Marta Canadell home page

 

Marta Canadell


ICERM Postdoctoral Institute Fellow
at ICERM, Brown University


 

 

I am originally from Barcelona, Catalunya. I did my degree in Mathematics and a Masters in Advanced and Professional Mathematics at the Universitat de Barcelona. I earned my PhD degree in Mathematics at the Universitat de Barcelona in July 2014. My PhD thesis was developed under the direction of Professor Àlex Haro, with the title Computation of Normally Hyperbolic Invariant Manifolds.

 

During the 2014-2015 year, I was a Visiting Assistant Professor at the School of Mathematics at Georgia Institute of Technology, where I was working with Professor Rafael de la Llave. Currently, I am an ICERM Postdoc Institute Fellow at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, where I will participate in the ICERM Semester Program on Dimension and Dynamics during the Spring 2016.

 

Research Interests

My research is in the computational and rigorous aspects of Dynamical Systems.

More specifically, I am developing a broadly based approach that encompasses both computation and rigorous theory of invariant objects. In particular, normally hyperbolic invariant manifolds (NHIM).

I also implement our methodologies to explore different mechanisms of breakdown of these invariant objects.

 

Apart from the interest of NHIM in mathematical problems, such as Arnold diffusion, it is known that NHIM are ubiquitous in problems of Physics, Chemistry, Biology, Economics, etc. Due to this fact, we are confident that the tools we already developed make it possible to study some specific applied problems.

 

Recently, I also started to work on non-autonomous dynamical systems, by proving the existence and giving properties of non-autonomous analogies of rotational tori (also called non-autonomous KAM tori).

 

Normally hyperbolic invariant cylinder

 

 

CV Research Statements

Publications

 

Preprints

  • Marta Canadell, Alex Haro. Computation of quasi-periodic normally hyperbolic invariant tori: algorithms, numerical explorations and mechanisms of breakdown (2016, submitted). PDF FILE
  • Marta Canadell, Alex Haro. Computation of quasi-periodic normally hyperbolic invariant tori: rigorous results (2016, submitted). PDF FILE

 

Others

  • Marta Canadell. Computation of normally hyperbolic invariant manifolds. PhD thesis, Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, July 2014. Thesis advisor: Alex Haro. LINK

Here you can find some selected talks and posters that I presented in different seminars and conferences.

  • A KAM-like theorem for quasi-periodic normally hyperbolic invariant tori leading to efficient algorithms Dynamical Systems Seminar, Boston, USA (March 2015). Seminar
  • Parameterization methods for computing normally hyperbolic invariant manifolds, AIMS 2014, Madrid, Spain (July 2014). Talk
  • Parameterization methods for computing normally hyperbolic invariant tori, Workshop IMA, Minneapolis, USA (February 2014). Poster
  • Parameterization method for computing normally hyperbolic invariant tori and its internal dynamics, 2CJI, Sevilla, Spain (September 2013). Talk
  • Parameterization method for computing quasi-periodic normally hyperbolic invariant tori, CEDYA 2013, Castellón, Spain (September 2013). Talk
  • Fast Computational Methods for Whiskered Tori and their Invariant Manifolds, JISD 2013, Barcelona, Catalunya (July 2013). Talk
  • Parameterization method for computing normally hyperbolic invariant tori and its internal dynamics, SIAM DS 2013, Utah, USA (May 2013). Talk
  • Parameterization method for computing normally hyperbolic invariant tori, First International Conference on Dynamics of Differential Equations, Atlanta, USA (March 2013). Invited talk

Material of some short courses

  • XV Jornada Didàctica Matemàtica d'ABEAM: Simulació de missions espacials amb Celestia: (in Catalan)

Teaching

  • Instructor of Math 2403 - Differential Equations, Spring 2015, Georgia Institute of Technology. Course website
  • Instructor of Math 2403 - Differential Equations, Fall 2014, Georgia Institute of Technology. Course website
  • Teaching Assistant of Scientific Programming, Spring 2014, Universitat de Barcelona.
  • Teaching Assistant of Ordinary Differential Equations, Spring 2014, Universitat de Barcelona.
  • Teaching Assistant of Introduction to Differentiable Calculus (Calculus I), Fall 2013, Universitat de Barcelona.
  • Teaching Assistant of Differentiable Calculus in several variables (Calculus III), Fall 2013, Universitat de Barcelona.