Asymptotic Theory of Finite Dimensional Normed Spaces (72095)

Asymptotic Theory of Finite Dimensional Normed Spaces (72095)

12:05pm-12:55pm Monday, Wendsday and Friday in room 376 MSB.

Instructor
Office hours:
Office:
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Some Suggested Reading

V.D. Milman and G. Schechtman, "Aysmptotic Theory of Finite Dimensional Normed Spaces".
G. Pisier, "The volume of Convex Bodies and Banach Space Geometry".
G. Schechtman "Lecture Notes on Asymptotic Geometric Analysis".
R. Gardner "The Brunn-Minkowski Inequality."
J. Matousek "Lectures on Discrete Geometry" (Springer, May 2002). Especially Chapter 15, Embedding finite metric spaces into normed spaces.

PLAN:

Monday (8/30/10) Introduction and Basic Definitions.
Wednesday (9/1/10) Duality.
Friday (9/3/10): MAKE UP CLASS 9:50-10:40. ROOM 211. Duality.
Friday (9/3/10) HOMEWORKS 1 and 2. Fritz John Theorem and Applications.
Monday (9/6/10) NO CLASS
Wednesday (9/8/10) Fritz John Theorem and Applications.
Friday (9/10/10) NO CLASS
Monday (9/13/10) N0 CLASS
Wednesday (9/15/10) NO CLASS
Friday (9/17/10) NO CLASS
Monday (9/20/10) HOMEWORKS 1 and 2 DUE. Brunn-Minkowski and Prekopa-Leindler Inequalities and Applications.
Wednesday (9/22/10) Brunn-Minkowski and Prekopa-Leindler Inequalities and Applications.
Friday (9/24/10): MAKE UP CLASS 9:50-10:40. ROOM 211. Concentration inequalities on the Sphere.
Friday (9/24/10) HOMEWORK 3. Concentration inequalities on the Sphere.
Monday (9/27/10)
Wednesday (9/29/10)
Friday (10/1/10): MAKE UP CLASS 9:50-10:40. ROOM 211.
Friday (10/1/10) HOMEWORK 3 DUE!
Monday (10/4/10) Haar Measure. HOMEWORK 4.
Wednesday (10/6/10) Haar Measure.
Friday (10/8/10) Dvoretzky - Rogers Lemma.
Monday (10/11/10) Dvoretzky's Theorem.
Wednesday (10/13/10) Dvoretzky's Theorem.
Friday (10/15/10) Dvoretzky's Theorem. HOMEWORK 5. Homework 4 Due.
Monday (10/18/10) Johnson-Lindenstrauss lemma.
Wednesday (10/20/10) Johnson-Lindenstrauss lemma.
Friday (10/22/10) Volume Ratio.