MATHEMATICS COLLOQUIUM

When: Wednesday, December 05, 2012 3:15 PM - 4:15 PM

Where: Math Building : http://en.wikipedia.org/wiki/Hillel_Furstenberg : Colloquium Room 3206

Event Type(s): Colloquium

Speaker: Hillel Furstenberg (Hebrew University)

Title: Multiple Recurrence Phenomena for Non-amenable

Groups and A Szemeredi- like Theorem for

the Free Group

Abstract:

Szemeredi's theorem in combinatorial number theory asserts that

any subset of the integers having positive density contains arithmetic

progressions of any length. It turns out that this is equivalent to a

"multiple" recurrence statement for measure preserving transformations.

Together with Eli Glasner we show that this has an analogue for group

actions that are only measure preserving "on the average". By analogy

the case of the integers, this multiple recurrence result leads to

a theorem guaranteeing existence of geometric progressions in non-

amenable groups. The result for a finitely generated free group can

be made quite explicit.

Website: http://www-math.umd.edu/research/colloquium.html

For more information, contact:

Linette D Berry

Department of Mathematics

+1 301 405 5058

lberry2@umd.edu

www-math.umd.edu/