Abstracts of Talks:

• 2:00    Thomas Brady (Dublin City University):  "Climbing elements in finite Coxeter groups"

• Suppose we have a fixed total order on the reflections of a finite
  Coxeter group W.  We will call an element w in W a climbing element if w
  has a reduced expression whose corresponding sequence of reflections is increasing
  in the total order.  We give a characterisation of climbing elements for
  certain fixed total orders.  This is joint work with Aisling Kenny and Colm
  Watt.

• 3:00    Graham Niblo (Southampton):  "Amenability, cohomology and property A"

• Amenability appears as one of the fundamental concepts bridging the  
  worlds of functional analysis and geometric group theory. A group is  
  said to be amenable if it admits an invariant mean on the space of  
  bounded functions on the group. While the definition can be extended  
  to an abstract metric space using Folner's criterion instead, in the  
  absence of a group action the notion is not sufficiently powerful to  
  encode the coarse geometry of the space and this is not a particularly  
  fruitful approach. In his work on the Novikov conjecture Yu introduced  
  an alternative non-equivariant generalisation of amenability, Yu's  
  Property A, in which equivariance is replaced by a controlled support  
  condition which captures more of the geometry. Spaces satisfying Yu's  
  condition also satisfy the Coarse Baum Connes conjecture. There are  
  several well known homological characterisations of amenability and  
  Higson asked if there are analogous characterisations of property A.  
  We will consider coarse generalisations of bounded cohomology and  
  Block & Weinberger's uniformly finite homology  which provide a  
  positive answer to Higson's question and illuminate the extent to  
  which property A provides asymptotic means on a group.

• 4:30    Jack Button (Cambridge):  "The 'size' of a finitely generated group: quantitative and qualitative aspects"

• There are various ideas in the literature on how we decide whether a
  given abstract group is "big" or "small", or on measuring how "big"
  it is. In this talk we focus on some of these concepts which apply
  to infinite finitely generated groups. We then report on recent
  results showing where finitely generated torsion groups appear in
  this picture.