Lecture 1. Paradoxical decompositions of groups and their actions.
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Lecture 2. First definitions of amenability, elementary operations that preserve it.
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Lecture 3. Elementary amenable groups.
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Lecture 4. Non-elementary amenable groups.
Grigorchuk's groups of the intermediate growth.
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Lecture 5. Non-elementary amenable groups.
The full topological group of Cantor minimal system: basic properties of the group.
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Lecture 6. The full topological group of Cantor minimal system:
simplicity of the commutator subgroup.
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Lecture 7. The full topological group of Cantor minimal subshift:
finite generacy of the commutator subgroup.
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Lecture 8. Non-elementary amenable groups. Basilica group.
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Lecture 9. Elementary subexponentialy amenable groups.
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Lecture 10. A collection of definitions of amenability. Almost invariant vector.
Kesten's criteria.
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Lecture 11. Hulanicki's criteria.
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Lecture 12. Weak containment of representations.
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Lecture 13. Fixed point property.
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Lecture 14. Paradoxical decomposition criteria. Tarski's number.
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Lecture 15. Gromov's doubling condition. Grasshopper criteria.
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Lecture 16: Kesten's criteria and random walks.
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Lecture 17. Grigorchuk's co-growth criteria.
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Lecture 18. Automata groups.
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Lecture 19. More on Tarski's number.
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Lecture 20. Extensive amenability.
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Lecture 21. Recurrent actions.
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Lecture 22. Amenability of the full topological group of Cantor minimal systems.
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This lectures were given during the graduate course at Northwestern University in fall 2014. Most of the lecture notes as well as found misprints are implemented into the book, which you can find on the separate page. The current page is likely to be less up to date then the webpage of the book.