# Seminar Dynamics of Polish groups and Model Theory (WS 2015/16)

Polish groups arise naturally in a number of contexts as infinite permutations groups
or automorphism groups of certain natural structures. Non locally compact polish
groups require new tools for them to be successfully analysed. This seminar will be an
introduction to these groups, their dynamics, their representations and their relations
with model theory and combinatorics. The seminar is for everyone with a basic
knowledge of group theory. Prerequisites will be kept minimal.
#### Literatur:

- A. Kirillov, Elements of the Theory of Representations, Springer.
- B. Bekka, P. de la Harpe, and A. Valette, Kazhdan's property (T), New Mathematical Monographs, vol. 11, Cambridge University
Press, Cambridge, 2008.
- T. Tsankov, Unitary representations of oligomorphic groups, Geom. Funct., Anal. 22 (2012), no. 2, 528-555.
- D. M. Evans, T. Tsankov, Free actions of free groups on countable structures and property (T), arXiv:1312.5140
- M. B. Bekka, Kazhdan's property (T) for the unitary group of a separable
Hilbert space, Geom. Funct. Anal., 13 (2003), no. 3,
509-520.
- D. Macpherson,
A survey of homogeneous structures,
Discrete Math. 311, (2011), no. 15, 1599.
- A.S. Kechris, Dynamics of non-archimedean Polish groups, 2012.
To appear in the Proceedings of the European Congress of
Mathematics, Krakow, Poland.
- A. S. Kechris, V. G. Pestov, and S. Todorcevic, Fraisse limits,
Ramsey theory, and topological dynamics of automorphism
groups, Geom. Funct. Anal. 15 (2005), no. 1, 106-189.
- K. Tent and M. Ziegler. A course in model theory, Lecture Notes in Logic, ASL, Cambridge University Press, 2012.
- D. Marker. Model theory: An Introduction, Graduate texts in mathematics,
Springer, 2002.
- I. Ben Yaacov, A. Berenstein, W. Henson and A. Usvyatsov. Model theory for metric structures, Model theory with applications
to algebra and analysis. Vol. 2, Cambridge University Press, 2008.

#### Zeit/Ort:

From 29.10. onwards,
the seminar will take place every Thursday, 10:30am-12noon, in SR1D.
The first talk was on Monday, 19.10.15.

#### Notes:

Here are some notes from the talks provided by the speakers or taken by
F. Jahnke: