PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Anatole Katok, Yakov Pesin.

Title:Randomness in functional analysis: towards universality ****THIS TALK WILL TAKE PLACE AT THE SYNERGISTIC ROOM****
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Roman Vershynin, UC Davis
Abstract:
The probabilistic method has redefined functional analysis in high dimensions. Random spaces and operators are to analysis what random graphs are to combinatorics. They provide a wealth of examples that are otherwise hard to construct, suggest what situations we should view as typical, and they have far-reaching applications, most notably in convex geometry and computer science. With the increase of our knowledge about random structures we begin to wonder about their universality. Is there a limiting picture as the dimension increases to infinity? Is this picture unique and independent of the distribution? What are deterministic implications of probabilistic methods? This talk will survey progress on some of these problems, in particular a proof of the conjecture of Von Neumann and Goldstine on random operators and its connections to various areas, including the Littlewood-Offord problem in additive combinatorics and recurrence problems in ergodic theory.

Room Reservation Information

Room Number:MB106
Date:01 / 28 / 2008
Time:03:35pm - 04:35pm