 JeanPhilippe Burelle: $P$Anosov representations of free groups in $\text{Sp}(2n,\mathbb{R})$
GuichardWienhard recently generalized the notion of Lusztig positivity
in order to define new
higher Teichmueller spaces. The symplectic group $\text{Sp}(2n,\mathbb{R})$ admits two
different kinds of positive
structures, one in the space of complete isotropic flags and one in the
Lagrangian Grassmannian.
I will explain how each type of positivity can be used to define
natural classes of Schottky groups
which are $P$Anosov representations of the free group. These generalize
previous constructions of
CharetteFrancoeurLareauDussault and BurelleTreib. We show that
every $P$Anosov representation
can be continuously deformed to a Schottky group in this sense, and
study the space of Schottky
groups. This is work in progress with Fanny Kassel and Virginie
Charette.
 Valentina Disarlo: Generalized stretch lines for surfaces with boundary
We will discuss some natural generalizations of Thurston's
distance for surfaces with boundary, in particular the arc metric. We will
construct a large family of geodesics for the Teichmueller space of surfaces
with boundary with respect to the arc metric, which we will call "
generalized stretch lines". We will prove that the Teichmueller space with
the arc metric is a geodesic metric space, and that it is a Finsler space.
This generalizes a result by Thurston on punctured surfaces. This is joint
work with Daniele Alessandrini (University of Heidelberg).
 Federica Fanoni: Curve graphs for infinitetype surfaces
For surfaces of finitetype, studying the action of the mapping class group
on a graph, called curve graph, has proved very useful to understand
properties of the group itself. In the case of infinitetype surfaces (e.g.
surfaces of infinite genus), the classical curve graph is not interesting
from the coarse geometry viewpoint. I will discuss why and when we can (or
can't) construct interesting graphs in the infinitetype case. Joint work
with Matt Durham and Nick Vlamis.
 Selim Ghazouani: Renormalisation in onedimensional dynamics and geometric structures on surfaces
Building upon work of Herman, Yoccoz, KhaninSinai from the 80s, I will try to give some motivations for questions concerning the generic behaviour of onedimensional dynamical systems, such as circle diffeormorphims with break points or more generally generalised interval
exchange transformations.
In turns out that in many cases moduli spaces of such dynamical systems bear a lot more structure than one would initially expect. We will try to explain how this extra structure comes from the connexion between such dynamical systems and corresponding geometric structures on
surfaces.
This connection allows for an interpretation of certain renormalisation operators as actions of the mapping class group.
We will try to illustrate all these considerations with two examples where this approach yields somewhat significant dynamical results. The corresponding structures are complex affine structures on compact surfaces and representations of the free group in $\text{PSL}(2,\mathbb{R})$ respectively.

Elise Goujard: MasurVeech volumes of principal strata, intersection numbers and
hyperbolic geometry
I will present a formula for the MasurVeech volumes of the principal
strata of halftranslation surfaces (as well as SiegelVeech constants) in
terms of intersection numbers involving psiclasses. This formula closely
relates the counting of squaretiled surfaces of fixed combinaotiral type
with Mirzakhani's counting of simple closed geodesic multicurves on
hyperbolic surfaces, and leads to several conjectures for the large genus
asymptotics. This is a joint work with V.Delecroix, P.Zograf and A.Zorich.
 François Guéritaud: Geometric transition and canonical triangulations for the punctured torus
There are many parallels between the isometry groups of hyperbolic 3space
and of antide Sitter (2+1)space, its Lorentzian counterpart. In particular,
quasifuchsian groups (limit curves, convex cores, bending laminations)
can be defined in both settings, and there is a continuous way of
"transitioning"
from one to the other. We will show that in the case of punctured torus
groups,
a natural "Delaunay decomposition" of the convex core (also related to the
bending)
is wellbehaved under this transition. This is joint work with Sara Maloni.
