Juan Margalef Roig falleció el 15 de marzo de 2024 en Las Rozas (Madrid). Nació el 11 de abril de 1939 en El Masroig (Tarragona). Después de realizar estudios en la Escuela de Comercio y en la Facultad de Económicas en Barcelona, se trasladó a Madrid para realizar la licenciatura de Ciencias (Sección de Matemáticas) en la Universidad de Madrid (actual Universidad Complutense de Madrid, UCM) desde 1964 hasta 1969. Obtuvo el grado de Licenciado con la tesina “Sobre el producto de identificaciones“, dirigida por Enrique Outerelo y leída el 28 de julio de 1970 con la calificación máxima de sobresaliente. Entre los compañeros de la licenciatura se encontraba María Nieves Bentabol Marinas, que más tarde sería, en segundas nupcias, su esposa. Han tenido tres hijos Carla, Berta y Juan. Del primer matrimonio, Juan ha tenido cuatro hijas: María del Mar, Belén, Luisa y Arancha.
Una vez terminada la licenciatura, Juan se incorporó a la docencia en la Facultad donde realizó sus estudios, y la ejerció desde 1969 hasta 1974, desempeñando puestos de Monitor de clases prácticas, Ayudante de clases prácticas, Profesor encargado de curso y Profesor adjunto. De la enseñanza impartida se destaca, por su influencia en su carrera científica, las clases prácticas de Topología y de Bioestadística (Sección de Biológicas). Además, durante este tiempo disfrutó de una beca del Ministerio de Educación y Ciencia dentro del programa Formación del Personal Investigador.
Desde el comienzo de su carrera científica, Juan siempre tuvo una gran capacidad para idear nuevos enfoques con gran originalidad. Así, junto con su compañero de Licenciatura Guillermo Fleitas, con quien escribiría un libro de Problemas de Topología General publicado por la Editorial Alhambra con dos ediciones (1970 y 1980), fueron los promotores de un seminario en la Facultad de Ciencias de la Universidad de Madrid. Este seminario, organizado por la Cátedra de Álgebra y Topología, la Cátedra de Geometría y Topología y la Agregaduría de Topología, versaba sobre Topología diferencial y Sistemas dinámicos. Con el nombre de Seminario de Topología, se inició en el año 1970 y terminó en 1975. Los temas expuestos se publicaron en 17 fascículos y los redactores principales de los mismos fueron Juan y Enrique. Esto fue el germen de muchos trabajos conjuntos en una colaboración científica que ha durado más de cincuenta años, hasta el fallecimiento de Juan [ver referencias 1,2].
Otra faceta a destacar de Juan fue su gran interés por la Lógica matemática, que se ha plasmado de forma importante en todas sus publicaciones científicas. Procuró siempre la utilización de un lenguaje matemáticamente preciso en las definiciones, la distinción clara de la hipótesis y de la tesis en los enunciados, en las proposiciones y en los teoremas, y una exquisita corrección científica de las demostraciones. La constatación de lo dicho es la publicación de un Apéndice con el título de Lógica matemática en un libro de divulgación [3].
En 1974, Juan obtuvo la plaza de Colaborador Científico del CSIC y su carrera científica transcurre en este organismo de investigación hasta su jubilación en 2009 con la categoría de Investigador Científico, que alcanzó en 1990, siendo posteriormente Emérito entre 2009 y 2017. Sin embargo, siempre mantuvo una relación muy estrecha con la Facultad para terminar su formación académica y formar parte de Ayudas y Proyectos de investigación. Para completar su formación académica, después de una estancia de nueve meses en el Institut des Hautes Etudes Scientifiques (IHES) de Paris en el año 1975, inició su Tesis Doctoral, bajo la dirección de Enrique, con el título R2-Acciones locales. En ella demostró, entre otras cosas, el análogo del teorema de Poincaré-Bendixson para flujos biparamétricos. Defendió la tesis el 12 de abril de 1977, obteniendo el grado de Doctor en Ciencias Matemáticas por la UCM con la calificación máxima de sobresaliente cum laude.
