Time/Place: Tue, 09:15-11:45, SG 3-11

If you are interested to participate please write us an email.

The aim of this seminar is to understand in depth various techniques behind proofs of ergodic theorems for amenable and non-amenable groups. After reviewing ergodic theorems in the case of amenable groups, we proceed with that of non-amenable ones, following in parts the book "The ergodic theory of lattice subgroups" by A. Gorodnik and A. Nevo. Necessary tools will be introduced and discussed.

25.4. | cancelled |

2.5. | An introduction to amenable groups, Vishal Gupta ([1-3]) |

9.5. | Mean ergodic theorem for amenable groups; pointwise ergodic theorem along Følner sequences with Tempelman condition I, Tabea Bacher ([4]) |

16.5. | Pointwise ergodic theorem along Følner sequences with Tempelman condition II, Mike Schnurr ([4]) |

30.5 | Pointwise ergodic theorem for amenable groups: the general case I, Konrad Zimmermann ([5]) |

20.6 | Pointwise ergodic theorem for amenable groups: the general case II, Tanja Eisner ([5]) Notes |

27.6 | Unitary representations of SL(n,R) and the mean ergodic theorem, Tobias Finis ([11], Chapter 5) |

4.7 | Unitary representations of SL(n,R) and decay of matrix coefficients, Tobias Finis ([11], Chapter 5) |

- A. Paterson, Amenability. American Mathematical Society, Providence, RI, 1988.
- T. Tao, Some notes on amenability, blog.
- A. Garrido, An introduction to amenable groups, lecture notes. (link)
- D. Ornstein, B. Weiss, "The Shannon-McMillan-Breiman theorem for a class of amenable groups", Israel J. Math. 44 (1983), 53–60.
- E. Lindenstrauss, "Pointwise theorems for amenable groups", Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 82-90. (link)
- A. Gorodnik, A. Nevo, The ergodic theory of lattice subgroups. Princeton University Press, Princeton, NJ, 2010.
- B. Bekka, P. de la Harpe, A. Valette, Kazhdan's property (T). Cambridge University Press, Cambridge, 2008. (link to pdf)
- G. A. Margulis, Discrete subgroups of semisimple Lie groups. Springer-Verlag, Berlin, 1991.
- G. A. Margulis, A. Nevo, E. M. Stein, "Analogs of Wiener's ergodic theorems for semisimple Lie groups, II", Duke Math. J. 103 (2000), 233–259.
- A. Nevo, E. M. Stein, "A generalization of Birkhoff's pointwise ergodic theorem", Acta Math. 173 (1994), 135–154.
- R. Howe, E.-Ch. Tan, Nonabelian harmonic analysis. Applications of SL(2,R). Springer-Verlag, New York, 1992.