This conference will focus on topological methods that are important with respect to applications in differential equations and dynamical systems, and consequently significant to the applied mathematics. It was approved to the schedule of official events at the Banach Centre by an international committee working in with a co-operation with the European Union of Mathematicians. It is a continuation of several earlier conferences, and workshops, under the same title (or with adjectives "singular" and "variational" added) organised at the Banach Centre in Warsaw or the University of Gdansk. The series of meeting, directed mainly to the European mathematician, is arranged parallel, and in collaboration, to conferences in Mexico on the same subject to give an opportunity for American scientists. This time the aim is to concentrate on the topological methods only but extend the variety of presented topics on this subject due a remarkable progress made recently.
In particular the following topics will be included: 1) A group of theorems of equivariant topology connected with the Borsuk-Ulam Theorems which allow to construct topological invariants used to study the multiplicity of solutions of variational problems with symmetry; 2) A modern, fine version of the Lusternik-Schnirelman category theory which together with the Floer cohomology theory lead to the solution of Arnold conjecture on the number of fixed points of a symplectic diffeomorphism; 3) The Nielsen and asymptotic Nielsen number theory which jointly with a use of the Thurston canonical form of a homeomorphism of a surface give o lot results on periodic points and minimal periods of an embedding of surfaces transforming the difficulty of investigation to a problem of the algebraic classification of Artin braids. The Nielsen theory for a description of the minimal set of periods of the torus and compact nil-manifold mappings; 4) The S1-equivariant degree used to study the existence periodic solutions of differential equations and the Conley index theory successful in the same subject but also in the existence of connecting orbits or non-existence flow invariant subsets which is connected with a chaos.