November 15, 2018

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

Lecture #5
October 17

Class Notes No Audio    
Lecture #6
October 21
Class Notes Audio    
Lecture #7
October 28
Lecture #8
November 4
Lecture #9
November 25
  No Audio    
Lecture #10
December 2

For more details on the thematic year, see Program Page