 Richard Kenyon: Dimers and Circle Patterns
A circle pattern is a way to draw a planar graph so that each
face is cyclic.
The dimer model is a probability measure on the set of dimer covers
(perfect matchings) of a planar graph.
There is a surprising link between the dimer model on a bipartite planar
graph and an associated circle pattern.
In fact for a given bipartite graph
there is an essentially bijective correspondence between circle patterns
with embedded dual
and dimer measures.
 Qiongling Li: Projective structures with holonomy in (Quasi)Hitchin representations
In this talk, we study the topology of manifold admitting
projective structures with holonomy in (Quasi)Hitchin representations of
surface groups into the Lie group $\text{SL}(n,\mathbb{R})$ or $\text{SL}(n,\mathbb{C})$. In particular, we
focus on representations in a small neighborhood of Fuchsian locus inside
the representation variety of $\text{SL}(n,\mathbb{R})/\text{SL}(n,\mathbb{C})$. This is joint work with
Daniele Alessandrini.
 Sara Maloni: Convex hulls of quasicircles in hyperbolic and antide Sitter space
Thurston conjectured that quasiFuchsian manifolds are determined by the induced hyperbolic
metrics on the boundary of their convex core and Mess generalized those conjectures to the context of
globally hyperbolic AdS spacetimes. In this talk I will discuss a generalization of these conjecture to
convex hulls of quasicircles in the boundary at infinity of hyperbolic and antide Sitter space. (This is
joint work in progress with Bonsante, Danciger and Schlenker.)
 Julien Maubon: Rigidity of maximal representations of complex hyperbolic lattices
Maximal representations of surface groups in Hermitian semisimple Lie groups form a very interesting class of representations.
Here we focus on the higher dimensional case, that is on maximal representations of cocompact lattices $\Gamma$ of ${\rm SU}(n,1)$, with $n \geq 2$.
I will explain that such maximal representations are strongly rigid and can be completely classified.
First, they exists if and only if every simple factor of the target Hermitian Lie group $G$ is isomorphic to ${\rm SU}(p,q)$ for some $(p,q)$ with $ p\geq nq$, or possibly, if $n=2$, to the exceptional group ${\rm E}_6$.
Moreover. they are essentially induced by a Lie group homomorphism from ${\rm SU}(n,1)$ to $G$.
This is a joint work with Vincent Koziarz.
 Hugo Parlier: Lengths of geodesics and moduli spaces
This talk will be about geodesics on hyperbolic surfaces and identities involving their lengths.
These identities are equations which relate lengths of certain geodesics and which remain true over entire moduli spaces.
The talk will be about an ongoing project with Ara Basmajian and Ser Tan Peow where we study a family of identities relating lengths of orthogeodesics that interpolate between identities of Basmajian and McShane, and which hold true for surfaces with geodesic, cusp or coneangle boundary.
 Anne Parreau: Boundary of higher Teichmuller spaces and geodesic currents
Geodesic currents were introduced by Bonahon to study Thurston's
compactification of the Teichmuller space. In higher rank, this
compactification can be generalized replacing the length function
by the Jordan projection, seen as a Weyl chamber valued length function.
Labourie, Martone and Zhang have constructed geodesic currents
associated to hitchin or maximal representations.
We will explain how this can be generalized to the boundary
and allow to understand some structure of the degenerations of such
representations. In particular we construct a natural nonempty open
domain of discontinuity for the action of the mapping class group on
the boundary. This is joint work with Marc Burger, Alessandra Iozzi, and
Beatrice Pozzetti.
