Curriculum Vitae
Jos´
e Antonio Vallejo Rodr´ıguez
Date: May 21 2013
Areas of specialization (MSC 2010)
53 Differential geometry (C80 global differential geometry: appli-cations to physics; D17 Poisson manifolds; Poisson groupoids and algebroids).
58 Global analysis, analysis on manifolds (C50 analysis on super-manifolds or graded super-manifolds; D17 Manifolds of metrics (esp. Rie-mannian); E11 Critical metrics).
81 Quantum theory (S10 geometry and quantization, symplectic methods).
Contents
Education 1
Teaching experience 2
Popular science talks and workshops 4
Research 4
Talks at scientific meetings 8
Academic advising 10
Grants and research projects 11
Curriculum Vitae
Jos´
e Antonio Vallejo Rodr´ıguez
Date: May 21 2013
Profesor Investigador Nivel VI Facultad de Ciencias UASLP Lat. Av. Salvador Nava s/n
78290 San Luis Potos´ı (SLP) M´exico Phone: +52 (444) 8262486 (ext. 2926) Email: [email protected] URL:http://galia.fc.uaslp.mx/~jvallejo
Fellow of the National Researchers System (SNI), level II
Education
1998 BSc in Physics, University of Valencia (Spain). 1998 BSc in Mathematics, University of Valencia (Spain). 2001 MSc in Mathematics, University of Valencia (Spain).
MSc Thesis: Critical points of functionals on spaces of map-pings between manifolds. Application to the Einstein equa-tions as a dynamical system.
Advisor: Dr. Olga Gil-Medrano.
2003 PhD in Mathematics, University of Valencia (Spain). Tesis: Geometric structures on supermanifolds. Applications to Physics. (Awarded Summa cum laude).
Advisor: Dr. Juan Monterde. PhD committee:
Dr. Jos´e Adolfo de Azc´arraga (University of Valencia-Spanish National Research Council), President.
Dra. Yvette Kosmann-Schwarzbach ( ´Ecole Polytechnique-Centre de Math´ematiques Laurent Schwartz, France). Dr. Angel Montesinos Amilibia (University of Valencia),´ Secretary.
Dr. Jaime Mu˜noz Masqu´e (Institute of Physics-Spanish Na-tional Research Council).
Dr. Adolfo S´anchez Valenzuela (Centro de Investigaci´on en Matem´aticas CIMAT A.C., Mexico).
Teaching experience
Courses at universities
Credit numbers between brackets (1 credit=10 hours). 2001–02 Universidad de Valencia (Spain):
Topology I (4.5),
Mathematics for Natural Sciences (1.5).
2003–04 Universidad Aut´onoma de San Luis Potos´ı (Mexico): Multivariate Calculus III (12),
Group Theory (12),
Introduction to Groups and Rings (12), Selected topics in Differential Geometry (12). 2004–05 Universidad Polit´ecnica de Catalu˜na (Spain): Mathematics for Engineering Sciences I (9), Probability and Statistics (6).
2005–06 Universidad Polit´ecnica de Catalu˜na (Espa˜na): Mathematics for Engineering Sciences I (9), Probability and Statistics (6).
2006–07 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Mathematical Analysis II (12),
Topology I (12), Linear Algebra (12),
Selected topics in Topology (12).
2007–08 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Mathematical Analysis I (12),
Complex Analysis I (12),
Geometric theory of Differential Equations (Postgraduate course, 12).
Methods of Probability and Statistics (Postgraduate course, 12).
Mathematical Analysis II (12), Algebraic Structures (12).
2008–09 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Mathematical Analysis I (12),
Multivariate Calculus III (12),
Methods in the theory of Differential Equations (Postgradu-ate course, 12).
Topology Seminar (12),
2009–10 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Calculus in one variable I (12),
Calculus in one variable II (12), Multivariate Calculus III (12),
Methods in the theory of Differential Equations (Postgradu-ate course, 12).
Non-Euclidean Geometry (12).
2010–11 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Differential Calculus in one variable (12),
Complements of Differential Calculus (12), Selected topics in Differential Geometry (12), Topology (Postgraduate course, 12),
Thesis Seminar (12),
Physical Chemistry I (BSc in Physics, 12).