En una estancia de Juan en la Facultad de Matemáticas de la Universidad de la Laguna (Tenerife) contactó con Edith Padrón y Sonia Armas que, posteriormente colaboraron con él en algunas publicaciones científicas. Dirigió la tesis doctoral de E. Padrón con el título Denominación de uno y varios tipos de Gérmenes Diferenciables que fue leída el 1 de marzo de 1991 en la citada Facultad.
Las aportaciones científicas de Juan se encuadran en los siguientes campos de la Matemática: Funciones reales; Topología general; Análisis global y Topología diferencial; Teoría de singularidades de funciones diferenciables y Teoría de Catástrofes; y Probabilidades, Procesos Estocásticos y Matemática Financiera y Actuarial.
Las tareas desarrolladas por Juan en el campo de las Funciones reales consistieron en la publicación de libros, en colaboración con otros autores, entre ellos su esposa M. N. Bentabol, que recogen los temas centrales, tratados con gran amplitud y profundidad, de Análisis Matemático correspondientes al primer y segundo curso de las Facultades de Ciencias y Escuelas Técnicas Superiores en la década de los años setenta del siglo pasado [4-7].
Los trabajos de Juan sobre Topología general se iniciaron con su tesina para obtener el grado de Licenciado que se publicó con ampliaciones en 1980 [8]. En colaboración con Enrique, obtuvo y publicó resultados sobre espacios paracompactos, colectivamente normales, uniformes y selecciones continuas. Además, publicaron un tratado sobre Topología general en cinco volúmenes [9], que ha marcado profundamente a toda una generación de matemáticos en España, y libros de texto, adaptados a los cursos de Topología general en la Licenciatura en Ciencias Matemáticas de la UCM [10]. Del tratado, se destaca el estudio de las Estructuras topógenas y sintopógenas con las cuales Á. Császár probó en 1960 el importante resultado de que las estructuras topológicas son estructuras de orden, distinguiéndolas así de las estructuras algebraicas.
Las investigaciones en Análisis global y Topología diferencial se centraron en el estudio de las variedades diferenciables infinito-dimensionales (de Hilbert y Banach) con borde anguloso, tema que comienza a desarrollarse a partir de la década de los años 60 del siglo pasado. Entre los numerosos resultados obtenidos se destacan los siguientes:
1.- Distinto comportamiento topológico de las variedades finito-dimensionales y las infinito-dimensionales [11].
2.- Teorema de existencia de variedad diferenciable cociente de una variedad diferenciable con borde y con borde anguloso. Este importante resultado extiende el establecido por R. Godement para variedades sin borde [12-14].
3.- Transversalidad y teoremas de densidad de la transversalidad [15-17].
4.- Inmersiones de variedades diferenciables con borde anguloso en espacios de Hilbert y de Banach [18,19].
5.- Geometría diferencial en variedades diferenciables infinito- dimensionales con borde anguloso. Utilizando las ideas de P. Liberman y J. Vilms para el caso finito-dimensional se encontró el procedimiento para definir una conexión en el caso infinito- dimensional [20-22].
Gran parte de estos resultados se publicaron en un libro con prólogo de Peter W. Michor de la Universidad de Viena [23], y el interés de los mismos llevaron a la publicación, por invitación, de un artículo en el libro Handbook of Global Analysis editado en el año 2008 [24]. En este artículo, se extiende el estudio de las variedades diferenciables de Banach a variedades modeladas sobre espacios vectoriales más generales, a saber, normados y localmente convexos, y se utiliza el cálculo diferencial sobre “convenient vector spaces” que ha adquirido gran interés en los últimos años en Análisis Global con los trabajos de P. W. Michor- A. Kriegl.
En la década de los años setenta del siglo pasado, R. Thom apoyándose en la teoría de singularidades de aplicaciones diferenciables, iniciada por H. Whitney (1955), y en la teoría de bifurcación de sistemas dinámicos, debida a H. Poincaré y Andronov-Pontriaguin (1937), elaboró la Teoría de Catástrofes. Esta teoría trata de ciertos fenómenos cuyo comportamiento cualitativo cambia bruscamente bajo pequeñas variaciones de los parámetros de control, es decir, fenómenos discontinuos en su evolución. Su aplicación a varias ramas del conocimiento dio lugar a una gran cantidad de críticas y controversias, ya que en muchas ocasiones no se satisfacían las hipótesis del Teorema de Thom, base fundacional de la teoría. Juan se interesó por el tema y junto con Enrique escribieron artículos presentando la teoría [25-27]. Los resultados más importantes, en este campo, los estableció Juan en Física cuántica en colaboración con Salvador Miret del entonces llamado Instituto de Matemática y Física Fundamental del CSIC, actual Instituto de Física Fundamental. Las aplicaciones de la teoría de catástrofes se centraron en diagramas de fase, formas de línea en procesos resonantes en las colisiones de átomo-superficie y cáusticas observadas en transiciones rugosas en superficies debido a la temperatura [28-35]. Todo este trabajo culminó en un artículo de revisión en la revista Surface Science Reports [35].
