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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 longstanding 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 FieldsMedalwinning 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 