2011–12 Universidad Aut´onoma de San Luis Potos´ı (M´exico): Differential Calculus in several variables (12), Theoretical Physics I (12),
Integral Calculus in several variables (12), Field theory (12).
2012–13 Universidad de Sonora (M´exico):
Differential Geometry I (Postgraduate course, 12), Research Seminar (Postgraduate course, 12) Differential Geometry II (Postgraduate course, 12), Research Seminar (Postgraduate course, 12) Refresher courses
For students of science, elementary and high-school teachers.
2008 Workshop: Uso de software en la ense˜nanza de las matem´ ati-cas (Using software to teach maths). Instituto Tecnol´ogico de Matehuala (SLP), 29-30 de Agosto.
2009 Workshop: Ecuaciones diferenciales y sistemas din´amicos con Maxima (ODEs and dynamical systems with Maxima CAS). Universidad del Papaloapan (Oax), 30 Noviembre-4 Diciembre.
2011 Course: Geometr´ıa local de EDO (Local geometry of ODEs). XXI Semana de Investigaci´on y Docencia en Matem´aticas. Universidad de Sonora (Son).
2012 Course: Sistemas din´amicos con software libre (Dynamical systems with free software). XXII Semana de Investigaci´on y Docencia en Matem´aticas. Universidad de Sonora (Son).
2012 Workshop: Matem´aticas con Maxima (Maths with Maxima CAS). Congreso Nacional Acad´emico 2012. Direcci´on Gen-eral de Educaci´on Superior Tecnol´ogica-SEP.
Instituto Tecnol´ogico de Matehuala (SLP), 24 de Mayo.
Popular science talks and workshops
For high-school alumni, and people without scientific knowledge.
2009 Workshop: Matem´aticas y criptograf´ıa (Maths and cryptog-raphy). III Semana de las Matem´aticas.
Colegio de estudios cient´ıficos y tecnol´ogicos del estado de San Luis Potos´ı (CECyTE-SLP), 3 al 6 de Noviembre. 2010 Workshop: Matem´aticas e Inform´atica (Maths and
comput-ers). IV Semana de las Matem´aticas.
Colegio de estudios cient´ıficos y tecnol´ogicos del estado de San Luis Potos´ı (CECyTE-SLP), 9 al 11 de Noviembre. 2010 Workshop: Taller de M´axima (Using Maxima CAS). V
Se-mana de las Matem´aticas.
Colegio de estudios cient´ıficos y tecnol´ogicos del estado de San Luis Potos´ı (CECyTE-SLP), 8 al 10 de Noviembre. 2012 Pl´atica: Lo que no pensaste que se pod´ıa hacer con las Matem´
ati-cas (Things you never thought could be done with maths). Semana de introducci´on a la licenciatura en Matem´aticas. Universidad de Sonora (Son), 7 Septiembre.
2006–now Several popular talks for students of the Colegio de Bachilleres de San Luis Potos´ı (COBACH, the high-school system of the state of San Luis) and the system of Centros de Estudios Tec-nol´ogicos y Cient´ıficos (high-school technical studies) of the state of San Luis (CECyTE)
Research
Published papers
2001 Nambu-Poisson manifolds and associated n-ary Lie algebroids. Jos´e A. Vallejo.
Journal of Physics A: Mathematics and General 34 (2001) 2867 − 2881.
2002 Poisson brackets of even symplectic forms on the algebra of differential forms.
Juan Monterde, Jos´e A. Vallejo.
Annals of Global Analysis and Geometry 22 (2002) 267−289. 2002 Modular class of even symplectic manifolds.
Juan Monterde, Jos´e A. Vallejo.
Theoretical and Mathematical Physics 132, n1 (2002) 934 − 941.
2003 The symplectic structure of Euler-Lagrange Superequations and Batalin-Vilkoviski formalism.
Juan Monterde, Jos´e A. Vallejo.
Journal of Physics A: Mathematics and General 36 (2003) 4993 − 5009.
2004 Generating operators of the Krasil’shchick-Schouten bracket. Jos´e A. Vallejo.
Letters in Mathematical Physics 68 (2004) 1 − 17.
