Yves
Benoist
Title: Invariant subsets of homogeneous spaces.
Abstract: Let G be a Lie group, X be a G-homogeneous space of finite volume, and H be a closed subgroup of G. What are the H-invariant closed subsets in X? I will focus on a joint work with J.-F. Quint addressing the case when G is simple and H is Zariski dense.
Olivier Biquard
Title: Complete Einstein metrics, symmetric spaces, and regularity.
Michel Boileau
Title: Commensurability of hyperbolic knot groups.
Abstract: By R. Schwartz' s result, two hyperbolic knot groups are commensurable iff they are quasi-isometric. In this talk we will discuss the commensurability relation between hyperbolic knot groups and deduce some results about the classification of hyperbolic knots up to quasi-isometries of the fundamental groups of their complements.
Title: Invariant subsets of homogeneous spaces.
Abstract: Let G be a Lie group, X be a G-homogeneous space of finite volume, and H be a closed subgroup of G. What are the H-invariant closed subsets in X? I will focus on a joint work with J.-F. Quint addressing the case when G is simple and H is Zariski dense.
Olivier Biquard
Title: Complete Einstein metrics, symmetric spaces, and regularity.
Michel Boileau
Title: Commensurability of hyperbolic knot groups.
Abstract: By R. Schwartz' s result, two hyperbolic knot groups are commensurable iff they are quasi-isometric. In this talk we will discuss the commensurability relation between hyperbolic knot groups and deduce some results about the classification of hyperbolic knots up to quasi-isometries of the fundamental groups of their complements.
Emmanuel
Breuillard
Title: Carnot-Caratheodory geometry and the asymptotics of the word metric on nilpotent groups.
Abstract: I will describe some recent progress regarding various counting problems on nilpotent groups in which Pansu's thesis plays a key role.
Pdf file here.
Marc Burger
Title: An extension criterion for lattice actions on the circle.
Abstract: We establish a necessary and sufficient condition for an action of a lattice by homeomorphisms of the circle to extend continuously to the ambient locally compact group. This condition is expressed in terms of the real bounded Euler class of this action. Combined with classical vanishing theorems in bounded cohomology, one recovers rigidity results of Ghys, Witte--Zimmer, Navas and Bader--Furman--Shaker in a unified manner.
Indira Chatterji
Title: On a question of Nori.
Abstract: Madhav Nori in 1983 asked the following: If H is a real algebraic subgroup of a real semi-simple algebraic group G, find sufficient conditions on H and G such that any Zariski dense subgroup of G which intersects H in a lattice in H, is itself a lattice in G. We shall discuss this question and in particular explain why, for n greater than 3, if Gamma is a discrete Zariski dense subgroup in SL(n,R) whose intersection with SL(n-1,R) is commensurable with SL(n-1,Z), then Gamma is commensurable with SL(n,Z). This is joint work with T.N. Venkataramana.
François Dahmani
Title: Property FA for random groups, and boundaries.
joint with Piotr Przytycki and Vincent Guirardel.
We study the impossibility of random groups (in the density model) to split as non trivial amalgamated free product or HNN extension. To do this, we first study, at fixed density, presentations with sufficiently large number of generators. Then we reduce the general case to the case of presentations with many generators. One corollary is that all random groups in the density model, with density <1/2 have their Gromov boundary homeomorphic to the Menger curve. This was proved by Champetier for densities less than 1/24.
Damien Gaboriau
Title: Non orbit-equivalent actions of countable groups.
Misha Gromov
Title: Crystals, proteins and isoperimetry.
Pdf file here.
François Guéritaud
Title: Alternating pseudo-Anosovs.
Abstract: Penner and Fathi gave a sufficient condition for a product of Dehn twists to be pseudo-Anosov, based on an idea of Thurston. We will describe a slightly more general construction with a completely new proof, involving angle structures on ideal triangulations. Joint work with D. Futer.
Vincent Guirardel
Title: Small cancellation in the mapping class group and Out(Fn).
Abstract: We prove that there exist normal free subgroups of the mappling class group all of whose non-trivial elements are pseudo-Anosov. This is done using small cancellation techniques for the action on the
complex of curves. Using Bestvina-Feighn's hyperbolic complex for Out(Fn), we get similar results for Out(Fn).
As further applications, we get that any non-elementary finitely generated subgroup of the mapping class group has many quotients. In particular, this gives a new proof that lattices in higher rank simple Lie groups don't embed in the mapping class group.
This is a joint work with Francois Dahmani.
Peter Haïssinsky
Title: A notion of invariant line fields for coarse conformal dynamical systems.
Abstract: We will focus on the dynamics of countable groups and finite branched coverings of the two-sphere. We will develop a notion of invariant line fields in this context which will enable us to characterize those dynamical systems which admit optimal metrics (in the sense of Hausdorff dimension). We obtain in particular a different approach to Bonk and Kleiner's characterisation of cocompact Kleinian groups.
Nicolas Juillet
Title: Ricci curvature in metric spaces: the case of the Heisenberg group.
