
JeanMarc Schlenker (Toulouse) A cyclic extension of the earthquake flow Monday July 25, 09:30, MS.02 
Abstract: The earthquake flow is a flow on the product of Teichmüller space by the space of measured laminations. Among its key properties are Thurston's Earthquake Theorem (given two hyperbolic metrics, there is a unique left earthquake sending one to the other), and McMullen's complex earthquakes, which extend earthquake lines as holomorphic disks. We will describe an extension of the earthquake flow, which is a circle action on the product of Teichmüller space with itself. When one of the factors tends projectively to a measured lamination, we recover the earthquake flow. Our extension shares many properties with the earthquake flow, in particular the two described above. The heuristics and some of the proofs use 3dimensional AdS geometry. This is joint work with Francesco Bonsante and Gabriele Mondello. 
Kasra Rafi (Oklahoma) Hyperbolicity in Teichmüller space Monday July 25, 11:00, MS.02 
Abstract: We develop a theory for applying combinatorial tools, for example the curve complex, in the study of geometric properties of Teichmüller space. We then use this theory to examine in what way Teichmüller space equipped with the Teichmüller metric resembles or differs from a Gromov hyperbolic space. 
Jack O. Button (Cambridge) Establishing largeness for a family of closed hyperbolic 3manifolds Monday July 25, 13:30, MS.02 
Abstract: A finitely generated group is said to be large if it has a finite index subgroup possessing a homomorphism onto a nonAbelian free group. This is a powerful notion, both in abstract group theory and in 3manifold topology. We first review the definition and consequences of largeness, then discuss results which are able to conclude largeness for the fundamental groups of some closed hyperbolic 3manifolds. 
Vaibhav Gadre (Harvard) Hitting measures on the Thurston boundary Monday July 25, 14:40, MS.02 
Abstract: Kaimanovich and Masur proved that a typical random walk on the mapping class group when projected into Teichmuller space, converges with probability 1 to the Thurston boundary. This defines a measure on the Thurston boundary giving the distribution of the limit points of sample paths. We show that if the initial distribution is finitely supported then the harmonic measure is singular with respect to the natural Lebesgue measure on Thurston boundary. This result is analogous to the result of Guivarc'h and LeJan that a finitely supported random walk on the fundamental group of a finite volume hyperbolic surface with cusps, when projected to the hyperbolic plane, gives a singular measure on S^{1}. 
Jeffrey Brock (Brown) The WeilPetersson metric on Teichmüller space, and the geometry of hyperbolic 3manifolds Monday July 25, 16:15, MS.02 
Abstract: In this talk I will discuss a range of analogies between the geometry and spectra of Teichmüller space with its WeilPetersson metric and the internal geometry of hyperbolic 3manifolds. In particular, connections between volume in 3dimensions and length in Teichmüller space seem too strong to be accidental, but I will present fundamental distinctions that arise in the thin part of moduli space. 
Bill Goldman (Maryland) Deformation spaces of 3dimensional affine space forms Tuesday July 26, 09:30, MS.02 
Abstract: In the early 1980's Margulis, answering a question of Milnor, discovered 3manifold quotients of Euclidean 3space by nonsolvable groups of affine transformations. Such groups are virtually free and appear naturally as fundamental groups of hyperbolic surfaces canonically associated to the 3manifolds. The 3manifolds themselves carry geodesically complete flat Lorentz metrics and correspond to deformations of hyperbolic surfaces. We describe the topology, dynamics, and classification of these 3manifolds. In particular the Fricke trace coordinates on the deformation spaces of complete hyperbolic surfaces extend, using a marked Lorentzian length spectrum due to Margulis, to coordinates on the space of proper affine deformations. This talk represents joint work with Charette, Drumm, Fried, Labourie and Margulis. 
Corinna Ulcigrai (Bristol) Ergodicity in Zcovers of translation surfaces Tuesday July 26, 11:00, MS.02 
Abstract: While the ergodic theory of compact translation surfaces is well understood, thanks to its connection with the Teichmüller flow, very little is known about infinite translation surfaces. Recently there has been a lot of interest in the ergodic properties of directional flows on infinite translation surfaces, in particular Zcovers of compact translation surfaces. Hubert and Weiss proved ergodicity for a.e. direction when the Veech group of the Zcover is a lattice. In joint work with K. Fraczek, we exhibit a class of Zcovers (whose Veech group is infintely generated) for which the directional flow is not ergodic for a.e. direction. 
