Workshop on Algebraic, Geometric and Probabilistic Aspects of Amenability
June 18 - July 13, 2007

Schedule of lectures for Week 1 (June 18 - June 22)

All lectures take place in the Boltzmann Lecture Hall

• Monday, June 18, 2007
  09:00 - 14:00: Registration
  14:00 - 14:50: Alexander Kechris (Caltech): Extreme amenability: Some new interactions between combinatorics, logic and topological dynamics, I
  Abstract: This minicourse will provide an introduction to the property of extreme amenability (or fixed point on compacta property) of topological groups, which arises in the context of topological dynamics and is related to asymptotic geometric analysis, especially concentration of measure phenomena, and describe its connections with ideas from finite combinatorics, particularly Ramsey theory, and logic.
  15:10 - 16:00: Alexander Kechris, II
  
  
• Tuesday, June 19, 2007
  11:00 - 11:50: Alexander Kechris, III
  15:00 - 15:50: Alexander Kechris, IV
  
  
• Wednesday, June 20, 2007
  11:00 - 11:50: Alexander Kechris, V
  
  
• Thursday, June 21, 2007
  11:00 - 11:50: Dietmar Bisch (Vanderbilt): The planar algebra of group-type subfactors
  Abstract: Haagerup and I introduced some 10 years ago a class of subfactors associated to outer actions of two finite groups. These subfactors play an important role in the theory, since they provide a very simple mechanism to construct irreducible subfactors whose standard invariant has infinite depth. We will review this construction and describe explicitly the planar algebra of these subfactors. We obtain natural IRF models in this way. This is joint work with Paramita Das and Shamindra Ghosh.
  15:00 - 15:50: Andrzej Bis (Lodz): Variational principle of preimage entropy for semigroups of continous maps
  Abstract: We generalize the result of Cheng and Newhouse [Ergod. Th. and Dynam. Sys. (2005) 25,1091-1113)] concerning the variational principle of preimage entropy. Instead of just one map, we deal with a semigroup of commuting transformations. The variational principle is provided for this setup. This is a joint work with Roland Gunesch.
  
  
• Friday, June 22, 2007
  11:00 - 11:50: Rostislav Grigorchuk (Texas A&M): On non-elementary amenability and nonamenability
  Abstract: This is a survey talk about algebraic aspects of the theory of amenable groups related to problems of John von Neimann and M. Day on existence of free subgroups in nonamenable groups and non-elementary amenability. A part of the material will be based on the theory of self-similar groups. We also plan to discuss the estimates of the Tarskii numbers of free Burnside groups.
  15.00 - 15.50: George Tomanov (Lyon): Locally divergent orbits under actions of split tori on homogeneous spaces and applications to number theory
  Abstract: We prove that if G is a direct product of n > 1 real and p-adic algebraic groups and L is an irreducible lattice in G then there are no divergent orbits under actions by left translations of maximal split algebraic tori of G on G/L. On the other hand, we give an explicit description of all locally divergent orbits under such actions. The latter result allows characterizing the rational decomposable forms in terms of their values at integral points.
  
  

Anna Erschler, Vadim Kaimanovich, Klaus Schmidt

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On 18 Jun 2007, 14:58.