Academic curriculum

I was born in Barcelona on January the 31st, 1977. I got my degree in mathematics by the Universitat de Barcelona on June 1999 and the same year I began to work on my PhD in Applied Mathematics at the same University and under the supervision of Prof. Dr. Carles Simó.

 From January 2000 I am at the departament de Matemàtica Aplicada i Anàlisi de la Universitat de Barcelona  . I had a PhD. grant from the Generalitat de Catalunya (Catalonia autonomous government) until September 2003. In October 2003 I became assistant professor at the same department.

After defending my thesis at the University of Barcelona, I entered the the Departament de Matemàtica Aplicada I of the Universitat Politècnica de Catalunya where I teach and belong to the  UPC Dynamical Systems Group.

My field of study are Dynamical Systems and S
ectral Theory of Schrödinger Operators.

Address

Joaquim Puig i Sadurní
Departament de Matemàtica Aplicada I
Universitat Politècnica de Catalunya
Diagonal 647
08028 Barcelona
Catalonia-Spain
Phone: +34 934054257
Fax: +34 934011713
E-mail: joaquim.puig[a-sign]upc.edu
Web: http://www.ma1.upc.edu/~jpuig

Preprints and Publications

Publications

• Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation
  Henk Broer, Joaquim Puig and Carles Simó
  Comm. Math. Phys. Vol. 241, Num. 2-3. Pag.: 467 - 503. [PDF]
  Preprint version: Abstract (ASCII file), PostScript (432 Kb), gzipped version (142 Kb).
• Cantor Spectrum for the Almost Mathieu Operator.
  Joaquim Puig 
  Comm. Math. Phys. Vol. 244, Num. 2 Pag.: 297 - 309. [PDF]
  Preprint version: Abstract (ASCII file), PostScript (355 Kb), gzipped version (116 Kb).
• The spectrum of Schrödinger operators with quasi-periodic potential: a dynamical approach
  Joaquim Puig and Carles Simó
  Proceedings of Equadiff 2003. [PDF]
  Preprint version: Abstract (ASCII file), PostScript (247 Kb), gzipped version (120 Kb).
• Reducibility of Quasi-Periodic Skew-Products and the Spectrum of Schrödinger Operators (PhD Thesis)
  Joaquim Puig
  Abstract (ASCII file), Gzipped PostScript (608 Kb), Erratum (PDF) (21 Kb).
• Analytic families of reducible linear quasi-periodic differential equations
  Joaquim Puig and Carles Simó
  Ergodic Theory and Dynamical Systems, Volume 26 Issue 02 (2006) pp 481-524. [PDF]
  Preprint version: Abstract (ASCII file), PDF (816 Kb), Postscript gzipped version (378 Kb).
• Cantor Spectrum for quasi-periodic Schrödinger Operators
  Joaquim Puig
  Mathematical Physics of Quantum Mechanics. Springer Lecture Notes in Physics, Vol. 690 pp (2006). Asch, Joachim; Joye, Alain (Eds.). ISBN: 3-540-31026-6.
  Preprint version: Abstract (ASCII file), PostScript (619 Kb), gzipped version (166 Kb)
• A solution of the Ten Martini Problem .
  Joaquim Puig .
  Newsletter of the European Mathematical Society. September 2005, Issue 57.
• El Problema dels Deu Martinis. Un aperitiu (Catalan)
  Joaquim Puig
  Butlletí digital de la FME, curs Einstein (2004-2005). ISBN 84-7653-882-0
  Preprint version: Abstract (ASCII file), PDF (1.8 Mb)
• A nonperturbative Eliasson's reducibility theorem
  Joaquim Puig
  Nonlinearity 19 (2006) 355-376. [PDF]
  Preprint version: Abstract (ASCII file), PDF (254 Kb)
• Nonperturbative Reducibility and Irreducibility
  Joaquim Puig
  Oberwolfach Reports, Volume 2, Issue 4, 2005 pp
  Preprint version: PDF (103 Kb)
• Resultados no perturbativos en dinámica cuasiperiódica lineal (Spanish)
  Joaquim Puig
  Boletín de la Sociedad Española de Matemática Aplicada. Número 34, marzo 2006, pp 118-123.
  Preprint version: Abstract (ASCII file), PDF (230 Kb)
• Cantor Spectrum and KDS Eigenstates
  Joaquim Puig
  Comm. Math. Phys. Vol. 267, Num. 3 Pag.:  735 - 740. [PDF]
  Preprint version: Abstract (ASCII file), PDF (77 Kb)
• Strange Nonchaotic Attractors in Harper Maps
  Àlex Haro and Joaquim Puig
  Chaos 16, 033127 (2006) (7 pages). [PDF]
  Preprint version: Abstract (ASCII file), PDF (865 Kb)
• Nonlinear evolution equations and dynamical systems 2007 (NEEDS proceedings)
David Gómez-Ullate, Andrew Hone, Sara Lombardo and Joaquim Puig (editors)
J. Nonlinear Math. Phys.  15  (2008),  suppl. 3.
• Resonance tongues and Spectral gaps in Quasi-Periodic Schrödinger operators with one or more frequencies. A numerical exploration
  Joaquim Puig and Carles Simó
  To appear in J. Dynam. Differential Equations. (2010) (22 pages)
  Preprint version: Abstract (ASCII file), PDF (4.1Mb), Gzipped PS (1.2Mb).
• Resonance tongues in the Quasi-Periodic Hill-Schr\"odinger Equation with three frequencies
  Joaquim Puig and Carles Simó
  To appear in Regul. Chaotic Dyn. (2010) (21 pages)
  Preprint version: Abstract (ASCII file), PDF (2.9Mb), Gzipped PS (0.8Mb).