David Dumas (UIC) Holonomy of projective structures and flat surfaces in hyperbolic space Tuesday July 26, 13:30, MS.02 
Abstract: We discuss a new application of the EpsteinThurston construction of locally convex surfaces in hyperbolic space as envelopes of horospheres. Starting with a holomorphic quadratic differential on a compact Riemann surface, we construct a map of the universal cover into hyperbolic space that is equivariant with respect to the holonomy representation of the associated complex projective structure. Using the geometry of these surfaces we characterize limit points of holonomy representations in the MorganShalen boundary of the character variety. If time permits we will discuss applications to skinning maps of hyperbolic 3manifolds. 
Hideki Miyachi (Osaka) Limits of geodesic rays and nonvisible points of Teichmüller space Tuesday July 26, 14:40, MS.02 
Abstract: I will talk about behaviours of various geodesic rays in Teichmüller space in the GardinerMasur compactification. I shall discuss the continuity and discontinuity of the limits on the Teichmüller geodesic rays when rays vary. We will also discuss nonvisible points in the boundary in terms of almost geodesics. 
Dick Canary (Michigan) Dynamics on character varieties Wednesday July 27, 09:30, MS.02 
Abstract: Given a closed surface F, the mapping class group Mod(F) of F acts on the PSL(2,R)character variety. This action is properly discontinuous on the components associated to the Teichmüller spaces of F and of F with the opposite orientation. It is conjectured to act ergodically on all other components. In this talk, we consider a compact 3manifold M with boundary. The outer automorphism group of the fundamental group of M acts on the PSL(2,C)character variety of M. It acts properly discontinuously on the interior of the space of (characters of) discrete faithful representations. We will discuss the dynamics of the action on the entire character variety. In particular, we will discuss work of Canary, Lee, Magid, Minsky and Storm which exhibits domains of discontinuity for this action which are larger than the interior of the space of discrete faithful representations. 
Frédéric Paulin (ParisSud) On the hyperbolic geometry of binary Hamiltonian forms Wednesday July 27, 11:00, MS.02 
Abstract: We use 5dimensional hyperbolic geometry (in particular volume computations of hyperbolic 4 and 5manifolds) to study various arithmetic properties of the binary quaternionic Hermitian forms: their geometric reduction theory, the asymptotic expansion of the number of their representations of integers, etc. This is a joint work with J. Parkkonen. 
Ken Bromberg (Utah) Bounded cohomology for groups with hyperbolic actions Wednesday July 27, 13:30, MS.02 
Abstract: Recently Hamenstädt has proven a collection of theorems that, for a variety of different types of groups G, the 2^{nd} bounded cohomology with coefficients in l^{p}(G) is infinite dimensional. In joint work with Bestvina and Fujiwara we give a unified approach to Hamenstadt's theorems. The key to our approach is an action of G on a quasitree, constructed in our earlier proof that the asymptotic dimension of the mapping class group is finite. This construction works for groups that act on δhyperbolic spaces with BestvinaFujiwara's weak proper discontinuity condition. It further works for groups that act on spaces that are not necessarily hyperbolic but exhibit some hyperbolic behavior, such as the action of the mapping class group on Teichmüller space and Out(F_{n}) on Outer space. 
Makoto Sakuma (Hiroshima) Simple loops on 2bridge spheres in 2bridge link complements Wednesday July 27, 14:40, MS.02 
Abstract: We give complete answers to the following problems. (1) For an essential simple loop on a 2bridge sphere in a 2bridge link complement, when is it: nullhomotopic in the link complement, peripheral, or primitive? (2) For two distinct essential simple loops on a 2bridge sphere in a 2bridge link complement, when are they homotopic in the link complement? We will also discuss an application of these results to the study of the end invariants of SL(2,C)representations of punctured torus groups, introduced by Bowditch and TanWongZhang. This is a joint work with Donghi Lee. 
Steve Kerckhoff (Stanford) Hyperbolic and AdS geometry in dimension 3 Wednesday July 27, 16:15, MS.02 
Abstract: In the early 90's Geoff Mess discovered a beautiful analogue in AdS geometry to the AhlforsBers theory of quasiFuchsian groups. This analogy has been reinforced by the connection between the work of Series and of Bonahon on almost Fuchsian quasiFuchsian groups and parallel work of Bonsante and Schlenker in the AdS setting. We will take a new look at this phenomenon from the point of view of Transitional Geometry, as recently developed by Jeff Danciger. 