Geometry, dynamics, and Anosov representations
5-7 July 2017

USACH

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

Plenary Speakers

Thierry Barbot – Université d´Avignon – France
Mario Jorge Dias Carneiro – Universidade Federal de Minas Gerais – Brazil
Andrés Navas – Universidad de Santiago de Chile – Chile
Jairo Bochi – Pontificia Universidad Católica de Chile – Chile
François Fillastre – Université de Cergy-Pontoise – France

Graham Smith – Universidade Federal do Rio de Janeiro – Brazil
Richard Urzúa – Universidad Católica del Norte – Chile
Carlos Maquera – Universidade de Sao Paulo – Brazil
Léo Brunswic – Université d´Avignon – France
Viviane Pardini Valerio – Universidade Federal de Sao Joao del-Rei – Brazil

Organizing & Scientific Committee

Thierry Barbot – Université d´Avignon – France
Mario Jorge Dias Carneiro – Universidade Federal de Minas Gerais – Brazil
Andrés Navas – Universidad de Santiago de Chile – Chile

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

 Register here

PROGRAM

Hr

July 5th

July 6th

9.30-10.30

Barbot I

Barbot II

10.30-11.00

Coffee

Coffee

11.00-12.00

Bochi

Brunswic

12.30-14.00

Lunch

Lunch

14.00-15.00

Fillastre

Navas

15.30-16.30

 Urzua

Pardini

PROGRAM

Hr

July 7th

 

10.00-11.00

Maquera

11.00-11.30

Coffee

11.30-12.30

Smith

12.30-14.00

Lunch

Name Last name Institution Country
Thierry Barbot Université d´Avignon France
Jairo Bochi Pontificia Universidad Católica de Chile Chile
Joaquín Brum Universidad de la República Uruguay
Léo Brunswic Université d´Avignon France
Mario Jorge Dias Carneiro Universidade Federal de Minas Gerais Brazil
León Carvajales Universidad de la República Uruguay
Francois Fillastre Université de Cergy-Pontoise France
Carlos Maquera Universidade de Sao Paulo Brazil
Andrés Navas USACH Chile
Viviane Pardini Valerio Universidade Federal de Sao Joao del-Rei Brazil
Cristóbal Rivas USACH Chile
Graham Smith Universidade Federal do Rio de Janeiro Brazil
Richard Urzúa Universidad Católica del Norte Chile
Cristobal Rivas USACH CHile
Julio Sánchez UCN Chile

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»
Abstract: In 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»
Abstract: 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

«Constant 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»
 Abstract: 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/

Weather in July (winter) in this part of Chile is very cold in the mornings (0-5°C) and then the temperature goes up 10-15°C in the afternoon, so bring your jacket and boots, and maybe an umbrella, because there is always the chance of rain. 

If you are entering to Chile with a passport issued by Australia or México, you will have to pay a Reciprocity Tax at the airport 

 

We are looking forward to see you in July!.


Attractions in and around Santiago:

La Campana National Park (UNESCO Biosphere Reserve)

Valparaíso (UNESCO World Heritage Site)

Isla Negra (One of Pablo Neruda’s houses)

Viña del Mar

Santiago

Portillo (Ski resort)

Vineyards and the Aconcagua Valley