Biringer  Growth of Betti numbers in higher rank locally symmetric spaces
Let X be a higher rank irreducible symmetric space of noncompact type. We will show that the growth of Betti numbers in any sequence of distinct, compact Xmanifolds with injectivity radius bounded below is controlled by the L2 Betti numbers of X. The key technique is a probabilistic version of GromovHausdorff convergence, adapted from BenjaminiSchramm convergence in graph theory.
Joint work with Abert, Bergeron, Gelander, Nikolov, Raimbault, Samet.
Brock
 The
WeilPetersson metric and the geometry of hyperbolic 3manifolds
Many coarse relationships support the existence of a deep connection between the synthetic geometry of the WeilPetersson metric and the geometry of hyperbolic 3manifolds. In this talk, I'll elaborate on some new, finer examples of such connections, as well as some contrary evidence to a fundamental link. This talk will present joint work with Yair Minsky and Juan Souto.
Canary
 Dynamics on character varieties
If $\Gamma$ is a finitely presented group and $G$ is a Lie group, it is natural to study the dynamics of the action of $Out(\Gamma)$ on the $G$character variety of $\Gamma$. In this talk, we will briefly survey previous work and then focus on recent work of Canary, Lee, Magid, Minsky and Storm in the setting where $\Gamma$ is a 3manifold group and $G=PSL(2,C)$.
Chatterji
 Distortion and bounded cohomology for Lie groups
I will explain how the distortion of central subgroups in Lie groups is related to the Borel cohomology in degree 2, and illustrate a few results on examples. This is joint work with Mislin, Pittet and SaloffCoste, as well as work in progress with Cornulier, Mislin and Pittet.
Clay
 The geometry of
rightangled Artin subgroups of the mapping class group
We describe sufficient conditions which guarantee that a finite set of mapping classes generate a rightangled Artin group quasiisometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmüller space is a quasiisometric embedding for both of the standard metrics.
Dreyer

Length
functions for Hitchin representations
Let
S be a closed oriented surface of negative Euler characteristic. We
consider the space Rep_n(S) of conjugacy classes of homomorphisms
from the fundamental group of S to PSL_n(R), with n > 2. Using
Higgs bundle techniques, N. Hitchin described the number of connected
components of Rep_n(S). In particular, he gave a parametrization of
one connected component, called the Hitchin space, which contains a
copy of the Teichmüller space of S. Given a closed curve c on S and
a representation r in the Hitchin space of S, we can consider the
eigenvalues of r(c). We first show how to extend these eigenvalue
functions to length functions on the space of measured geodesic
currents on S, or more generally on the space of Hölder geodesic
currents. Then we introduce cataclysm deformations for Hitchin
representations and study the effect of these deformations on the
length functions of a Hitchin representation.
This work is based on Labourie's dynamical characterization of Hitchin representations.
Kerckhoff

Complex projective surfaces bounding 3manifolds
A
number of properties of the space of complex projective structures on
surfaces bounding a 3manifold will be derived from Poincare duality.
A simple formula for the Goldman complex symplectic structure
implies Kleinian and quasiFuchsian reciprocity and the lagrangian
nature of various sections, such as Bers slices.
Maher
 Exponential decay
in the mapping class group
We show that a random walk on the mapping class group gives a nonpseudoAnosov element with a probability which decays exponentially in the length of the random walk. More generally, we show that the probability that a random walk gives an element with bounded translation distance on the curve complex decays exponentially.
Tao
 Geodesics in Teichmuller Space Equipped with Thurston's
Lipschitz Metric
Thurston defined an asymmetric metric
on Teichmuller space using Lipschitz maps and proved that distances
can be computed using hyperbolic length ratios between curves. This
contrasts with the Teichmuller metric on Teichmuller space, defined
using quasiconformal maps, which by Kerckhoff's formula can be
computed using extremal length ratios between curves. In joint work
with Anna Lenzhen and Kasra Rafi, we study geodesics in the Lipschitz
metric. We show that if the endpoints of a Lipschitz geodesic have
bounded combinatorics, then it fellow travels the unique Teichmuller
geodesic with the same endpoints. For arbitrary Lipschitz geodesics,
we show that their projection to the curve complex are unparametrized
quasigeodesics. The proof in the latter is inspired by the recent
work of BestvinaFeighn on the hyperbolicity of the free factor
complex.