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Romain Tessera

(CNRS, ENS De Lyon)

Amenability, affine isometric actions and embedding of trees in Banach spaces

Лекции состоятся 9, 11 и 12 сентября в ауд.307 с 19:20 до 21:00. Сдача курса засчитывается за 1/2 кредита

plan of the course:

  1. introduction to amenable groups (Von Neumann and Folner criterion, stability properties, examples and counterexamples)

  2. large-scale geometry of locally compact groups, and Cayley-Abels graphs. Example of amenable group whose CA graph is a tree: the affine group over Q_p.

  3. Isometric actions on normed vector spaces. Relation between displacement of the action, and distortion of the orbits.

  4. Central result: a Banachic version of a result of Delorme for isometric actions of the affine group over Q_p.

  5. Corollary: a new and original proof of Bourgain's theorem that a 3-regular tree does not embed bi-lipschitz into a superreflexive Banach space.

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