Abstract: We present the recent definition of "metric measure space with non-negative Ricci curvature", due to Lott-Villani and Sturm independentely. We show that the subRiemannian Heisenberg group does not satisfy this condition. Nevertheless it satisfies the Measure Contraction Property, a weaker condition that will also be presented in this talk.
Pdf file here.
Vincent Lafforgue
Title: Strengthened Property (T) and applications.
Abstract: We first give an idea of the proof of strengthened property (T) for G=SL3(F) where F is a non-archimedean local field. It says roughly that the trivial representation is isolated among representations of G with small exponential growth in Banach spaces of type >1. From it we deduce that expanders built from G do not embed coarsely in Banach spaces of type >1, and that any affine isometric action of G in such a Banach space has a fixed point. At the end we will discuss open questions : how to extend these results to SL3(R) and SL3(C), to expanders with large girth and to Banach space of finite cotype?
François Ledrappier
Title: Linear drift for covers of compact manifolds.
Abstract: We consider a regular Riemannian cover M~ of a compact Riemannian manifold. The linear drift L and the Kaimanovich entropy h are geometric invariants defined by asymptotic properties of the Brownian motion on M~. We discuss the relation with other asymptotic quantities. In particular, we show that L^2 < or = h.
Nicolas Monod
Title: CAT(0) groups and lattices.
Stefano Nardulli
Title: Semianalyticity of isoperimetric profiles (d'après Renata Grimaldi, Stefano Nardulli et Pierre Pansu).
Abstract: It is shown that, in dimensions < 8, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic. The proof relies on previous results coming from my Ph.D. thesis, advised by Pierre Pansu.
Pdf file here.
Viktor Schroeder
Title: Ptolemy spaces with many circles.
Abstract: The boundary of a CAT(-1) space carries a natural class of metrics which satisfy the Ptolemy condition. In these spaces there is a natural concept of circles. In this talk we study Ptolemy spaces with many circles and give applications to CAT(-1) spaces.
Jacek Swiatkowski
Title: Gromov boundaries with interesting topology
Abstract: In the first part of my talk I will describe a family of explicit topological spaces of dimension 3 which occur as Gromov boundaries of some hyperbolic groups (joint work with Piotr Przytycki). In the second part I will present two exotic topological properties of Gromov boundaries of 7-systolic groups (these are hyperbolic groups occuring in the context of negative simplicial curvature, as introduced by Januszkiewicz and myself). These properties reflect on the boundary level the fact that high-dimensional 7-systolic groups are very different from fundamental groups of nonposititively curved manifolds. One of those properties was observed by Damian Osajda, and the other by myself.
Alain Valette
Title: Proper isometric actions on $L^p$-spaces.
Abstract: This is joint work with Y. de Cornulier and R. Tessera. The starting point was several recent results on proper isometric actions of groups on Banach spaces, including Yu's result that an hyperbolic group $\Gamma$ admits a proper isometric action on $\ell^p(\Gamma\times \Gamma)$ for $p$ large. We say that a locally compact group $G$ has property $(BP_0)$ if every isometric action on a Banach space, whose linear part is a $C_0$-representation, either has bounded orbits or is proper. We prove that every solvable group and every connected Lie group has $(BP_0)$. Combining this with a result of Pansu on the non-vanishing of the first $L^p$-cohomology for rank 1 simple Lie groups, we prove that such a group $G$ admits a proper isometric action on $L^p(G)$ if $p$ is larger than the critical exponent of $G$.
Title: Carnot-Caratheodory geometry and the asymptotics of the word metric on nilpotent groups.
Abstract: I will describe some recent progress regarding various counting problems on nilpotent groups in which Pansu's thesis plays a key role.
Pdf file here.
Marc Burger
Title: An extension criterion for lattice actions on the circle.
Abstract: We establish a necessary and sufficient condition for an action of a lattice by homeomorphisms of the circle to extend continuously to the ambient locally compact group. This condition is expressed in terms of the real bounded Euler class of this action. Combined with classical vanishing theorems in bounded cohomology, one recovers rigidity results of Ghys, Witte--Zimmer, Navas and Bader--Furman--Shaker in a unified manner.
Indira Chatterji
Title: On a question of Nori.
Abstract: Madhav Nori in 1983 asked the following: If H is a real algebraic subgroup of a real semi-simple algebraic group G, find sufficient conditions on H and G such that any Zariski dense subgroup of G which intersects H in a lattice in H, is itself a lattice in G. We shall discuss this question and in particular explain why, for n greater than 3, if Gamma is a discrete Zariski dense subgroup in SL(n,R) whose intersection with SL(n-1,R) is commensurable with SL(n-1,Z), then Gamma is commensurable with SL(n,Z). This is joint work with T.N. Venkataramana.
François Dahmani
Title: Property FA for random groups, and boundaries.
joint with Piotr Przytycki and Vincent Guirardel.
We study the impossibility of random groups (in the density model) to split as non trivial amalgamated free product or HNN extension. To do this, we first study, at fixed density, presentations with sufficiently large number of generators. Then we reduce the general case to the case of presentations with many generators. One corollary is that all random groups in the density model, with density <1/2 have their Gromov boundary homeomorphic to the Menger curve. This was proved by Champetier for densities less than 1/24.