Juan siempre tuvo gran interés sobre cuestiones de Probabilidades y Matemática financiera. Como ya se ha comentado, realizó estudios en el campo de la Matemática financiera antes de iniciar los estudios de matemáticas. En relación con las probabilidades, impartió la asignatura de Bioestadística, en el curso 1971-1972, en la Sección de Biológicas de la Facultad de Ciencias de la Universidad de Madrid. Posteriormente, siguió interviniendo en seminarios sobre estos temas en la Facultad de Ciencias Económicas de la Universidad del País Vasco (junio de 1977), en el Instituto de Análisis Económico del CSIC (Campus de la Universidad Autónoma de Barcelona, 2001), en el Centro de Investigaciones Matemáticas (Centre de Recerca per a l’Educació Cientifica i Matemàtica) de la U. A. de Barcelona (1999, 2000). En este último centro, contactó con el gran especialista en estos temas, A. N. Shiryaev. Desde 1999 a 2005 impartió cursos de Doctorado en la Facultad de Matemáticas de la Universidad de La Laguna sobre Probabilidad y Economía. En esta Universidad tuvo la ocasión de intercambiar ideas sobre cuestiones de la Teoría del riesgo con Manuel Linares, especialista en este tema. Toda esta actividad científica de Juan se ha traducido, con colaboración de Enrique y Salvador, en la publicación de artículos y libros [36-46], en los que se han incorporado técnicas recientes (de la denominada Matemática cuántica, es decir, las herramientas matemáticas utilizadas en la Mecánica cuántica) para determinar el precio de las opciones sobre activos financieros y el estudio de las estructuras temporales de tipos de interés (bonos).
Finalmente, es digno de destacar su compromiso con la comunidad matemática española, siendo miembro del Comité Nacional del IMU desde 1986 hasta 1996.
Instituto Jorge Juan de Matemáticas
Cuando Juan se integró al CSIC en 1974, lo hizo al Instituto Jorge Juan de Matemáticas, siendo Director del mismo Pedro Abellanas. Este Instituto se extinguió en 1984. El grupo de matemáticos del Instituto Jorge Juan, que dependían de la Presidencia del CSIC, fueron absorbidos en un instituto de reciente creación, denominado Instituto de Matemáticas y Física Fundamental (IMAFF) en 1992. Juan fue durante un período de tiempo Jefe de Departamento de Matemáticas y jugó un papel muy destacado y decisivo. A pesar de que fueron años difíciles, pues era un Instituto con muchos miembros y que presentaba problemáticas muy diversas debido a la gran variedad de investigaciones punteras que se llevaban a cabo, siempre fue un hombre que buscaba consensos y buen clima entre los matemáticos y los físicos que conformaban el IMAFF. Siempre fue un hombre de paz. Este instituto dio lugar a otros tres institutos posteriormente a partir de 2007: El Instituto de Ciencias Matemáticas (ICMAT), el instituto de Física Teórica (IFT) y el Instituto de Física Fundamental (IFF). Juan, aunque apoyó inicialmente la creación del ICMAT, decidió finalmente quedarse en el IFF porque ya se había establecido una colaboración larga, fuerte y muy fructífera con Salvador.
Con el fallecimiento de Juan, Enrique y yo hemos perdido ante todo a un gran amigo, amistad forjada a lo largo de muchos años de trabajo y de multitud de discusiones sobre todo lo divino y lo humano. Siempre fue un analista profundo de la realidad social, histórica, religiosa y política de España. Un gran catalán afincado en Madrid. Hemos perdido un gran matemático del cual hemos aprendido mucho con su sentido de la lógica, su agudeza y su gran intuición matemática y de sus charlas siempre muy sosegadas y amenas. Le echaremos mucho de menos y siempre permanecerá su huella imborrable en nuestros corazones. D. E. P.