Preprints

You can also have a look at the following survey on the reducibility of linear equations with quasi-periodic coefficients

• Reducibility of linear differential equations with quasi-periodic coefficients: a survey
  Joaquim Puig
  Abstract (ASCII file), PS (1604 Kb). Gzipped PS (478 Kb).

Presentations

Here you will find a selection of slides of presentations in seminars and congresses. Please note that these have not been revised and they may have misprints.

• The Ten Martini Problem (166Kb), AMS Joint Mathematics Meeting. Phoenix (USA) 7-01-2004.
• The Ten Martini Problem (The Proof) (98Kb), Caltech Mathematical Physics Seminar Caltech, Pasadena (USA) 21-01-2004.
• Reducibility of Quasi-Periodic Skew-Products and the Spectrum of Schrödinger Operators (PhD) (495Kb), Universitat de Barcelona Barcelona 22-06-2004.
• Cantor Spectrum for Quasi-Periodic Schrödinger Operators (262Kb), QMath9. Giens (France) 12-09-2004.
• Reducibility of Quasi-Periodic Skew-Products and the Spectrum of Schrödinger Operators (497Kb), Nonlinear Dynamics, Ergodic Theory and Renormalization Leiden (Netherlands) 20-09-2004.
• El Problema de los 10 Martinis (1.3Mb), Primer Congrés Conjunt de Matemàtiques RSME-SCM-SEIO-SEMA València 4-02-2005.
• El problema dels 10 Martinis(1.3Mb). Conferència a la Facultat de Matemàtiques i Estadística de la UPC. Barcelona, 9 de març de 2005.
• Nonperturbative Reducibility and Irreducibility(85Kb). Talk at the Workshop Dynamics of Cocycles and One-Dimensional Spectral Theory. Oberwolfach (Germany), November 13th 2005.
• Strange Nonchaotic Attractors in Harper maps(1.1Mb). Talk at the Workshop Workshop on Strange Nonchaotic Attractors. Barcelona, March 27th 2006.

Events

Some of the events in which I have taken part as an organizer:

• Carles Simó Fest. S'agaró (Catalonia), May 29th - June 3rd 2006. 
• NEEDS 2007: School + Workshop. L'Ametlla de Mar (Catalonia), June 15th - 24th 2007.
• SAGE Days 16. FME (UPC), Barcelona, June 22nd -27th 2009.

Some Links...

• UPC Dynamical Systems Group.
• Joan Puig Reixach. Paintings and Drawings
• GMB Soluciones contra incendios: Detectores de humos, alarmas, pulsadores, sirenas y centrales de incendio.
• El Molino de Alcóntar: Casa de turismo rural en Alcóntar, provincia de Almería. Antiguo molino rehabilitado para turismo rural en plena sierra de los Filabres

...We are such stuff
As dreams are made on, and our little life
Is rounded with a sleep...

W. Shakespeare: The Tempest.