| Date: | February 21, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Konrad Wrobel, Texas A&M University |
| Title: | Ornstein Theory I: Bernoulli Shifts and the Rokhlin Lemma |
| Abstract: | Ornstein theory is a collection of techniques used to
prove the Orstein Isomorphism Theorem, a beautiful and deep result which
gives a complete classification of Bernoulli shifts by their entropy.
Bernoulli shifts arise in many contexts including the theory of flows on
manifolds, stochastic processes, transformations of the torus, symbolic
coding, statistical mechanics, and ergodic theory.
I'll introduce Bernoulli shifts and state the Kolmogorov-Ornstein Isomorphism Theorem. Then, I'll discuss a geometric representation of the Bernoulli shift in the form of the Rokhlin Lemma. |
|
| Date: | February 27, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | James O'Quinn |
| Title: | Ornstein Theory II: Stacks and Gadgets |
| Abstract: | This talk will be a continuation of the talk given last week. During this talk, The geometric representation of p.m.p. actions given by the Rokhlin lemma will be developed even further, which will lead to the definitions of gadgets and their labeling properties. Chapters 3 & 4 of the following notes will be covered:
https://www.impan.pl/~gutman/The%20Theory%20of%20Bernoulli%20Shifts.pdf |
|
| Date: | March 5, 2020 |
| Time: | 3:00pm |
| Location: | BLOC 220 |
| Speaker: | Konrad Wrobel |
| Title: | Ornstein Theory III: Metrics on Partitions and Gadgets |
| Abstract: | Last time, we were introduced to gadgets which are one of the basic tools in Ornstein's proof. This time we'll consider some metrics on partitions and a metric on gadgets. We'll then observe the properties of these metrics and how they relate to isomorphism of actions. This is primarily taken from chapter 5 of Paul Shields' book
https://www.impan.pl/~gutman/The%20Theory%20of%20Bernoulli%20Shifts.pdf. |
|
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