[1] M. García Marrero, J. Margalef, C. Olano, E. Outerelo, Seminario de Topología. Fascículo I: Variedades diferenciables reales.
Facultad de Ciencias. Sección de Matemáticas. Universidad de Madrid, 1970 (1ª Edición) y 1972 (2ª Edición corregida y aumentada).
[2] M. García Marrero, J. Margalef, E. Outerelo, J. L. Vázquez, Seminario de Topología. Fascículo XVII: Foliaciones.
Facultad de Matemáticas, UCM, 1975.
[3] J. Margalef, E. Outerelo, Matemáticas al alcance de todos (matemáticas sin demasiadas ecuaciones).
Pearson-Alhambra, Madrid, 1ª edición (2007), 2ª edición (2008).
[4] R. Barbolla, M. García, J. Margalef, E. Outerelo, J.L. Pinilla, J.M. Sánchez, Introducción al Análisis Real.
Editorial AC, Madrid, 1975.
[5] R. Barbolla, M. García, J. Margalef, E. Outerelo, J.L. Pinilla, J.M. Sánchez, Introducción al Análisis Real, (2ª edición ampliada con dos capítulos).
Editorial Alhambra Universidad, Madrid, 1981.
[6] M. N. Bentabol, J. Margalef, E. Outerelo, J, L. Pinilla, Análisis Matemático. Cálculo diferencial en espacios Euclídeos.
Editorial Pirámide, Madrid, 1981.
[7] M. N. Bentabol, J. Margalef, E. Outerelo, Análisis Matemático. Cálculo integral en espacios Euclídeos.
Editorial Pirámide, Madrid, 1982.
[8] J. Margalef, E. Outerelo, Caracterización de los espacios localmente compactos en la clase de los γ-espacios.
Rev. Mat. Hispano-americana, V. Xl, 5-6, 168-176, 1980.
[9] J. Margalef, E. Outerelo, J. L. Pinilla, Topología, V. I (1975), V. II (1979), V. III (1980), V. IV (1980), V. V (1982).
Editorial Alhambra, Madrid.
[10] J. Margalef, E, Outerelo, E. Padrón, Topología general.
Editorial Sanz y Torres, Madrid, 2000.
[11] J. Margalef, E. Outerelo, Una variedad diferenciable de dimensión infinita separada y no regular.
Rev. Mat. Hispano-americana, V. XLII, 1-2-3, 51-55, 1982.
[12] J. Margalef, E. Outerelo, Variedad cociente de variedades con borde anguloso. Teorema de existencia.
Rev. Real Acad. de C. E. F. y N., V. LXXX, 4, 581-592, 1986.
[13] S. Armas, J. Margalef, E. Outerelo, E. Padrón, Teorema fundamental para variedades cocientes con borde.
Actas de las XIV jornadas Hispano-Lusas de Matemáticas, 649-653.
Universidad de La Laguna (Tenerife), 1990.
[14] J. Margalef, E. Outerelo, E. Padrón, On Submersions Preserving the Boundary and Quotient Manifolds.
Int. Conf. on Diff. Geom. and its Applic. Brno (Chequia), 1989.
World Scient. Editors J. Janyska-D. Krupka, 119-128, Singapur, 1990.
[15] J. Margalef, E. Outerelo, Density of the Transversality on Manifolds with Corners.
Collectanea Mathematica, V. XXXVII, fascículo 3, 277-285, 1986.
[16] J. Margalef, E. Outerelo, Densidad de la transversalidad en multijets de variedades con borde anguloso.
Rev. Real Acad. de C. E. F. y N., V. LXXXI, 4, 725-737, 1987.
[17] S. Armas, J. Margalef, E. Outerelo, E. Padrón, Transversality on Manifolds with Corners.
The Proceeding of the winter school Geometry and Topology Srni 1992.
Suppl. Rendiconti del Circulo Mat. di Palermo, S. II, 32, 21-30, 1992.
[18] S. Armas, J. Margalef, E. Outerelo, E. Padrón, Embedding of an Urysohn Differentiable Manifold with Corners in a Real Banach Space.
