September 9 - December 16
Mondays at 1:30

The course will begin with a presentation of some of the most important one-dimensional pigeon-hole principles, including theorems of Hindman, Gowers, Hales-Jewett, and Halpern-Lauchli. In the second part of the course we will present a general scheme for stepping-up any such a pigeon-hole principle to the infinite dimension, and obtain Galvin-Prikry theorem and some of its generalizations.

The third, and final, part of the course will be devoted to applications of these ideas to the Banach space theory. In particular, we will prove the Rosenthal l_1 theorem and the Gowers dichotomy for Banach spaces.