quantum field theory on the space-time lattice.


The following eight sessions will be organized:

a) Difference algebra and integrable maps
b) Discrete differential geometry and integrable lattices
c) Discrete Painleve equations and Garnier systems and nonlinear special functions
d) Numerical algorithms and integrability
e) Orthogonal polynomials and discrete complex function theory
f) Quantum discrete systems and integrability
g) Spectral theory and solution methods
h) Symmetries and conservation laws

Information concerning the format of the conference and all the logistic matters, such as the accomodation costs, will follow in the next months.


There is a summer school at Ningbo University before the conference: 4-8 June, 2012 (arrival day 3 June, departure day 9 June). The related announcement will be launched separately soon by organizing committee of the summer school.  

Location

NordfjordThe Sophus Lie Conference Center, Nordfjordeid, Norway.

Organizers

The Editors of the Journal of Nonlinear MathematicalPhysics

Description

The conference is a celebration of the twentieth anniversary of the Journal of Nonlinear Mathematical Physics (JNMP), which is published jointly by World Scientific and Atlantis Press. It aims to bring together experts and young scientists in the area of Mathematical Physics that concern Nonlinear Problems in Physics and Mathematics. The main topic of the conference is centered around the scope of JNMP: continuous and discrete integrable systems including ultradiscrete systems, nonlinear differential- and difference equations, applications of Lie transformation groups and Lie algebras, nonlocal transformations and symmetries, differential-geometric aspects of integrable systems, classical and quantum groups, super geometry and super integrable systems. 

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