This meeting is supported by LMS Scheme 3 grant 3716 and we are extremely grateful for their support

Tim Riley

Bristol

Martin Bridson

Oxford

Graham Niblo

Southampton

The inaugural meeting of this new joint research network took place at the University of Southampton on February 15th 2008. The next meeting will be on Monday Dec 5th at the University of Southampton and all are welcome to attend. Further details will be published here and at

http://www.maths.ox.ac.uk/~bridson/BOS-ox.htm.

Details of previous meetings can be found at the Scheme 3 meetings link in the menu bar.

These events are sponsored by the London Mathematical Society Scheme 3 grant 3716 and requests from graduate students for financial support are strongly encouraged. Please contact G.A.Niblo@soton.ac.uk for further information

PROGRAMME

11.30-12.30 Introductory talk: What is amenability? What is a Dehn function? Tim RIley (Bristol)

12.30-13.30 Lunch

Lecture venue to be announced

13.30-14.30 Andzrej Zuk (Paris 7)

                    “Growth of groups”

14.40-15.40 Graham Niblo (Southampton)

                    "Amenability at infinity for discrete groups"

15.40-16.10 Afternoon tea

16.10-17.10 Robert Young (IHES)

                    "A polynomial Dehn function for SL(n,Z)"

The introductory lecture before lunch is aimed at graduate students and researchers from other fields and is intended to provide some background for the main talks. Talks will be held in seminar room on the 4th floor of Howard House.

Abstracts

Andrzej Zuk (Paris 7)

                    Growth of groups

We will discuss recent developments concerning growth of amenable groups.

Graham Niblo (University of 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.

Robert 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.