THEMATIC PROGRAMS

Set Theory and Analysis Program

Graduate Course Information

Partition Theory and Banach Spaces
Directors: Ilijas Farah and Stevo Todorcevic.

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.

Lecture #1 September 9	Class Notes	Audio	Exercises	Solutions
Lecture #2 September 13	Class Notes	Audio	Exercises
Lecture #3 September 23	Class Notes	No Audio	Exercises
Lecture #4 September 30		Audio
Lecture #5 October 17	Class Notes	No Audio
Lecture #6 October 21	Class Notes	Audio
Lecture #7 October 28		Audio
Lecture #8 November 4		Audio
Lecture #9 November 25		No Audio
Lecture #10 December 2		Audio

For more details on the thematic year, see Program Page