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Graduate Seminar

Jason Rute
Carnegie Mellon University
Title: The Ergodic Theoretic Proof of Szemeredi's Theorem

Abstract: In 1975 Endre Szemeredi solved a long-standing conjecture of Erdos and Turan that any dense set of integers has arbitrarily long arithmetic progressions. In 1977, Hillel Furstenberg showed that Szemeredi's theorem can be reduced to a recurrence result in dynamical systems theory, a branch of mathematics used first used to study planetary motion! This correspondence has been the basis of Fields-Medal-winning mathematics. I will sketch Furstenberg's proof focusing on the correspondence between numbers and recurrence.

(While Furstenberg's result uses graduate level analysis, most of my talk will be basic probability theory, easily understandable by an advanced undergraduate or first year graduate student.)

Date: Tuesday, November 27, 2012
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell