Man

Andres Ignacio Navas Flores

Full time Professor

DPTO DE MATEMATICA Y CC, USACH

Santiago, Chile

Líneas de Investigación


Geometry, Group Theory, Dynamical Systems

Educación

  •  Mathematics, Universite d'Orsay Paris 11. Francia, 2000
  •  Mathematics, IMPA. Brasil, 1999
  •  Mathematics, Universidad de Santiago de Chile. Chile, 1998
  •  mathematics, ECOLE NORMALE SUPERIEURE DE LYON. Francia, 2003

Experiencia Académica

  •   post-doc Full Time

    IHES (Institut des Hautes Etudes Scientifiques)

    Francia

    2004 - 2005

  •   Profesor Asociado Full Time

    UNIVERSIDAD DE SANTIAGO DE CHILE

    Science

    Santiago, Chile

    2007 - At present

  •   Profesor Part Time

    UNIVERSIDAD DE CHILE

    Science

    Santiago, Chile

    2007 - 2013

  •   Assistant Professor Part Time

    UNIVERSIDAD DE CHILE

    Science

    Santiago, Chile

    2004 - 2006

Formación de Capital Humano


Supervision of Postdocs:
- Mahsa Allahbakhshi, USACH (2015-2016).
- Matthieu Calvez, USACH, Fondecyt (2013-2014) and USACH (2015-2016),
- Mahdi Teymuri Garakani, USACH, Dicyt (2013-2014),
- Mickael Crampon, USACH, Fondecyt (2011-2013),
- Alvaro Castañeda, U. de Chile, Fondecyt (2010-2012)

- Carlos Gómez, USACH (2006), undergraduate.
- Leslie Jiménez, U. de Chile (2006-2008), Master Thesis: Aspectos dinámicos de grupos ordenables.
- Eduardo Jorquera, U. de Chile (2006-2009), PhD Thesis: On groups of diffeomorphisms of the circle and the interval.
- Cristóbal Rivas, Univ. de Chile (2008-2010), PhD Thesis: Left-orderable groups.
- Gonzalo Castro, USACH (2013, co-advised with R. Tessera from ENS Lyon), PhD Thesis: On certain probabilistic aspects of groups, graphs, and actions.
- Rodolfo Viera, USACH (2016-2020): PhD Thesis: On the geometry of discrete sets.
- Gleen Foos, Master USACH (expected for 2021).
- Leinardo Dinamarca, PhD USACH (expected for 2022).

Publications:
Books:
- Groups of Circle Diffeomorphisms. Chicago Lectures in Mathematics, University of Chicago Press (2011).
Versión en castellano publicada en Ensaios Matemáticos, Soc. Brasileira de Mat. (2007).
- Groups, Orders, and Dynamics (junto a B. Deroin and C. Rivas). Submitted to American Math. Society. Prepublished http://arxiv.org/abs/1408.5805
- Un Viaje a las Ideas. Editorial Planeta (dissemination book).
- Lecciones de Matemáticas para el Recreo. Editorial Planeta (dissemination book).


Difusión y Transferencia


- Miembro del comité académico de la Olimpiada Nacional de Matemática desde 2006.
- Miembro del comité organizador permanente del Festival de Matemática.
- Columnista de divulgación matemática para El Mostrador, RedCiencia (CONICYT), Chile Científico e Images des Mathématiques (CNRS); en esta última revista especializada, autor de 13 artículos bilingües:
- Un caso de inconciencia (?)
- Un viaje entretenido: problemas de matemáticas en el metro.
- Un error geométrico en la Liga de Campeones.
- Una bandera áurea perdida en la historia.
- Una nueva prueba del teorema de Pitágoras.
- Un pequeño teorema de distanciamiento físico.
- Otro teorema de distanciamiento físico.
- Regalando cuadrados mágicos.
- El cuadrado mágico de Khajuraho es un hipercubo.
- La cuadratura del triángulo.
- Más matemáticas en un balón de fútbol.
- ¿Cómo multiplicar sin saber las tablas de multiplicación? (junto a J. Levrault)
- ¿Cómo multiplicar conociendo apenas la tabla del 2? (junto a J. Levrault)
- Presentaciones en actividades culturales como:
- Festival Puerto de Ideas de Antofagasta (2028).
- Feria del Libro de Guadalajara (2018).
- Inauguración del Museo de Ciencia de la UNAM (2020).
- Festival les Maths dans tous leurs états, Toulouse (2021).
- Festival de Matemáticas de Serbia (2021).


Premios y Distinciones

  •   Mathematical OCuncil of the Americas Prize

    Mathematical Council of the Americas

    México, 2013

    Five prizes have been awarded to mathematicians who have obtained their PhD. 12 years at the most, previous to the beginning of the Congress from an institution in the American continent, or they actually hold a position in one or more of its countries. These awardees have contributed with outstanding mathematical achievements in their early stages of their careers.

  •   William Hodge felowship

    Institut des Hautes Etudes Scietifiques

    Francia, 2004

    The William Hodge Fellowships offers one young researcher in mathematics or theoretical physics a postdoctoral position at IHÉS of one or two years.­ The fellowship, named after Sir William Hodge, the eminent British mathematician whose speciality was algebra and differentila geometry, was created in 2001­ in partnership with the E­ngineering and ­P­hys­ical Sciences Research Council (EPSRC)­. The EPSRC, based in London, has been supporting the Institut des Hautes Études Scientifiques for many years, in order to develop links between the British and French research institutions. It encourages British mathematicians and theoretical physicists to apply to IHÉS.­

  •   Chilean Math Olympiads

    Math Olympiads

    Chile, 1991

    Silver Medal

  •   Chilean Math Olympiads

    Math Olympiads

    Chile, 1992

    Silver Medal

  •   Math Olympiads Cono Sur

    Math Olympiads

    Chile, 1991

    Gold Medal

  •   Iberoamerican Math Olympiads

    Math Olympiads

    Chile, 1993

    Gold Medal

  •   Iberoamerican Math Olympiads

    Math Olympiads

    Chile, 1994

    Gold Medal

  •   Jorge Billeke award for undergraduate studies

    UNIVERSIDAD DE CHILE

    Chile, 1999

    Jorge Billeke award for undergraduate studies.

  •   Premio UMALCA

    Union Matemática de América Latina y El Caribe

    Colombia, 2016

    Premio por investigación científica en matemática otorgado a 4 matemáticos latinoamericanos des hasta 40 años entregado cada 4 años en el marco del Congreso UMALCA.

  •   Invited Speaker ICM

    International Mathematical Union

    Brasil, 2018

    Invitation to deserve a 45 minutes talk in the Special Session "Dynamical Systems and Ordinary Differential Equations" of the 2018 ICM (the most important conference in mathematics in the world.)

  •   Premio a la excelencia en vinculación con el medio

    UNIVERSIDAD DE SANTIAGO DE CHILE

    Chile, 2020

    Reconocimiento al trabajo de divulgación desarrollado desde la universidad.


 

Article (53)

