Warwick Mathematics Institute
Seminar organised by Samuel Lelièvre (January to March 2008) and Saul Schleimer (from April 2008).
Thursday 31 January 2008 at 13:40, room B1.01 Vladimir Kisil (Leeds) Erlangen program at large: starting with the group SL(2,R) 
Abstract: The Erlangen program collects dust at a respectful place in the Mathematical History Museum on the shelves of the glorious XIX century. Taking the group SL(2,R) as an example we demonstrate that it can be still in use. Erlangen approach provides useful insights much beyond the traditional geometry: e.g. in analytic function theory, functional calculus and noncommutative geometry. 
Thursday 7 February 2008 at 13:40, room B1.01 Gabriele Mondello (Imperial) Triangulated Riemann surfaces and the WeilPetersson Poisson structure 
Abstract:
The Teichmüller space T(S) of a Riemann surface with boundary is a
realanalytic manifold that parametrises hyperbolic metrics on S with
geodesic boundary up to isotopy. It comes endowed with a Poisson
structure, defined (by Weil) using Petersson's pairing of modular
forms.

Thursday 14 February 2008 at 17:10, room B1.01 Alastair Fletcher (Nottingham) Asymptotic Teichmüller space 
Abstract: For a hyperbolic Riemann surface M, the asymptotic Teichmüller space AT(M) is a quotient of Teichmüller space. The Bers embedding induces a biholomorphic mapping from AT(M) onto a bounded open set in a quotient space of holomorphic quadratic differentials $Q(M)/Q_{0}(M)$. Using this asymptotic Bers embedding and the result that if M is a Riemann surface of infinite analytic type then $Q(M)/Q_{0}(M)$ is isomorphic to $l^{\infty}/c_{0}$, it can be shown that if M and N are two such Riemann surfaces, then AT(M) and AT(N) are locally biLipschitz equivalent. 
Thursday 21 February 2008 at 15:00, room A1.01 Anna Pratoussevitch (Liverpool) Higher spin structures on Riemann surfaces 
Abstract:
A higher spin structure on a Riemann surface is a line bundle with mth
tensor power isomorphic to the cotangent bundle. In the talk I will
show how the space of mspin structures on a Riemann surface can be
interpreted as a finite affine space of Z/mZvalued functions on the
fundamental group of the surface.

Thursday 28 February 2008 at 16:00, room B1.01 Arthur Bartels (Imperial) Topological rigidity and wordhyperbolic groups 
Abstract: The Borel conjecture asserts that aspherical manifolds are topologically rigid, i.e., every homotopy equivalence between such manifolds is homotopic to a homeomorphism. This conjecture is strongly related to the FarrellJones conjectures in algebraic K and Ltheory. We will give an introduction to these conjectures and discuss the proof of the Borel conjecture for highdimensional aspherical manifolds with wordhyperbolic fundamental groups. 
Thursday 6 March 2008 at 16:00, room B1.01 Jessica Purcell (Brigham Young / Oxford) Volume change under Dehn filling 
Abstract: Any 3manifold can be obtained by gluing solid tori into components of a link complement in the 3sphere. This process is called Dehn filling. When the original manifold and the Dehn filled manifold both admit hyperbolic structures, Thurston showed that the volume of the Dehn filled manifold is strictly less than that of the original. Recently, we found an explicit lower bound on the amount the volume decreases based on the length of the slope of the Dehn filling. We will discuss this bound as well as several applications to knots and links in the 3sphere. This is joint work with David Futer and Efstratia Kalfagianni. 
Thursday 13 March 2008 at 16:00, room B1.16 Cornelia Drutu (Oxford) Property (T) and aTmenability from the median spaces viewpoint, applications to the mapping class groups 
Abstract: Both Kazhdan's property (T) and aTmenability turn out to be related to actions of groups on median spaces and on spaces with measured walls. These relationships allow to study the connection between Kazhdan property (T) and the fixed point property for affine actions on L^p spaces, on one hand. On the other hand, they allow to discuss conjugacy classes of subgroups with property (T) in Mapping Class Groups. The latter result is due to the existence of a natural structure of measured walls on the asymptotic cone of a Mapping Class Group. The talk is on joint work with I. Chatterji and F. Haglund (first part), and J. Behrstock and M. Sapir (second part). 