2006 Composition operators on weighted spaces of holomorphic functions on J B∗−triples.
Michael Mackey, Pablo Sevilla-Peris, Jos´e A. Vallejo. Letters in Mathematical Physics 76 (2006) 19 − 26. 2006 The Poincar´e-Cartan form in superfield theories.
Juan Monterde, Jaime Mu˜noz Masqu´e, Jos´e A. Vallejo. International Journal of Geometric Methods in Modern Physics 3 (4) June 2006, 775 − 823.
2006 Calculus of variations and field theory on graded fiber bun-dles.
Juan Monterde, Jaime Mu˜noz Masqu´e, Jos´e A. Vallejo. Publicaciones de la Real Sociedad Matem´atica Espa˜nola vol. X, 218 − 224.
2009 The structure of Fedosov supermanifolds.
Juan Monterde, Jaime Mu˜noz Masqu´e, Jos´e A. Vallejo. Journal of Geometry and Physics 59 (2009) 540 − 553. 2009 Supersymmetric sigma models and harmonic superfunctions.
Jaime Mu˜noz Masqu´e, Jos´e A. Vallejo.
International Journal of Geometric Methods in Modern Physics 6 (2009) no. 5, 839-849.
2009 Harmonicity in supermanifolds and sigma models. Jaime Mu˜noz Masqu´e, Jos´e A. Vallejo.
Proceedings of the American Insitute of Physics. Vol. 1130 Geometry and Physics (2009) 171 − 175.
2009 The meaning of time and covariant superderivatives in su-permechanics.
Gil Salgado, Jos´e A. Vallejo.
Advances in Mathematical Physics. Vol. 2009, Article ID 987524, 21 pages, 2009. doi:10.1155/2009/987524.
2009 Euler-Lagrange equations for functionals defined on Fr´echet manifolds.
Jos´e A. Vallejo.
Journal of Nonlinear Mathematical Physics. Vol. 16 4 (2009) 443-454.
2010 Introducci´on a la supersimetr´ıa (Introduction to supersym-metry, in Spanish).
Jos´e A. Vallejo.
Matem`atiques 5 (2010) no. 1, 3-57.
2011 Software libre para el estudio de sistemas din´amicos (Free software for the study of dynamical systems, in Spanish). Antonio Morante, Jos´e A. Vallejo.
La Gaceta de la Real Sociedad Matem´atica Espa˜nola, Vol. 14 (2011), N. 1, Pp. 111-132.
2011 An approach to omni-Lie algebroids using quasi-derivations. Dennise Garc´ıa-Beltr´an, Jos´e A. Vallejo.
International Journal of Generalized Lie Theory and Appli-cations. Vol. 5 (2011), Article ID G100801.
doi:10.4303/jglta/G100801.
2011 Modelling the landing of a plane in a calculus lab. Antonio Morante, Jos´e A. Vallejo.
International Journal of Mathematical Education in Science and Technology. DOI:10.1080/0020739X.2011.633626 (2011). 2012 On Lie algebroids and Poisson algebras.
Dennise Garc´ıa-Beltr´an, Jos´e A. Vallejo, Yuri˘ı Vorobjev. Symmetry, Integrability, Geometric Methods and Applica-tions. Vol 8 6 (2012) 1-14.
2012 Symplectic connections and Fedosov quantization on super-manifolds.
Jos´e A. Vallejo.
Journal of Physics: Conference Series 343 (2012) 012124. 2012 Implementing the RSA cryptosystem with Maxima CAS.
Juan Monterde, Jos´e A. Vallejo.
Electronic Journal of Mathematics and Technology 6 1 (2012) 1-20. Printed version reproduced in Research Journal of Mathematics & Technology 1 n.1 (2012) 28-48.
2012 The Principle of Stationary Action in the Calculus of Vari-ations.
Emanuel L´opez-Cerd´a, Alberto Molgado, Jos´e A. Vallejo. Communications in Mathematics 20 2 (2012) 89-116. Available athttp://cm.osu.cz/20-2.
2013 Chaotic dynamics with Maxima. A. Morante, Jos´e A. Vallejo.
To appear: Electronic Journal of Mathematics and Technol-ogy.
