Ramsey theory will be developed starting with the Hales-Jewett theorem about monochromatic lines in hypercube colorings. From this result follows van der Waerden's famous theorem on arithmetic progressions in partitions of the natural numbers. Shelah's revolutionary new proof of this theorem showed that the complexity of the numbers involved was quite different from what had been previously thought. Rado's complete characterization of regular systems of equations - a generalization of Schur's result on sumfree sets - is at the same time based on van der Waerden's result. A hot topic is euclidian Ramsey theory where partitions of euclidian spaces are studied.
In design theory some of the possible topics are the existence of orthogonal latin squares and the advanced asymptotic theory of Wilson. The main result is that necessary conditions for the existence of a block design are also sufficient, provided the size is large enough. The proof of this result is a combination of direct onstructions, pure existence proofs, and numerous recursive methods.
Transversal Theory may be extended to the vast topic of matroids. Transversal matroids are just one of many fundamental classes of matroids.
The participants are all expected to give a seminar in one of the topics.