Uniformly perfect finitely generated simple left orderable groups
Groups with infinitely many ends acting analytically on the circle
Group actions on 1-manifolds=> a list of very concrete questions
On the ergodic theory of free group actions by real-analytic circle diffeomorphisms
On the sharp regularity for arbitrary actions of nilpotent groups on the interval=> the case of N-4
WANDERING DOMAINS FOR DIFFEOMORPHISMS OF THE k-TORUS=> A REMARK ON A THEOREM BY NORTON AND SULLIVAN
Rigidity for C-1 actions on the interval arising from hyperbolicity I=> solvable groups
A remark concerning bi-Lipschitz equivalence of Delone sets
Open problems and conjectures related to the Theory of Mathematical Quasicrystals.
A geometric path from zero Lyapunov exponents to rotation cocycles
A geometric path from zero Lyapunov exponents to rotation cocycles
Algunas consideraciones geométricas sobre el diseño de la bandera de la Independencia de Chile.
Almost reduction and perturbation of matrix cocycles
Almost reduction and perturbation of matrix cocycles
Almost reduction and perturbation of matrix cocycles
On the reconciliation by cojugation in 1 dimension and classification C1
Sharp regularity for certain nilpotent group actions on the circle
Sharp regularity for certain nilpotent group actions on the interval
Sur les rapprochements par conjugaison en dimension 1 et classe
A Livsic type theorem for germs of analytic diffeomorphisms
A Livsic type theorem for germs of analytic diffeomorphisms
An L-1 ergodic theorem with values in a non-positively curved space via a canonical barycenter map
ON BOUNDED COCYCLES OF ISOMETRIES OVER MINIMAL DYNAMICS
ON CENTRALIZERS OF INTERVAL DIFFEOMORPHISMS IN CRITICAL (INTERMEDIATE) REGULARITY
On the invariant distributions of C-2 circle diffeomorphisms of irrational rotation number
SYMMETRIC RANDOM WALKS ON Homeo(+)(R)
On the dynamics of nonreducible cylindrical vortices
A remarkable family of left-ordered groups: Central extensions of Hecke groups
Nielsen-Thurston orders and the space of braid orderings
A finitely generated, locally indicable group with no faithful action by C-1 diffeomorphisms of the interval
Describing all bi-orderings on Thompson's group F
ON THE DYNAMICS OF (LEFT) ORDERABLE GROUPS
ON THE DYNAMICS OF (LEFT) ORDERABLE GROUPS
A new characterization of Conrad's property for group orderings, with applications
ON THE QUESTION OF ERGODICITY FOR MINIMAL GROUP ACTIONS ON THE CIRCLE
A continuous Bowen-Mane type phenomenon
A DENJOY TYPE THEOREM FOR COMMUTING CIRCLE DIFFEOMORPHISMS WITH DERIVATIVES HAVING DIFFERENT HOLDER DIFFERENTIABILITY CLASSES
Growth of groups and diffeomorphisms of the interval
Sur la dynamique unidimensionnelle en régularité intermédiaire
The unidimensional dynamic of intermediary regularity
On uniformly quasisymmetric groups of circle diffeomorphisms
Reduction of cocycles and groups of diffeomorphisms of the circle
Quelques nouveaux phénomènes de rang 1 pour les groupes de difféomorphismes du cercle
Several new grade 1 phenomena for circle diffeomorphism groups
Groupes résolubles de difféomorphisms de l'intervalle, du cercle et de la droite
On Schrodinger-Boussinesq equations
Quelques Groupes Moyennables de Difféomorphismes de L'intervalle
Sur les groupes de difféomorphismes du cercle engendrés par des éléments proches des rotations
Actions de groupes de Kazhdan sur le cercle
Groupes de Neretin et propriété (T) de Kazhdan
The further chameleon groups of Richard Thompson and Graham Higman=> Automorphisms via dynamics for the Higman groups Gn,r
On conjugates and the asymptotic distortion of 1-dimensional C1+bv diffeomorphisms
Three results on cocycles of Banach space isometries over a minimal dynamics .

Proyecto (15)

Groups of homeomorphisms of manifolds
Fortalecimiento institucional del Festival de Matemáticas
"GDAR=> geometry, dynamics, and Anosov representations".
Anillo "Geometría en La Frontera"
Geometry and dynamics of groups and spaces
Redes internacionales de investigación
Anillo “Center of Dynamical Systems and Related Fields”
Fondecyt No. 1120131
Fondecyt No. 1100536
MathAmsud DySet
Anillo “Low Dimensional Dynamics”
Fondecyt Regular No. 1060829
Prosul "Dynamical Systems"
Proyecto de Reinserción Andrés Navas
Iniciación a la Investigación
41
Andres Navas

Full time Professor

Mathematics

DPTO DE MATEMATICA Y CC, USACH

Santiago, Chile

3
Mario Ponce

Dean

Mathematics

Pontificia Universidad Católica de Chile

Santiago, Chile

2
Alvaro Coronel

Associate professor

Mathematics

Pontificia Universidad Católica de Chile

Santiago, Chile

2
Jairo Bochi

Associate professor

Mathematics

PUC-Chile

Santiago, Chile

2
Cristóbal Rivas

Profesor Asistente

Matemáticas y Ciencias de la Computación

Universidad de Santiago de Chile

Santiago, Chile

1
Carlos Vásquez

Full Professor

Pontificia Universidad Católica de Valparaiso

Valparaiso, Chile