Title. Asymptotic Geometric Analysis
Brief description. The course will be an introduction to Convex Geometry in high
dimensions, local theory of Banach spaces and modern trends in high
dimension probability. The course is organized as follows:
-- Brunn-Minkowski inequality, functional forms and applications.
Symmetrization and related inequalities. The concentration of measure
phenomenon. Poincare and log-Sobolev inequalities. Semi-group techniques
and the Brascamp-Lieb family of inequalities.
--Convex bodies and their ``Positions". Dvoretzky-Rogers factorization
and Dvoretzky's theorem. Kashin's theorem and applications to RIP matrices.
-- Type cotype and Lp spaces. K-convex spacesa nd Pisier's theorem.
Entropy numbers, M-positions of convex bodies and the Bourgain-Milman
theorem. The quotient of subspace theorem.