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Introduction to Ergodic Theory and Additive Combinatorics |
| August 25, 2008 to August 29, 2008 |
| Organized By: Ben Green (University of Cambridge), Bryna Kra (Northwestern University), Emmanuel Lesigne (University of Tours), Anthony Quas (University of Victoria), and Mate Wierdl (University of Memphis) |
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| Parent Programs: |
| Ergodic Theory and Additive Combinatorics |
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| Return to Workshop Description |
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Correspondence principle and finitary ergodic theory, I
Thursday August 28, 2008
09:30AM - 10:30AM
Speakers:
Terence Tao
Abstract:
In this mini-course we will explore two related links between traditional (or "infinitary") ergodic theory, which deals with the asymptotic behaviour of averages, and quantitative (or "finitary") ergodic theory, which deals with averages of a fixed (large) length.
In the first lecture we revisit the Furstenberg correspondence principle linking these two theories, in particular giving a proof of a model case of the "relative Szemeredi theorem" that was used to establish long arithmetic progressions in the primes. In the second lecture we discuss quantitative analogues of infinitary ergodic theorems, starting with the classical mean ergodic theorem and then discussing the more recent ergodic theorem for multiple commuting shifts. In the third lecture we discuss quantitative versions of equidistribution theorems for nilmanifolds.
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