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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