KULeuven - UCLouvain working seminar, Fall 2011

Simple finitely generated amenable groups (after Grigorchuk and Medynets)

Abstract: In this series of talks we discuss a recent article by Grigorchuk and Medynets, providing simple finitely generated infinite amenable groups. These groups arise in the context of minimal homeomorphisms of the Cantor set. In the first lectures we will treat all the necessary background concerning amenability, Cantor minimal systems, their full groups and classification.

Organisers: Pierre-Emmanuel Caprace and Stefaan Vaes

Locations

The talks will be given alternatively at the KUL and at the UCL.
All the talks at KUL take place in room B.02.18 of the Math building, located Celestijnenlaan 200B, 3001 Heverlee. Directions can be found here.
All the talks at UCL take place in room Cycl 08 of the Math building, located chemin du Cyclotron 2, 1348 Louvain-la-Neuve. Directions can be found here.

Main references

[BHV] B. Bekka, P. de la Harpe and A. Valette, Kazhdan's property (T), New Mathematical Monographs, 11. Cambridge University Press, 2008.

[BezMed] S. Bezuglyi and K. Medynets, Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems. Coll. Math. 110 (2008), 409-429.

[Dye1] H.A. Dye, On groups of measure preserving transformations, I. Amer. J. Math. 81 (1959), 119-159.

[Dye2] H.A. Dye, On groups of measure preserving transformations, II. Amer. J. Math. 81 (1959), 551-576.

[GriMed] R. Grigorchuk and K. Medynets, On simple finitely generated amenable groups. Preprint, arXiv:1105.0719

[Matui] H. Matui, Some remarks on topological full groups of Cantor minimal systems. Int. J. Math. 17 (2006), 231-251.

Schedule

Monday 17th October 2011 at UCL

14:30 Pierre-Emmanuel Caprace (UCL): Introduction: simplicity versus amenability.

16:00 Jan Keersmaekers (KUL): Amenability of groups.

Monday 24th October 2011 at KUL

14:30 Stefaan Vaes (KUL): Group actions and full groups: measurable and topological.

16:00 Colin Reid (UCL): The topological full group of a Cantor minimal system has a simple commutator subgroup.

Monday 14th November 2011 at UCL

14:30 Corina Ciobotaru (UCL): Topological full groups and finite generation.

16:00 Sven Raum (KUL): Classification of Cantor minimal systems up to flip conjugacy.

Monday 28th November 2011 at KUL

13:30 Mathieu Carette (UCL): Amenability of topological full groups, I.

14:30 Dennis Dreesen (UCL): Amenability of topological full groups, II.

15:45 Arnaud Brothier (KUL): The topological entropy of a transformation and an uncountable family of minimal subshifts.

Tuesday 12th June 2012 at KUL: Closing talks

15:00 Kate Juschenko (EPFL, Lausanne): Cantor systems, piecewise translations and simple amenable groups, I.

16:30 Kate Juschenko (EPFL, Lausanne): Cantor systems, piecewise translations and simple amenable groups , II.

Abstract:	In this series of talks we discuss a recent article by Grigorchuk and Medynets, providing simple finitely generated infinite amenable groups. These groups arise in the context of minimal homeomorphisms of the Cantor set. In the first lectures we will treat all the necessary background concerning amenability, Cantor minimal systems, their full groups and classification.

Organisers:	Pierre-Emmanuel Caprace and Stefaan Vaes

[BHV]	B. Bekka, P. de la Harpe and A. Valette, Kazhdan's property (T), New Mathematical Monographs, 11. Cambridge University Press, 2008.
[BezMed]	S. Bezuglyi and K. Medynets, Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems. Coll. Math. 110 (2008), 409-429.
[Dye1]	H.A. Dye, On groups of measure preserving transformations, I. Amer. J. Math. 81 (1959), 119-159.
[Dye2]	H.A. Dye, On groups of measure preserving transformations, II. Amer. J. Math. 81 (1959), 551-576.
[GriMed]	R. Grigorchuk and K. Medynets, On simple finitely generated amenable groups. Preprint, arXiv:1105.0719
[Matui]	H. Matui, Some remarks on topological full groups of Cantor minimal systems. Int. J. Math. 17 (2006), 231-251.

14:30	Pierre-Emmanuel Caprace (UCL): Introduction: simplicity versus amenability.

16:00	Jan Keersmaekers (KUL): Amenability of groups.

14:30	Stefaan Vaes (KUL): Group actions and full groups: measurable and topological.

16:00	Colin Reid (UCL): The topological full group of a Cantor minimal system has a simple commutator subgroup.

14:30	Corina Ciobotaru (UCL): Topological full groups and finite generation.

16:00	Sven Raum (KUL): Classification of Cantor minimal systems up to flip conjugacy.

13:30	Mathieu Carette (UCL): Amenability of topological full groups, I.

14:30	Dennis Dreesen (UCL): Amenability of topological full groups, II.

15:45	Arnaud Brothier (KUL): The topological entropy of a transformation and an uncountable family of minimal subshifts.

15:00	Kate Juschenko (EPFL, Lausanne): Cantor systems, piecewise translations and simple amenable groups, I.

16:30	Kate Juschenko (EPFL, Lausanne): Cantor systems, piecewise translations and simple amenable groups , II.