This workshop is aimed mainly at students (PhD and undergraduate) interested in geometric group theory and will take place in Będlewo (near Poznań) from the 5th until the 10th of May 2013.
The scientific programme will consist of a few lecture series and shorter talks given by the participants about their current research interests. The event will have a rather informal atmosphere, with plenty of time for discussions and interactions between the participants.
More information will appear on this page in due course.
Marcin Kotowski, Michał Kotowski, Tomasz Prytuła, Piotr Przytycki, Paweł Zawiślak
Contact: Tomasz Prytuła
List of abstracts
Short lecture series by:
Łukasz Grabowski (University of Oxford):
L^2 invariants and decidability
I will start by introducing L^2 invariants of groups - these are invariants defined by looking at the boundary map in CW-complexes, treated as an operator on an infinite-dimensional Hilbert space. An example is the random walk operator on Z^2 - we will see how this and other operators arise as boundary maps of CW-complexes. The main part of the lecture will focus on cases where concrete calculations are possible, i.e. when we have a group which is a semidirect product, acting on a manifold. As the main application, we will see how one can study classical problems from group ring theory - in particular, the problem of the existence of zero divisors - from the perspective of decidability theory.
Piotr Przytycki (IMPAN):
Automorphisms of surfaces
In this lecture course we will give a proof of Thurston's classification of surface automorphisms. The theorem says that every surface automorphism is periodic, reducible or pseudo-Anosov. We will follow the book of Casson and Bleiler, where (measured) geodesic laminations are used.
Marcin Kotowski, Michał Kotowski:
Random groups and Property (T)
In our lectures we will introduce the Gromov model of random groups, the notion of Kazhdan’s Property (T) and prove that random groups for densities d > 1/3 satisfy Kazhdan’s Property (T). Along the way we will prove the spectral criterion for property (T) and review relevant results from spectral graph theory and random graphs (random regular graphs and Erdos-Renyi graphs).
In addition to the courses there will be shorter talks by the participants (the list will appear here in due course).List of participants
- Sylwia Antoniuk, Adam Mickiewicz University
- Maurice Chiodo, University of Milan
- Światosław Gal, University of Wrocław
- Łukasz Garncarek, University of Wrocław
- Łukasz Grabowski, University of Oxford
- Marcin Kotowski, University of Toronto
- Michał Kotowski, University of Toronto
- Katarzyna Jankiewicz, University of Warsaw
- Michał Marcinkowski, University of Wrocław
- Tomasz Odrzygóźdź, University of Warsaw
- Damian Orlef, University of Warsaw
- Tomasz Prytuła, University of Warsaw
- Janusz Przewocki, IMPAN
- Piotr Przytycki, IMPAN
- Karol Strzałkowski, IMPAN
- Piotr Suwara, University of Warsaw
- Krzysztof Święcicki, University of Warsaw
- Robert Tang, University of Warwick/IMPAN