Preprint available athttp://arxiv.org/abs/1301.3240. Books
2003 Title: Geometric structures on supermanifolds. Applications to Physics.
Publicaciones de la Universidad de Valencia. Pages: 122.
ISBN: 84 − 370 − 5722 − 1WorldCat registry
Preprints
2013 Quillen superconnections and connections on supermanifolds. Jos´e V. Beltr´an, J. Monterde, Jos´e A. Vallejo.
Preprint available athttp://arxiv.org/abs/1305.3677. 2013 A simple global representation for second-order normal forms
of Hamiltonian systems relative to periodic flows. M. Avenda˜no-Camacho, J. A. Vallejo and Yu. Vorobjev. Preprint available athttp://arxiv.org/abs/1301.3244. 2013 Higher order corrections to adiabatic invariants of
general-ized slow-fast Hamiltonian systems.
M. Avenda˜no-Camacho, J. A. Vallejo and Yu. Vorobjev. Preprint available athttp://arxiv.org/abs/1305.3974. Software development
2012 Software: Topotitlan.
Scientific software. Coauthor: Valdemar Emigdio Arce Gue-vara. Available under AFL (Academic Free License) at Source-Forge.
Talks at scientific meetings
2001 Even Poisson brackets on supermanifolds.
V Joint Meeting Sociedad Matem´atica Mexicana - American Mathematical Society.
Morelia (Mich), Mexico.
2003 The Poincar´e-Cartan form in superfields theory.
XXXVI Congreso de la Sociedad Matem´atica Mexicana. Pachuca (Hgo), Mexico.
2004 Jet bundle formalism for variational problems on superman-ifolds.
VI Joint Meeting Sociedad Matem´atica Mexicana - Ameri-can Mathematical Society.
Houston (TX), USA.
2005 Calculus of variations and field theory on graded fiber bun-dles.
XIV Fall Workshop on Geometry and Physics. Bilbao, Spain.
2006 (Riemann, Finsler and) Metric geometries.
I International Workshop on semi-Riemannian and Finsler geometry.
UASLP, San Luis Potos´ı, Mexico.
2006 Global Calculus of Variations on Spaces of Mappings. II Catalan-Czech Conference in Mathematics. Barcelona, Spain.
2008 Harmonicity in supermanifolds and sigma models.
XVII International Fall Workshop on Geometry and Physics. Santander, Spain.
2008 Funciones arm´onicas y modelos sigma en supervariedades. XLI Congreso de la Sociedad Matem´atica Mexicana. Valle de Bravo (Edo. Mex.), Mexico.
2009 Geogebra y Maxima (una alternativa en cursos de matem´ ati-cas).
I Congreso Internacional sobre la ense˜nanza de las Matem´ ati-cas.
Cuautitl´an Izcalli (Edo. Mex.), Mexico.
2010 On some generalizations of the notion of Lie algebra. Joint Mathematical Conference CSASC 2010. Prague, Czech Republic.
2011 Universal spaces for Lie and Loday algebras.
IX International Workshop Applied Category Theory Graph-Operad-Logic.
San Antonio (TX), USA.
2011 Fedosov quantization on supermanifolds. Quantum Theory and Symmetries VII. Prague, Czech Republic.
2011 Lie algebroids of Poisson type.
Joint Mathematical Conference CSASC 2011. Krems, ¨Osterreich.
2012 Conexiones de Connes, conexiones de Quillen y superconex-iones.
II Reuni´on Conjunta RSME-SMM. M´alaga, Spain.
2012 Sistemas Din´amicos con software libre. XLV Congreso Nacional de la SMM. Quer´etaro, Mexico.
Organization of scientific meetings
2005 Organizing committee and session chairman: Session “Al-gebra, Geometry and Physics”. First Joint Meeting of the Spanish Mathematical Associations.
Valencia (Spain), January 31- February 5.
URL:http://www.uv.es/mat.es2005/sessionsc.shtml
2005 Organizing committee: III International Meeting on Lorentzian Geometry.
Castelldefels (Spain), November 21 − 23.
URL:http://galia.fc.uaslp.mx/~jvallejo/Lorentz2005. 2009 Organizing committee: I Escuela conjunta de Matem´aticas
UVEG-UASLP.
San Luis Potos´ı (M´exico), Junio-Julio.
