Bristol University, February 9, 2009

Meeting of the Bristol–Oxford–Southampton joint research group in
Geometric and Analytic Methods in Group Theory

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11:30 12:30 Introductory talk — Tim Riley, Bristol
What is amenability? What is a Dehn function?
This two-part talk will be aimed at graduate students and researchers from other fields, and will be intended to provide some background for the main talks.

12:30 1:30 Lunch

1:30 2:30Andrzej Zuk, Paris 7
Growth of groups
We will discuss recent developments concerning growth of amenable groups.

2:40 3:40Graham Niblo, Southampton
Amenability at infinity for discrete groups
Property A is a non-equivariant analogue of amenability defined by Guoliang Yu for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional CAT(0) cube complexes have Property A. The methods allow us to give a strengthened form of a result of Caprace concerning amenability for stabilisers at infinity for groups acting properly on a finite-dimensional CAT(0) cube complex.

3:40 4:10 Tea

4:10 5:10Robert Young, IHES
A polynomial Dehn function for SL(n,Z)
It is known that SL(2,Z) is hyperbolic and has a linear Dehn function, and that SL(3,Z) contains a solvable group in such a way that its Dehn function is exponential, but the behavior of the Dehn function in higher dimensions has been a long-open conjecture. In this talk, I will describe some of the background of the problem and some of the geometry of the quotient SL(n,Z)\SL(n,R), and use this geometry to sketch a proof that SL(n,Z) has a quartic Dehn function for n at least 5.

Photo by Joe Dunckley (
Practical information

— Talks will be in the seminar room on the 4th floor of Howard House (follow the link for directions).
— A group will go for lunch at the university staff dining room at The Hawthorns after the introductory talk. Alternatively, there are many sandwich shops near Howard House and there is a common room on the 4th floor where people could congregate.
— Tea will be served in the common room on the 4th floor of Howard House.
— Dinner in a local restaurant will be arranged; all are welcome.
Maps and travel advice
Information on visiting Bristol and places to stay


We are grateful to the LMS for support via Scheme 3 grant 3716. Funds are available to assist graduate students to attend the meeting. Please contact Graham Niblo or Tim Riley for further information.


Meeting organiser Tim Riley
Network organisers Martin Bridson, Graham Niblo, Tim Riley