The Proceeding of the winter school Geometry and Topology Srni 1991.
Suppl. Rendic. del Circulo Mat. di Palermo, S. II, 30, 143-152, 1993.
[19] J. Margalef, E. Outerelo, Embedding of Hilbert Manifolds with Smooth Boundary into Semispace of Hilbert Spaces.
Archivum Mathematicum, T. 30, 3, 145-164, 1994.
[20] J. Margalef, E. Outerelo, Lie Group Actions over Manifolds with Corners.
Math. Japonica, 38, No. 3, 577-582, 1993.
[21] J. Margalef, E. Outerelo, E. Padrón, Principal Bundles on Infinite Dimensional Manifolds with Corners.
Acta Math. Hungar., 72, 1-2, 105-119, 1996.
[22] J. Margalef, E. Outerelo, E. Padrón, Connections on Infinite Manifolds with Corners.
Rend. Sem. Mat. Univ. Padova, V. 98, 21-55, 1997.
[23] J. Margalef, E. Outerelo, Differential Topology.
Mathematics Studies, 173. Editor: Leopoldo Nachbin.
North.Holland, Amsterdam, 1992.
[24] J. Margalef, E. Outerelo, Topology of Manifolds with Corners.
Handbook of Global Analysis, Demeter Krupka and David Saunders.
Elsevier, 983-1033, 2008.
[25] J. Margalef, E. Outerelo, Teoría de catástrofes aplicada.
Rev. Real Acad. C. E. F. y N. Madrid, T. XXVIII, C. 1-2, 1-6, 1984.
[26] J. Margalef, E. Outerelo, Teoría de catástrofes, Aplicaciones.
Memorias de la Real Acad. C. E. F. y N. Madrid, T. XVII, 5-30
[27] J. Margalef, E. Outerelo, Notas sobre la teoría de catástrofes y sus aplicaciones.
Instituto Jorge Juan de Matemáticas del C.S.I.C., 1-90, 1978.
[28] S. Miret, J. Margalef, R. Guantes, F. Borondo, Ch. Jaffé,
Classical Singularities in Chaotic Atom-surface Scattering.
Physical Review B, V. 54, n. 15, 10397-10400, 1996.
[29] R. Guantes, F. Borondo, J. Margalef, S. Miret, J. R. Manson,
Threshold Resonances in Classical Chaotic Atom-surface Scattering.
Surface Science, V. 375, L379-L384, 1997.
[30] J. Gaite, J. Margalef, S. Miret, Analysis of a Three-component Phase Diagram by Catastrophe Theory.
Physical Review B, V. 57, n. 21, 13527-13534, 1998.
[31] J. Gaite, J, Margalef, S, Miret, Analyse of a Three-component Model Phase Diagram by Catastrophe Theory: Potential with Two Order Parameters.
Physical Review B, V. 59, n. 13, 8593-8601, 1999.
[32] S. Miret, J. P. Toennies, J. Margalef, Catastrophe Theory and Resonance Line Shapes in Atom-surfaces Scattering.
Physical Review B, V. 60, n. 9, 6529-6534, 1999.
[33] J. Margalef, S. Miret, A. Todo-Labbé, Characterization of Elementary Chemical Reactions from Bifurcation Theory.
J. Phys. Chem. A, v. 104, 11589-11592, 2000.
[34] J. Margalef, S. Miret, Resonance Line Shapes and Catastrophes in Particle-surface Scattering.
Physical Review B, V. 63, 094302-094410, 2000.
[35] R. Guantes, A. Sanz, J. Margalef, S. Miret, Atom-surface Difraction: A Trajectory Description.
Surface Science Reports, V. 53, n. 6-8, 199-230, 2004.
[36] J. Margalef, S. Miret, Cálculo estocástico aplicado a las finanzas: Precio de las opciones según el modelo de Black-Scoles-Merton y algunas generalizaciones.
Contribuciones matemáticas. Libro homenaje al Profesor D. Enrique Outerelo Domínguez, 281-313.
Editorial Complutense, Madrid, 2004.
[37] J. Margalef, E. Outerelo, Probabilidad y Economía 1. Mercados financieros finitos.
Editorial Sanz y Torres, Madrid, 2010.