2009 Coordinator of the Session “Mathematical Physics”: I Joint Meeting RSME-SMM.
Oaxaca (M´exico), 22-24 Julio.
URL:http://www.smm.org.mx/smm-rsme/coordinadores. 2010 Organizing committee: II Escuela conjunta de Matem´aticas
UVEG-UASLP.
2011 Organizing committee: II Taller de Geometr´ıa y Sistemas Din´amicos.
San Carlos Guaymas (Sonora), 3-5 Marzo.
2011 Organizing committee: III Escuela conjunta de Matem´aticas UVEG-UASLP.
San Luis Potos´ı (M´exico), 27 Junio-8 Julio.
URL:http://galia.fc.uaslp.mx/escuelaverano. 2011 Organizing committee: XLIV Congreso Nacional de la
So-ciedad Matem´atica Mexicana (Local Committee coordina-tor).
San Luis Potos´ı (M´exico), 9-14 Octubre. URL:http://smm.org.mx/slp2011/node/3.
2011 Coordinator of the Posters Session: XLIV Congreso Na-cional de la Sociedad Matem´atica Mexicana.
San Luis Potos´ı (M´exico), 9-14 Octubre. URL:http://smm.org.mx/slp2011.
2012 Organizing committee: IV Escuela conjunta de Matem´aticas UVEG-UASLP.
San Luis Potos´ı (M´exico), 2-13 Julio.
URL:http://galia.fc.uaslp.mx/escuelaverano. 2012 Organizing committee: VIII Encuentro Nacional de Biolog´ıa
Matem´atica y XIV Escuela de Oto˜no de Biolog´ıa Matem´atica. San Luis Potos´ı (M´exico), 15-19 Octubre.
URL:http://www.eobm.mx.
Academic advising
Postgraduate students (USA-grads)
2009 Sergio Tirado Torres: Algebroides de Lie y supervariedades. MSc Thesis. Facultad de Ciencias UASLP.
2011 Dennise Garc´ıa Beltr´an: Lie algebroids of Poisson type (coad-visor: Yu. Vorobjev). MSc Thesis. Facultad de Ciencias UASLP.
2012 Valdemar Arce Guevara: Topotitlan: Un software para la visualizaci´on de m´etricas en R2. MSc Thesis. Facultad de
Graduate students (USA-undergrads)
2009 Jonathan Rivera: Dimensi´on topol´ogica y geometr´ıa fractal. BSc Thesis. Facultad de Ciencias UASLP.
2009 Denisse Garc´ıa Beltr´an: Estructuras algebraicas relacionadas con algebroides de Loday.
BSc Thesis. Facultad de Ciencias UASLP.
This thesis was awarded the Sotero Prieto 2010 prize to the best BSc thesis in Mathematics in Mexico, by the So-ciedad Matem´atica Mexicana (Mexican Mathematical Soci-ety).
2012 Emanuel L´opez-Cerd´a: El principio de acci´on estacionaria en el c´alculo de variaciones.
BSc Thesis. Facultad de Ciencias UASLP.
Grants and research projects
1998–01 Research project. Spanish Ministerio de Ciencia y Tecnolog´ıa, from 10/01/98 to 09/30/01.
Code: PB97-1386 Geometr´ıa de estructuras graduadas. Main researcher: Dr. Juan Monterde.
2003–05 Research Project. Mexican Secretar´ıa de Educaci´on P´ublica, SEP-PROMEP, from 12/01/03 to 11/31/05.
Code: Estructuras Geom´etricas en F´ısica Matem´atica. Main researcher: Dr. Jos´e A. Vallejo.
2005 Research grant. Generalitat de Catalunya DURSI (Spain), from 06/23/05 to 09/07/05.
Code: Sistemas bihamilonianos en super´algebras de Lie. 2005–08 Research project. Spanish Ministerio de Educaci´on y
Cien-cia, from 11/01/05 to 10/31/08.
Code: MTM2005-04947 Geometry and control: applications in Physics and Technology.
Main researcher: Dr. Narciso Rom´an-Roy.
2008–11 Research project. Mexican Consejo Nacional de Ciencia y Tecnologa (CONACyT).
