**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 Lagrangian forms, 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?

**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.