07/20: Federico Rodriguez Hertz
Non-rigidity of partially hyperbolic abelian 
-actions on tori
Abstract: Joint with Zhiren Wang we show some small
Category: Talks
07/13: Sebastian Hensel
Quasi-morphisms on surface diffeomorphism groups
Abstract: We will construct nontrivial quasimorphisms on the group of diffeomorphisms of a surface of genus at least 1 which are isotopic to the identity. This involves considering the graph whose vertices
correspond to curves on the surface (not up to isotopy!), and transferring usual curve graph methods to this setting. In particular, we show that it is hyperbolic, and we construct elements of Diff_0(S) which act as independent enough hyperbolic elements on it. As a consequence, we also solve a question by Burago-Ivanov-Polterovich on the unboundedness of the fragmentation norm. This is joint work with Jonathan Bowden and Richard Webb.
06/29: Danijela Damjanovic
Global rigidity of some partially hyperbolic abelian actions
Abstract: We consider abelian actions with sufficiently many partially hyperbolic elements and compact center foliation with trivial holonomy and leaves of dimension ≤ 2. Under some extra conditions we obtain that the action is essentially a product over affine Anosov action or even essentially algebraic. I will explain in the talk all these notions and some of the mechanisms in the proof. This is joint work with Amie Wilkinson and Disheng Xu.
07/06: Rémi Boutonnet
On the unitary dual of higher rank semi-simple lattices
Abstract: In this talk, based on joint work with Cyril Houdayer, I
will present a curious property of the unitary representations of
lattices in semi-simple higher rank Lie groups: either they contain a
finite dimensional invariant subspace or they are factorizations of
the regular representation, in a strong sense. I will explain how this
result generalizes and unifies recent advances in operator algebras.
Our approach relies on ergodic theory and stationary dynamical
systems.
06/22: Karin Melnick
A D’Ambra Theorem in conformal Lorentzian geometry
Abstract: D’Ambra proved in 1988 that the isometry group of a compact, simply connected, real-analytic Lorentzian manifold must be compact. I will discuss my recent theorem that the conformal group of such a manifold must also be compact, and how it relates to the Lorentzian Lichnerowicz Conjecture.
06/15: Amir Mohammadi
Geodesic planes in hyperbolic 3-manifolds
Abstract: Let M be a hyperbolic 3-manifold, a geodesic plane in M is a totally geodesic immersion of the hyperbolic plane into M. In this talk we will give an overview of some results which highlight how geometric, topological, and arithmetic properties of M affect the behavior of geodesic planes in M. This talk is based on joint works.
06/08: Asaf Katz
Measure rigidity of Anosov flows via the factorization method
Abstract: Anosov flows are central objects in dynamics, generalizing the basic example of a geodesic flow over a negatively curved surface.
In the talk we will introduce those flows and their dynamical behavior. Moreover, we show how the factorization method, pioneered by Eskin and Mirzakhani in their groundbreaking work about measure rigidity for the moduli space of translation surfaces, can be adapted to smooth ergodic theory and in particular towards the study of Anosov flows. Using this adaption, we show that for a quantitatively non-integrable Anosov flow, every generalized u-Gibbs measure is absolutely continuous with respect to the whole unstable manifold. In the talk I will introduce the factorization method, the relations to previous works (Eskin-Mirzakhani, Eskin-Lindenstrauss) and the result together with some examples and applications. Technical details will be given on the second part.
06/01: Kathryn Mann
Topological stability of actions on spheres at infinity
Abstract: The fundamental group of a negatively curved compact manifold acts by homeomorphisms on the visual boundary of its universal cover. In joint work with Jonathan Bowden, we show these actions are C^0 stable: any perturbation is a topological factor of the original action. One can do even better when the manifold is a surface and the visual sphere a circle, and along the same lines can also obtain a stronger result for actions “at infinity” of 3-manifold groups on circle that come from skew-Anosov foliations. However, in this talk, I will focus on the general rigidity result, applicable in all dimensions, and show some interesting slightly wild examples.
05/25: Weikun He
Quantitative equidistribution of random walks on the torus.
Abstract: Under a proximality assumption, Bourgain, Furman, Lindenstrauss and Mozes established a quantitative equidistribution result for linear random walks on the torus. I will discuss some recent progress in this topic, including a joint work with Nicolas de Saxcé which relaxed the proximality assumption and a joint with Tsviqa Lakrec and Elon Lindenstrauss which generalizes (to some extent) the result to affine random walks.
05/18: Or Landesberg
Horospherically invariant measures on geometrically infinite quotients
Abstract: We consider a locally finite (Radon) measure on 
invariant under a horospherical subgroup of where 
is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not admit any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable flow (geodesic flow). We deduce measure classification results. One such result in the context of finitely generated Kleinian groups in 
will be highlighted. Most of the talk will be based on joint work with Elon Lindenstrauss.
invariant under a horospherical subgroup of where is a discrete, but not necessarily geometrically finite, subgroup. We show that whenever the measure does not admit any additional invariance properties then it must be supported on a set of points with geometrically degenerate trajectories under the corresponding contracting 1-parameter diagonalizable flow (geodesic flow). We deduce measure classification results. One such result in the context of finitely generated Kleinian groups in will be highlighted. Most of the talk will be based on joint work with Elon Lindenstrauss.