Ciencia B´asica 2007-01, mode “J2, J´ovenes investigadores”. Code: CB-78791 Estructuras algebraicas y geom´etricas de inter´es en F´ısica. From 01/01/2009 hasta 12/31/2011. Main researcher: Dr. Jos´e A. Vallejo.
This project was selected as a successful project at the 2012 CONACyT Congreso Nacional de Investigaci´on Cien-t´ıfica B´asica.
2009–10 International Cooperation Project. Funded by the Spanish Agencia Espa˜nola de Cooperaci´on Internacional para el De-sarrollo (AECID), program “Cooperaci´on Interuniversitaria e Investigaci´on Cient´ıfica entre Espa˜na e Iberoam´erica”. From 01/01/2009 to 12/31/2009.
Main researchers: Drs. Juan Monterde y Jos´e A. Vallejo. 2012 Proyecto de investigaci´on. Mexican Consejo Nacional de
Ciencia y Tecnologa (CONACyT). Ciencia B´asica 2012-01, mode “Profesor Investigador (continuaci´on)”. Code: CB-179115 Estructuras algebraicas y geom´etricas de inter´es en F´ısica II.
Main researcher: Dr. Jos´e A. Vallejo.
Service
2013–now Member of the Editorial Board of the Electronic Journal of Mathematics and Technology (starting June 2013).
2001–now Referee for the journals:
• Bolet´ın de la Sociedad Matem´atica Mexicana • Journal of Physics A: Mathematical and Theoretical • International Journal of Theoretical Physics
• International Journal of Mathematics and Mathemati-cal Sciences
• Acta Sinica Mathematica
• Balkan Journal of Geometry and its Applications • International Journal of Computer Mathematics • Journal of Mathematical Physics.
• Journal of Geometric Mechanics.
• Discrete and Continuous Dynamical Systems - Series A 2005–now Mathematical Reviews (MathSciNet) reviewer. Reviewer
Number: 039143.
2007 External Referee. XII Convocatoria del Programa de Apoyo a Proyectos de Investigaci´on ( ´Area Ciencias de la ingenier´ıa y tecnolog´ıa). Universidad Aut´onoma de Baja California. 2007 External Referee. Convocatoria 2007 del Programa Nacional
de Posgrados de Calidad. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2008 External Referee. Convocatoria 2007 de Proyectos de Inves-tigaci´on Cient´ıfica B´asica. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2008 External Referee. Convocatoria 2008-2009 del Programa In-tegral de Fortalecimiento Institucional (PIFI). Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2008 External Referee. Convocatoria 2008 del Programa de Fon-dos Mixtos (FOMIX). Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2008 External Referee. Proceso de evaluaci´on de r´eplicas del Pro-grama Nacional de Posgrados de Calidad. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Edu-caci´on P´ublica (SEP), M´exico.
2008 External Referee. XIII Convocatoria del Programa de Apoyo a Proyectos de Investigaci´on (modalidad Cuerpos Acad´ emi-cos). Universidad Aut´onoma de Baja California.
2009 External Referee. Convocatoria 2009 del Programa Nacional de Posgrados de Calidad. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2010 External Referee. Editorial de la Universidad Aut´onoma de Yucat´an (Mexico). Direcci´on general de desarrollo acad´emico. 2010 External Referee. Convocatoria 2010-2012 del Programa
In-tegral de Fortalecimiento Institucional (PIFI). Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2010 External Referee. Convocatoria 2010 de Proyectos de Inves-tigaci´on Cient´ıfica B´asica. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2012 External Referee. XVI Convocatoria del Programa de Apoyo a Proyectos de Investigaci´on ( ´Area Ciencias de la ingenier´ıa y tecnolog´ıa). Universidad Aut´onoma de Baja California. 2012 External Referee. Convocatoria 2012-2013 del Programa
In-tegral de Fortalecimiento Institucional (PIFI). Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2012 External Referee. Convocatoria 2012 de Proyectos de Inves-tigaci´on Cient´ıfica B´asica. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´exico.
2012 External Referee. Experts Committee of the CONACyT sci-entific journals. Consejo Nacional de Ciencia y Tecnolog´ıa (CONACyT) y Secretar´ıa de Educaci´on P´ublica (SEP), M´ ex-ico.
