Program
 Nicolas Bergeron: Arithmetics and Hyperbolic Manifolds
In these lectures I will explain the construction of arithmetic hyperbolic manifolds. I will then focus on their homology, free part and then torsion part. Finally, I will explain why 3 dimensional arithmetic manifolds are good candidates for being « topological expanders » and what it is good for.
Exercises

Ken Bromberg: Renormalized volume of hyperbolic 3manifolds
I will begin with some basics on deformations of Riemannian metrics with a special emphasis on hyperbolic metrics
in dimensions 2 and 3. Then I will describe some of the basic properties of convex cocompact hyperbolic 3manfiolds
and their renormalized volume.
In the final lecture I will survey some recent results and open problems.
Exercises

Indira Chatterji: $CAT(0)$ Cubical Complexes
We will discuss CAT(0) cubical complexes and spaces with walls. We shall see how one can construct a cubulation, that is a proper cocompact action on a CAT(0) cubical complex, from a space with walls. We will also discuss BergeronWise boundary criterion for cubulation, that allowed them to build on results by KahnMarkovic to cubulate fundamental groups of closed hyperbolic 3 manifolds.
Exercises

David Dumas: Introduction to Opers
Opers are a class of geometric structures on a compact Riemann surface
$X$ that are associated with a reductive complex Lie group $G$. In
these lectures we will discuss the general theory and the construction
of some examples, focusing on the case $G=\mathrm{SL}(n,\mathbb{C})$.
Here, an oper can be seen in several equivalent guises: As a rank$n$
holomorphic vector bundle over $X$ with a connection (satisfying
certain axioms), as an immersion of the universal cover of $X$ in the
projective space $\mathbb{CP}^{n1}$ (satisfying a transversality
condition), or as a linear ordinary differential operator of order $n$
acting on a line bundle over $X$. Will we discuss the equivalences
between these different perspectives, the identification between opers
for $\mathrm{SL}(2,\mathbb{C})$ and complex projective structures, and
the parameterization of the space of $\mathrm{SL}(n,\mathbb{C})$opers
by tuples of holomorphic differentials on $X$.
Exercises
 Alessandra Iozzi: A dual interpretation of Gromov's proof of Mostow Rigidity theorem as in Thurston's notes
I will present a rigidity theorem for representations of the fundamental group of a hyperbolic nmanifold into SO(1,n).
This gives as a corollary a different interpretation of a proof of Mostow Rigidity theorem,
for which we basically replace smearing and straightening by bounded cohomology.
Indeed the proof will be preceded by a gentle introduction to continuous bounded cohomology in its most useful reincarnation.
Exercises