In 2003-2004, the seminar was organised by Choi Young Eun.
Kasra Rafi (Univ of California, Santa Barbara, USA)
Geometry of Teichmuller space and the complex of curves
Abstract: Using techniques developed by Masur and Minsky, we study geodesics in Teichmuller space. We give a characterization of short curves along a geodesic and give an estimate for the shortest length of a curve. As a consequence we provide a combinatorial formula for the distance between two points in Teichmuller space.
Javier Aramayona (Southampton)
The Weil-Petersson geometry of the five-times punctured sphere
Reza Chamanara (Indiana)
Simultaneous bending of projectively convex piecewise circular Jordan arcs (CONTINUED)
Reza Chamanara (Indiana University, USA)
Simultaneous bending of projectively convex piecewise circular Jordan arcs
Mary Rees (Liverpool)
The geometric model and coarse Lipschitz equivalence direct from Teichmuller geodesics
Abstract: We shall explain a proof of the Ending Lamination Conjecture which uses Teichmuller geodesics directly, restricted, for simplicity, to the case when the ending laminations data is a pair of minimal laminations.
Caroline Series (Warwick)
Thurston's bending measure conjecture for once punctured torus groups
Abstract: We prove Thurston's bending measure conjecture for quasifuchsian once punctured torus groups. The conjecture states that the bending measures of the two components of the convex hull boundary uniquely determine the group.
Cliff Earle (Cornell University)
A dynamical approach to the conformal barycenter
Abstract: The conformal barycenter of a probability measure on the unit circle is a central ingredient in Douady and Earle's theory of the barycentric extension of circle homeomorphisms. Recently, Abikoff developed an iteration scheme, called the MAY iterator, for calculating the conformal barycenter. New work by Abikoff, Mitra, and me uses the MAY iterator to provide a new definition of the conformal barycenter. This definition applies to a wider class of probability measures and allows the extension of continuous degree one monotone maps of the circle that are not necessarilty homeomorphisms.
Al Marden (University of Minnesota)
On PSL(2,C)-representation varieties for Kleinian groups
Abstract: I will give a survey of some results centered on the represention variety of a geometrically finite kleinian group. The most detailed information available is for the special case of a fuchsian surface group. For this case the principal tool to be discussed is the covering of the representation variety by the bundle of complex projective structures, in particular, grafting. The method of complex scaling offers another approach. I will give McMullen's proof of a prototypical case of ``bumping'' of components of the discreteness locus of the representation variety. Apart from this proof the talk will be entirely expository.
Cyril Lecuire (Warwick)
Bending laminations and convergence of metrics
Abstract: In this talk I will conclude the proof of the main theorem of the first talk which gave necessary conditions for a geodesic measured lamination to be the bending lamination of some convex cocompact hyperbolic metric.
Cyril Lecuire (Warwick)
Bending laminations and algebraic convergence
Abstract: In this third talk, I will show that if we have a sequence of faithful and discrete representations with converging bending measures (with some restrictions on the limit) then there is a subsequence that converges algebraically.
Cyril Lecuire (Warwick)
Convex cores of hyperbolic 3-manifolds and bending measured geodesic laminations (continued)
Cyril Lecuire (Warwick)
Convex cores of hyperbolic 3-manifolds and bending measured geodesic laminations
Abstract: This is the first talk in a series of four. I will give some basic definitions, especially that of a convex core, bending measured laminations and characteristic submanifolds of hyperbolic 3-manifolds. I will then explain some properties of the bending geodesic measured laminations.
Emmanuel Dufraine (Warwick)
Actions of Surface Groups on Real Trees -- Skora's Theorem (Otal's book, chapter 8)
Kentaro Ito (Nagoya University, Japan)
Bumping of components of quasi-fuchsian projective structures
Abstract: Let S be a closed hyperbolic surface. Let P(S) be the space of marked projective structures on S and let Q(S) be the subset of P(S) consisting of projective structures with quasi-fuchsian holonomy. It is known that Q(S) has infinitely many components: there is only one component called "standard" and all other components are called "exotic".
In this talk, we explain that each exotic component bumps into the standard component. Moreover we show that each exotic component self-bumps. As a consequence, we can also show that any two components bump. One of the main tools used here is the grafting operation on a projective surface.
Caroline Series (Warwick)
Chapter 6 of Otal's book "The Hyperbolisation Theorem for Fibred 3-Manifolds"
Caroline Series (Warwick)
Chapter 6 of Otal's book "The Hyperbolisation Theorem for Fibred 3-Manifolds"
Akira Ushijima (Warwick, Kanazawa University)
Volumes of Hyperbolic Tetrahedra
Reading seminar of "The hyperbolization theorem for fibered 3-manifolds" by Jean-Pierre Otal
Co-organized with Emmanuel Dufraine.