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Banach spaces and Ramsey theory, Spring 2007
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Classes begin 12-Mar-07 and end 02-May-07.

This is a half semester course on the geometry of Banach spaces with a heavy emphasis on the applications of combinatorial, model-theoretical, and descriptive set theoretical methods. The goal is to introduce the fundamental notions about Schauder bases, which are the natural generalisation of vector-space bases to the infinite dimension, and then rapidly go on to prove some of the deep results of the subject.

An overview:

There is no required reading, but several excellent textbooks are available.

Graduate Texts in Mathematics, 233. Springer, New York, 2006. xii+373 pp.

CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 8. Springer-Verlag, New York, 2001. x+451 pp.

Graduate Texts in Mathematics, 92. Springer-Verlag, New York, 1984. xii+261 pp.

Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser Verlag, Basel, 2005. viii+257 pp.

Cours Specialises, 12. Societe Mathematique de France, Paris, 2004. xxiv+627 pp.

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