 Joan Porti: A local characterization of Anosov representations
Let $X=G/K$ be a symmetric space of noncompact type and
$\Gamma$ a hyperbolic group. For a representation of $\Gamma$ in $G$, I
give a characterization for this representation to be Anosov in terms of
the image of finitely many elements of $\Gamma$. This is joint work
with M. Kapovich and B. Leeb
 Beatrice Pozzetti: Critical exponent and Hausdorff dimension for Anosov representations
Whenever $G$ is a convex cocompact subgroup of the group of isometries of
the hyperbolic space, PattersonSullivan theory allows to relate the
asymptotic growth rate of orbit points for the action of $G$ on $\mathbb{H}^n$ and
the Hausdorff dimension of the limit set of $G$ on the boundary at
infinity. The relation between the Hausdorff dimension of the limit set
of an Anosov representation and a suitable orbit growth rate is much
more elusive since, on the one hand, the action of a higher rank group
on its boundaries is not conformal, and, on the other, many different
orbit growth functions can be considered. In my talk I'll report on
joint work with A. Sambarino and A. Wienhard in which we find large
classes of Anosov representations for which we can obtain such a
relation.
 Richard Schwartz: Iterated Barycentric subdivision
The barycentric subdivision of a simplex
can be iterated, producing an infinite family of
simplices. I'll explain why the set of these
simplices is dense in 2,3, and 4 dimensions. The
2 dimensional case, due to Barany, Beardon and Carne,
and the 3 dimensional case, are pretty easy. I
needed a computerassisted proof for the 4 dimensional
case.
 Andrea Seppi: Examples of fourdimensional geometric transition
Roughly speaking, a geometric transition is a deformation of geometric
structures on a manifold, by "transitioning" between different geometries.
Danciger introduced a new such transition, which enables to deform from
hyperbolic structures to Antide Sitter structure, going through another type
of real projective structures called "halfpipe", and provided conditions for
a compact 3manifold to admit a geometric transition of this type. By
extending a construction of Kerckhoff and Storm, I will describe examples of
finitevolume geometric transition in dimension 4. This is joint work with
Stefano Riolo.
 Ilia Smilga: Milnorian and nonMilnorian representations
In 1977, Milnor formulated the following conjecture: every discrete
group of affine transformations acting properly on the affine space is
virtually solvable. We now know that this statement is false; the
current goal is to gain a better understanding of the counterexamples to
this conjecture. Every group that violates this conjecture "lives" in a
certain algebraic affine group, which can be specified by giving a
linear group and a representation thereof. Representations that give
rise to counterexamples are said to be nonMilnorian. We will talk about
the progress made so far towards classification of these nonMilnorian
representations.
 Jérémy Toulisse: Compact connected components of relative character varieties
In a recent paper, Bertrand Deroin and Nicolas Tholozan
introduced the notion of supramaximal representations of the fundamental
group of the punctured sphere into $\text{PSL}(2,\mathbb{R})$. These representations have
many surprising properties and form compact connected components of the
relative character variety. In this talk, I will explain how the theory of
parabolic Higgs bundles gives a way to construct similar representations
into more general Hermitian Lie groups like $\text{SU}(p,q)$. The corresponding
components are compact and isomorphic to certain quiver varieties. This is
joint work with Nicolas Tholozan.
 Tengren Zhang: Affine actions with Hitchin linear part
We prove that if a surface group acts properly on $\mathbb{R}^d$ via affine
transformations, then its linear part is not the lift of a $\text{PSL}(d,\mathbb{R})$Hitchin
representation. To do this, we proved two theorems that are of independent
interest. First, we showed that $\text{PSO}(n,n)$Hitchin representations, when
viewed as representations into $\text{PSL}(2n,\mathbb{R})$, are never Anosov with respect to
the stabilizer of the $n$plane. Following DancigerGueritaudKassel, we also
view affine actions on $\mathbb{R}^{n,n1}$ as a geometric limit of isometric actions
on $\mathbb{H}^{n,n1}$. The second theorem we prove is a criterion for when an affine
action on $\mathbb{R}^{n,n1}$ is proper, in terms of the isometric actions on
$\mathbb{H}^{n,n1}$ that converge to it. This is joint work with Jeff Danciger, with
some overlap with independent work by Sourav Ghosh.