Speaker: Raquel Diaz (Complutense Univ, Madrid)
Title: Schottky type uniformizations
Abstract: Schottky groups are characterized as finitely generated free purely loxodromic Kleinian groups. Noded Schottky groups are the same but parabolic elements are permited. We will call {it Schottky type group} to a Kleinian group containing a noded Schottky group as a finite index normal subgroup. A 2-Riemann orbifold with nodes is uniformized by a Schottky type group $K$ if it is conformally equivalent to $Omega/K$, where $Omega$ is the discontinuity region of $K$.
Any Riemann surface and any Riemann surface with nodes can be uniformized by Schottky and noded Schottky gorps, respectively. These are results of Koebe and Hidalgo. On the other hand, Reni-Zimmermann characterize which Riemann 2-orbifolds can be uniformized by Schottky type groups and D'iaz-Hidalgo give some partial answers for Riemann 2-orbifolds with nodes.
In this talk I will discuss some of the previous results.

Speaker: Thilo, Kuessner
Title: Chern-Simons invariants of 3-manifold groups in SL(4,R)
Abstract: For (closed or cusped) 3-manifolds, we compute the Chern-Simons invariants of all flat 4-dimensional bundles with holonomy factoring over SL(2, C), by computing their fundamental class in the extended Bloch group and applying the extended Rogers' dilogarithm. We concentrate on those representations coming from the isomorphism PSL(2,C)=SO(3,1), because this is the hardest case. We discuss the consequences of our computations for the number of connected components of SL(4, R)-character varieties. We also use volumes of representations to show that there are knots whose SL(n, C)-character varietiy has an arbitrarily large number of connected components corresponding to representations with vanishing Chern-Simons invariant.

Speaker: Juhyun Lee
Title: Classification of tight contact structures on hyperbolic 3-manifolds up to contact isotopy
Abstract: By coarse classification theorem of tight contact structures, it is known that every closed, atoroidal 3-manifolds attains at most finite tight contact structures up to contact isotopy. However, the explicit number, even the existence, of the tight contact structures remains a mystery. In this talk we first show that the existance of dividing curve components minimizing convex fiber in the case of surface bundle over the circle with arbitrary pseudo-Anosov monodromy and, after that, investigate the number of tight contact structures of these manifolds up to contact isotopy using convex decomposition technique.

Speaker: Ken'ichi Ohshika (Osaka Univ, Osaka)
Title: Various compactifications of Teichmuller spaces and their relations
Abstract: It is known that there are various kinds of “natural” compactifications of Teichmuller spaces: the Teichmuller ray compactification, the Thurston compactification, the Bers compactification, the Gardiner-Masur compactification etc. In this series of talks, I shall show that we can understand their relations by considering what I call “reduced compactifications”.

Speaker: Andy Sanders ( Univ Chicago illinoi)
Title: Complex deformations of Anosov representations
Abstract: Anosov representations of surface groups are generalizations of convex-cocompact representations to higher rank Lie groups G. Due to work of Guichard-Wienhard, there exist closed (G,X)-manifolds with holonomy a given Anosov representation. When the Lie group G is complex, these quotient manifolds are complex manifolds locally modelled on flag varieties. In these talks, we will study the complex deformation theory of these manifolds and relate it to their deformation theory as (G,X) manifolds. A basic motivating question concerns the existence of a uniformization theorem for Anosov representations; we will indicate some small progress towards this question. Along the way, we will show that these manifolds usually fail to be Kahler. These talks represent joint work with David Dumas.


Speaker: Matthew Stover (Temple University)
Title: Character varieties of knot complements and arithmetic geometry
Abstract: Let K be a hyperbolic knot. I will discuss recent work with Ted Chinburg and Alan Reid on how the arithmetic geometry of the associated SL_2(C) character variety, given simple conditions on the Alexander polynomial, puts strong restrictions on invariants of hyperbolic Dehn surgeries on K.

Speaker: Zhe Sun (Max Plack Institute)
Title & Abstract:

Speaker: Genkai Zhang (Chalmers Univ, Goteborg)
Title: Local rigidity of hyperbolic lattices in semi-simple Lie groups
Abstract: Let $Gamma$ be a uniform lattice in $SU(n, 1)$. We study some natural imbeddings of the hyperbolic ball in classical and exceptional Riemannian symmetric spaces G/K and consider the local rigidity of $Gamma$ in $G$ via the homomorphisms from $SU(n, 1)$ to $G$.