[38] J. Margalef, E. Outerelo, Probabilidad y Economía 2. Espacios de Probabilidad generales.
Editorial Sanz y Torres, Madrid, 2013.
[39] J. Margalef, S. Miret, E. Outerelo, Probabilidad y Economía 3. Procesos estocásticos.
Editorial Sanz y Torres, Madrid, 2014.
[40] J. Margalef, S. Miret, E. Outerelo, Probabilidad y Economía 4. Mercados Financieros continuos.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 4. Madrid, 2016.
[41] J. Margalef, S. Miret, E. Outerelo, Probabilidades en espacios topológicos.
A Mathematical Tribute to Professor José María Montesinos Amilibia, 463-490.
Departamento de Geometría y Topología. Facultad de Ciencias Matemáticas de la UCM, Madrid, 2016.
[42] J. Margalef, S. Miret, E. Outerelo, Probabilidad y Economía 5. Bonos y opciones sobre bonos.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 5, Madrid, 2017.
[43] J. Margalef, S. Miret, E. Outerelo, Teoría del Riesgo. Modelos de Riesgo en Seguros, V.1.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 6, Madrid, 2019.
[44] J. Margalef, S. Miret, E. Outerelo, Teoría del Riesgo. Modelos de Riesgo en Finanzas, V.2.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 7, Madrid, 2020.
[45] J. Margalef, S. Miret, E. Outerelo, Probabilidad y Economía 6. Opciones dependientes del camino en el modelo Black-Scholes-Merton.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 8, Madrid, 2022.
[46] J. Margalef, S. Miret, E. Outerelo, Probabilidad y Economía 7. Integral de caminos de Feynman. Aplicaciones a las Finanzas.
Editorial Sanz y Torres. Colección Matemática Financiera y Actuarial, V. 9, Madrid, 2023.
Prof. Maria del Carmen Refolio passed away on October 20th, 2020, surrounded by her family and close friends. Carmen Refolio dedicated an important part of her life to science, addressing it from both the theoretical and experimental points of view. Throughout her life she worked in research management and scientific policy, both nationally and internationally. She soon moved on to other scientific research activities. Her work was developed in various fields, dedicating herself equally to experimental and theoretical research. In her final stage she drifted to teaching and dissemination of science, to which she dedicated herself with special interest and generosity. Carmen was always efficient and enthusiastic, enjoying her diverse activities. She was a wonderful colleague and friend, affectionate and cheerful, always ready to help others.
Carmen Refolio graduated in Chemical Sciences at the Complutense University of Madrid (UCM) in 1965. She enjoyed several fellowships at the CSIC Torres Quevedo Institute and OECD at the Paris headquarters until 1969. In 1970 she was appointed by the Gabinete Técnico of the Patronato Juan de la Cierva (CSIC), where she was coordinator of the Sub-commission of Chemical Technology. She was also representative of the Secretary of State of the Spanish Science Ministry in the Management Committee and “Task force” of the European Network Program for Materials Factual Data Bank of the EU. She soon moved on to the lab, obtaining in 1975 a doctorate in physics at the Faculty of Physical Sciences of the UCM, with an experimental work on the relationship between physical adsorption, chemisorption and catalytic reactions on solid surfaces.
During 1977 she worked in the Department of Inorganic, Physical and Industrial Chemistry, at the University of Liverpool. On this subject she continued working at the Institute of Materials Sciences (CSIC) until 1985, using diverse techniques such as spectrometry of desorbed species or field emission microscopy. From that date on, she began a collaboration with Professor Juan Rubio Bernal and his group, which led to a series of works with a quantum chemical approach to chemisorption. Electronic states on surfaces were determined using theoretical methods based on Green’s function, relating these surface states to chemisorption and catalysis processes. The theoretical methods developed were then applied to the determination of electronic properties of two-dimensional systems, closely related to superconductivity.
She joined our Institute in 1997, where she remained until 2020, the last nine years as Doctor ad Honorem. Throughout her research career, she participated in over one hundred publications. In 1995 she started a collaboration with “El CSIC en la Escuela” – a program of the Institute of Fundamental Physics and the CSIC Vice-presidency for Scientific Culture – meant to the training of teachers of the early stages of education. She developed didactic methods aimed at facilitating the understanding of simple scientific models to teachers and students, always considering science as an important part of human culture. She also participated in the publication of several books and in over fifty courses for schoolteachers, taking always into account gender equality issues.
