Monday 9:10-12:00, Goldschlager Multidisciplinary Engineering building (bldg. 203), room 315
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Grading |
For those taking the course for a grade, and for those seeking a particular form of pleasure,
here is the FINAL FORM OF THE EXERCISE SHEET. Please note, some of the exercises themselves have been updated over the course of the semester. It is due on 26.5.24 (first day of second semester), and should be sent to me by email.
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| Notes |
A reference for the proof of Van der Waerden's theorem using topological dynamics, and a classical source of other applications of ergodic theory in combinatorics, is the book Recurrence in Ergodic Theory and Combinatorial Number Theory by Hillel Furstenberg.
In the lecture of January 15, I discussed mixing, and tried to show the following video of a taffy puller. For more information on the mathematics of applied dynamical systems, and other fun stuff like the math of flipping burgers, see the webpage of Jean-Luc Thiffeault. In the lecture of January 22, I omitted a computation using Folner sets in the proof of the mean ergodic theorem for amenable groups. The computation is here page 1 page 2. In the lecture of February 12, I omitted the proof of a Lemma on properties of the concave envelope. The statement and proof of the Lemma are here. In the lecture of March 4 I sketched a proof of the Poincare theorem, that a regular hyperbolic n-gon with angles 2pi/k tiles the hyperbolic plane by hyperbolic reflections. I underestimated the complexity of a completely rigorous proof, a complete proof is given in this paper. Also in the same lecture, I skipped the proof of the polar decomposition for SL(2,R). In the lecture of March 11 I gave an (intentionally) incorrect proof of the main proposition used for proving measure classification for U-invariant ergodic measures (using mixing). Here are notes and a correct proof. |
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| References |
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