Category: Uncategorized

By awb1472 on Talks, Uncategorized tagged

11/09: Andrew Zimmer

Convex co-compact representations of 3-manifold groups

Abstract: A representation of a finitely generated group into the projective linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. In this talk I will discuss the case of 3-manifold groups and prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean × Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. This extends a result of Benoist about convex real projective structures on closed 3-manifolds. In each case, I will also describe what these representations look like. This is joint work with Mitul Islam (a graduate student at the University of Michigan).

 

Slides

By awb1472 on Talks, Uncategorized

10/05: Davi Obata

Open sets of partially hyperbolic systems having a unique SRB measure

Abstract: For a dynamical system, a physical measure is an ergodic invariant measure that captures the asymptotic statistical behavior of the orbits of a set with positive Lebesgue measure. A natural question in the theory is to know when such measures exist.

It is expected that a “typical” system with enough hyperbolicity (such as partial hyperbolicity) should have such measures. A special type of physical measure is the so-called hyperbolic SRB (Sinai-Ruelle-Bowen) measure. Since the 70`s the study of SRB measures has been a very active topic of research.
In this talk, we will see some new examples of open sets of partially hyperbolic systems with two dimensional centers having a unique SRB measure.  One of the key features for these examples is a rigidity result for a special type of measure (the so-called u-Gibbs measure) which allows us to conclude the existence of the SRB measures.

By awb1472 on Talks, Uncategorized

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.

By awb1472 on Talks, Uncategorized

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.

 

Slides

By awb1472 on Talks, Uncategorized

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.

 

Slides

By awb1472 on Talks, Uncategorized

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.

By awb1472 on Talks, Uncategorized

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.

By awb1472 on Talks, Uncategorized

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.

By awb1472 on Talks, Uncategorized

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.

Slides