# Dynamical systems workgroup

Furstenberg’s proof of Szemeredi’s Theorem

Brian McDonald, U of R

Wednesday, December 18th, 2019

1:00 PM - 2:15 PM

Hylan 101

1:00 PM - 2:15 PM

Hylan 101

In 1936, Erdos and Turan conjectured that any subset of the integers of positive upper density contains infinitely many 3-term arithmetic progressions. This was proven by Roth in 1952, and in 1975 Szemeredi strengthened this to arithmetic progressions of arbitrary length. In 1976, Furstenberg translated Szemeredi’s Theorem into a statement on measure preserving dynamical systems, and gave a new proof of Szemeredi’s theorem using Ergodic Theory. We will discuss Furstenberg’s proof, and mention a few other examples of Furstenberg’s correspondence principle.

Event contact: sliu72 at ur dot rochester dot edu

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