Titles and Abstracts

I International Workshop on Geometry, Dynamics and Anosov Representations - I GDAR 
MATH-AmSud Project GDAR - France, Brazil and Chile 
July 5 - 7, 2017, Santiago – Chile


Plenary Speakers 

Thierry Barbot - Université d´Avignon - France

"GDAR I: Anosov representations and conformally flat spacetimes" 
Abstract: I will present the connections between Anosov representations and conformally flat spacetimes. The talk will be based on the material of the recent survey: https://arxiv.org/pdf/1609.03863.pdf

"GDAR 2: Singularities in spacetimes and piecewise transformations of the circle"
Abstract: I will present the connexion between particles in (2+1)-dimensional spacetimes and the theory of projective transformations on a projective circle. The main objective is to formulate the classification problem of collisions of tachyons, gravitons and other black hole. The content of the talk will be greatly extracted from sections 3 and 5 of https://arxiv.org/pdf/1010.3602.pdf

Andrés Navas - Universidad de Santiago de Chile - Chile

"Some questions concerning groups of piecewise affine and piecewise projective diffeomorphisms"
AbstractIn this talk we will review some recent results concerning obstructions for C^1 actions on the circle of certain groups of homeomorphisms and stress that these questions remain open for certain groups of piecewise-projective homeomorphisms.

Jairo Bochi - Pontificia Universidad Católica de Chile - Chile

"Anosov representations and dominated splittings"
The concept of dominated splitting comes from ODE and differentiable dynamics. It turns out that Anosov representations are a manifestation of domination. I will discuss these relations. I will also sketch our proof of a result of Kapovich, Leeb, and Porti stating that only Gromov-hyperbolic groups admit Anosov representations. This talk is based on my joint work with Rafael Potrie and Andrés Sambarino. 

François Fillastre - Université de Cergy-Pontoise - France

"Constant curvature -1 3d spaces and Teichmüller theory"
Abstract: "We briefly review the 3d model spaces of curvature -1, which are hyperbolic space, anti-de Sitter space and co-Minkowski (or half-pipe) space. We then give some examples of relations with Teichmüller space of compact surfaces, mainly focusing on co-Minkowski space. This talk is coming from the surveys arxiv.org/1605.04563 and arXiv:1611.01065"

Graham Smith - Universidade Federal do Rio de Janeiro - Brazil

onstant scalar curvature hypersurfaces in (3+1)-dimensional GHMC Minkowski spacetimes"
Abstract: We prove that every (3+1)-dimensional flat GHMC Minkowski spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is smooth.

Richard Urzúa - Universidad Católica del Norte - Chile

"Acciones libres afines de Z^p sobre el toro T^q"
Abstract: Toda acción de Z^p  sobre Z^q que actúa por automorfismos de Z^q, con conjunto de puntos fijos diferente de cero, induce una acción unipotente máxima de Z^p sobre Z^q´, que determina si la acción original es la parte lineal de una acción afín libre de Z^p sobre el toro T^q.

Carlos Maquera - Universidade de Sao Paulo - Brazil

"Some insights in Anosov actions"
Abstract: In this talk we will discuss the problem of classification of Anosov actions of abelian (or nilpotent) Lie groups. Our emphasis will be on the case where the action is of codimension one.

Léo Brunswic - Université d´Avignon - France

"Polyhedral Cauchy-surfaces of singular flat Cauchy-compact spacetimes
Abstract :  We present two constructions of polyhedral Cauchy-surfaces in flat globally hyperbolic Cauchy-compact spacetimes. The first construction is inspired by a 1987 paper of Penner on so-called decorated Teichmüller space : the convex hull method. We give a new interpretation of this construction in the context of Cauchy-compact flat spacetimes with BTZ-like singularities giving a bijective map from the moduli space of a marked Cauchy-compact spacetimes with BTZ of linear holonomy to the moduli space of marked closed polyhedral surface. The starting point of the second construction  is the inverse of this map ; essentially described by Penner, we give a generalization with the prospect of extending this correspondance to spacetimes with massive particles and BTZ singularities.

Viviane Pardini Valerio - Universidade Federal de Sao Joao del-Rei - Brazil

"On the Anosov character of the Pappus-Schwartz representations"
The talk will be devoted to the Pappus-Schwartz representation and their recent generalization. The reference for this talk is https://arxiv.org/pdf/1610.04049.pdf

Link to the GDAR website: http://gdar.fr/