Damien Gaboriau
Title: Non orbit-equivalent actions of countable groups.
Misha Gromov
Title: Crystals, proteins and isoperimetry.
Pdf file here.
François Guéritaud
Title: Alternating pseudo-Anosovs.
Abstract: Penner and Fathi gave a sufficient condition for a product of Dehn twists to be pseudo-Anosov, based on an idea of Thurston. We will describe a slightly more general construction with a completely new proof, involving angle structures on ideal triangulations. Joint work with D. Futer.
Vincent Guirardel
Title: Small cancellation in the mapping class group and Out(Fn).
Abstract: We prove that there exist normal free subgroups of the mappling class group all of whose non-trivial elements are pseudo-Anosov. This is done using small cancellation techniques for the action on the
complex of curves. Using Bestvina-Feighn's hyperbolic complex for Out(Fn), we get similar results for Out(Fn).
As further applications, we get that any non-elementary finitely generated subgroup of the mapping class group has many quotients. In particular, this gives a new proof that lattices in higher rank simple Lie groups don't embed in the mapping class group.
This is a joint work with Francois Dahmani.
Peter Haïssinsky
Title: A notion of invariant line fields for coarse conformal dynamical systems.
Abstract: We will focus on the dynamics of countable groups and finite branched coverings of the two-sphere. We will develop a notion of invariant line fields in this context which will enable us to characterize those dynamical systems which admit optimal metrics (in the sense of Hausdorff dimension). We obtain in particular a different approach to Bonk and Kleiner's characterisation of cocompact Kleinian groups.
Nicolas Juillet
Title: Ricci curvature in metric spaces: the case of the Heisenberg group.
Abstract: We present the recent definition of "metric measure space with non-negative Ricci curvature", due to Lott-Villani and Sturm independentely. We show that the subRiemannian Heisenberg group does not satisfy this condition. Nevertheless it satisfies the Measure Contraction Property, a weaker condition that will also be presented in this talk.
Pdf file here.
Vincent Lafforgue
Title: Strengthened Property (T) and applications.
Abstract: We first give an idea of the proof of strengthened property (T) for G=SL3(F) where F is a non-archimedean local field. It says roughly that the trivial representation is isolated among representations of G with small exponential growth in Banach spaces of type >1. From it we deduce that expanders built from G do not embed coarsely in Banach spaces of type >1, and that any affine isometric action of G in such a Banach space has a fixed point. At the end we will discuss open questions : how to extend these results to SL3(R) and SL3(C), to expanders with large girth and to Banach space of finite cotype?
François Ledrappier
Title: Linear drift for covers of compact manifolds.
Abstract: We consider a regular Riemannian cover M~ of a compact Riemannian manifold. The linear drift L and the Kaimanovich entropy h are geometric invariants defined by asymptotic properties of the Brownian motion on M~. We discuss the relation with other asymptotic quantities. In particular, we show that L^2 < or = h.
Nicolas Monod
Title: CAT(0) groups and lattices.
Stefano Nardulli
Title: Semianalyticity of isoperimetric profiles (d'après Renata Grimaldi, Stefano Nardulli et Pierre Pansu).
Abstract: It is shown that, in dimensions < 8, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic. The proof relies on previous results coming from my Ph.D. thesis, advised by Pierre Pansu.
Pdf file here.
Viktor Schroeder
Title: Ptolemy spaces with many circles.
Abstract: The boundary of a CAT(-1) space carries a natural class of metrics which satisfy the Ptolemy condition. In these spaces there is a natural concept of circles. In this talk we study Ptolemy spaces with many circles and give applications to CAT(-1) spaces.
Jacek Swiatkowski
Title: Gromov boundaries with interesting topology
Abstract: In the first part of my talk I will describe a family of explicit topological spaces of dimension 3 which occur as Gromov boundaries of some hyperbolic groups (joint work with Piotr Przytycki). In the second part I will present two exotic topological properties of Gromov boundaries of 7-systolic groups (these are hyperbolic groups occuring in the context of negative simplicial curvature, as introduced by Januszkiewicz and myself). These properties reflect on the boundary level the fact that high-dimensional 7-systolic groups are very different from fundamental groups of nonposititively curved manifolds. One of those properties was observed by Damian Osajda, and the other by myself.
Alain Valette
Title: Proper isometric actions on $L^p$-spaces.
Abstract: This is joint work with Y. de Cornulier and R. Tessera. The starting point was several recent results on proper isometric actions of groups on Banach spaces, including Yu's result that an hyperbolic group $\Gamma$ admits a proper isometric action on $\ell^p(\Gamma\times \Gamma)$ for $p$ large. We say that a locally compact group $G$ has property $(BP_0)$ if every isometric action on a Banach space, whose linear part is a $C_0$-representation, either has bounded orbits or is proper. We prove that every solvable group and every connected Lie group has $(BP_0)$. Combining this with a result of Pansu on the non-vanishing of the first $L^p$-cohomology for rank 1 simple Lie groups, we prove that such a group $G$ admits a proper isometric action on $L^p(G)$ if $p$ is larger than the critical exponent of $G$.