An excellent companion, dedicated friend, scientist by vocation and passionate disseminator, she will be remembered fondly by all of us who had the privilege of working with her.
Authors: M. C. Refolio and J. M. López Sancho
Title: Adsorption of C2H4 on tungsten by ESD and TDS
Journal: Le Vide, les couches minces 201 (1980) 376 – 378
Authors: J. Rubio, M. C. Refolio, M. P. López Sancho and J. M. López Sancho
Title: Correlation effects in photoemission from adsorbates: Hydrogen on narrow band metals
Journal: Physical Review B, 38 (1988), 3142 – 3147
DOI: 10.1103/PhysRevB.38.3142
Authors: J. Rubio, M. C. Refolio, M. P. López Sancho and J. M. López Sancho
Title: Configuration-lattice approach to electron spectroscopies: Application to inverse photoemission
Journal: Physical Review B, 41 (1990), 7856 – 7859
DOI: 10.1103/PhysRevB.41.7856
Authors: M. C. Refolio, J. M. López Sancho, and J. Rubio
Title: The one-electron Green´s function of the half-filled Hubbard model on a triangular lattice
Cond-mat/0103459 (2001)
Authors: M. C. Refolio, J.M. López Sancho, and J. Rubio
Title: Critical behavior of the single-particle spectral weight in the ionic Hubbard model
Journal: Physical Review B, 72, 35121 (2005)
DOI: doi.org/10.1103/PhysRevB.72.035121
Authors: M. C. Refolio, J. M. López Sancho, J. Rubio and J. A. Verges
Title: The single-particle spectral function of quasi-one-dimensional insulating materials
Journal: Journal of Physics and Chemistry of Solids 67, (2006), 72 – 76
DOI: 10.1016/j.jpcs.2005.10.051
On July 26, 2018, Prof. Gerardo Delgado Barrio passed away in Madrid after a long illness. Born in Santiago de Compostela on April 9, 1946, in a family of teachers, Gerardo gratefully kept up the memories of some excellent professors of high school who sowed in him an early scientific vocation. After a year at the University of Santiago, he moved to Madrid where he graduated in Physics at the Complutense University (UCM) on June 1968. He started working in the biophysics group of Carlos Dávila at the Nuclear Energy Board (JEN), meeting Marina Téllez de Cepeda there, a specialist in Medical Physics, who later became his wife. They had four daughters, Marina, Ana, Laura, and Mar, who have given them six grandchildren to date.
After a short time in JEN he contacted Yves Gabriel Smeyers, one of the pioneers in Spain on Quantum Chemistry, at the Rocasolano Institute of the Higher Council for Scientific Research (CSIC), leaving JEN to do the PhD under his supervision on novel methods of calculation of electronic structure in small molecular entities. Even though their first joint paper was a semi-empirical study of nucleic acid bases using the ω technique [1], his thesis focused on the use of the so-called Half-Projected Hartree–Fock method, which includes electron correlation by considering an almost pure spin wave function [2]. The thesis was defended at the UCM in 1973.
Gerardo then began a postdoctoral stay at the Laboratory of Molecular Photophysics in Orsay (Paris-Sud), where he collaborated with Roger Prat on deformed states of atomic species improving the traditional spherical solutions [3], and simultaneously he interacted with Roland Lefebvre’s group, in particular with Juan Alberto Beswick and Osman Atabek, and began to collaborate with them on problems of nuclear dynamics (collisions, photo-fragmentation, etc.) proposing and using different methodologies in both the energy domain as well as in the time domain. Alberto soon became a close friend with whom he maintained a nearly constant scientific collaboration over the years. Their first joint work was on the quenching of an electronically excited oxygen atom by collinear collisions with nitrogen molecules [4], that served as a starting point to tackle three-dimensional collisional quenching of excited alkaline atoms by diatomic molecules a few years later [5]. In one of his visits to Orsay, and in teamwork with Alberto and Joshua Jortner, one of the first numerical simulations on the vibrational predissociation (VP) of the van der Waals (vdW) molecule HeI2(B) was published only one year after the pioneering experiment of Don Levy at the University of Chicago, attaining an outstanding agreement [6]. Soon later Alberto and Gerardo applied a clever rotational decoupling scheme [7] to deal with VP of this type of complexes that was the origin of several papers and different PhD thesis supervised by Gerardo. The very fruitful collaboration was maintained and deepened in the study on VP of triatomic weakly bound complexes, e g. full three-dimensional close-coupling benchmark calculations [8], opening the gate to further applications to other complexes as HeBr2 [9],or the first version of the Golden Rule approach in the time domain by using wave packets propagation [10]. These studies were seminal to later address molecular clusters of increasing size and complexity.
