Course:
Math 290-85, CRN 60280
Title:
VIGRE Study Group in
Geometric Functional Analysis
When: W 3:10-4:00P
Where: Kerr 693
Instructor: Roman Vershynin
Office: Kerr 671
Email: vershynin_at_math.ucdavis.edu
Office Hours:
Geometric functional analysis, or "asymptotic convex geometry", is
functional analysis on finite dimensional spaces, whose dimension grows
to infitity. It is a bridge between functional analysis,
combinatorics, probability and convex geometry, with various
applications (including those in
computer science). Geometric functional analysis is especially focused
on high-dimensional
structures found throughout mathematics, on systems that depend on
a number of parameters which is finite but grows to infinity.
This study group will do an informal but thourough introduction to
geometric functional analysis. It will be more informal than a reading
seminar. We will gather for an in-depth (but possibly slow) study of a
major concept or a method. The aim is to gain a working knowledge of
the methods of geometric functional analysis.
Textbook: V.Milman,
G.Schechtman, Asymptotic theory
of finite-dimensional normed spaces.
Lecture Notes in Mathematics, 1200. Springer-Verlag,
Berlin, 1986.
I will keep a copy of this textbook in my mailbox. Feel free to make
copies or borrow it during the day. Please return it to my mailbox at
the end of the day.
Prerequisites: basic
knowledge of Banach and Hilbert spaces (covered e.g. in Analysis
201A,B), and basic Probability Theory (undergraduate probability course
should
be fine, graduate probability would help a lot)
Students who partecipate regularly can register for one credit;
students who lead a study of a topic can register for three
credits.
Meetings:
April 6, 13, 20, 27
May 4, 11, 18,25
June 1, 8
Web:
http://www.math.ucdavis.edu/~vershynin/teaching/RFG04/studygroup.html