In 1975 Gerardo returned to Madrid and, after a one-year postdoc at Rocasolano Institute of CSIC, he was hired as Associate Professor in the Department of Quantum Chemistry at the Universidad Autónoma de Madrid (UAM, 1976-79). Then he got permanent positions as Scientific Collaborator (CSIC, 1979-82), Associate Professor (UCM, 1982-83), again a Scientific Collaborator (CSIC, 1983-86), Scientific Researcher (IEM-CSIC, 1986-87), Full Professor (CSIC, 1988-2016), and finally Doctor Ad Honorem (CSIC, 2016-18). Gerardo managed to direct or co-supervise up to fifteen Theses along his career, and created a Department of Atomic, Molecular and Aggregates Physics first in the Institute of Matter Structure (IEM-CSIC), after in the Institute of Mathematics and Fundamental Physics (IMAFF-CSIC), and then at the Institute of Fundamental Physics (IFF-CSIC), institutes of which he was Director (IMAFF, 2006-2009, IFF, 2009-2016).
As mentioned above, in 1979 he got a permanent position in CSIC, initiating the formation of a research group of physicists and chemists to study the dynamics of nuclei involved in atomic and molecular collisions and photodissociation processes. Based on classical trajectories, he proposed in 1983 a successful quasi-classical model to study the VP of HeI2(B) [11], later extended to larger clusters [12, 13].
Among his many collaborations, the one that Gerardo started in 1983 with Steve Berry’s group at the University of Chicago, as a result of a Fullbright scholarship and later through projects funded by the Joint Spanish-American Committee for Scientific Cooperation, can be considered essential. They proposed and applied various quantum approximations and different coordinates for the simulation of the ro-vibrational spectrum of the water molecule [14,15] that were later extended to tetra-atomic species [16].
Another of the most notable collaborations maintained until the last days was the one that began in 1984 with the group of Franco Gianturco at the University of Rome “La Sapienza”. The first works focused on rotational predissociation processes of van der Waals complexes [17], continued dealing with ionic clusters [18], and followed by the study of Efimov states in extremely weakly bound trimers [19, 20].
At the beginning, theoretical studies of van der Waals clusters were performed using empirical although reasonable forms to describe the corresponding potential energy surfaces (PES). Presently,
however, ab initio methods have advanced in such a way that they are currently used to deal with weakly bound complexes. In fact, through high-level electronic structure calculations, the corresponding PES for the ground and excited electronic states have been available, and several vdW systems have been revisited [21-23].
With Julius Jellinek (Argonne Nat. Lab.), the Rome group, and researchers of the Université Marne-la-Vallée (Paris-Est), a line of research on doped helium clusters has been developed by Gerardo and his group in the recent years using nuclear quantum chemistry-like methodologies [24-27]. The goal was the simulation of spectra of molecules immersed in helium nano-drops of bosonic or fermionic character explaining the effect of superfluidity of the environment. Monte Carlo methods were then used in doped helium aggregates adapted to the case of attached dopants, explicitly incorporating temperature via Feynman path integrals [28-30], and also the Path Integral Molecular Dynamics approach was tuned to study the formation of rubidium dimers along the surface of helium droplets, his last published paper [31]. Among his recent works it can also be found the structures, energetics, and spectroscopy of hydrogen cations HN+of astrophysical interest [32-34], the study of the properties of pure liquid water [35] and clathrates there [36], and the energetic, structural, dielectric, and nuclear magnetic shielding properties of linear formamide clusters as an example of species of biological interest [37]. In some way, this research line would close a circle initiated by Gerardo with the study of nucleic acids [1].
In addition to his scientific contributions (more than 250 publications, edition of several books, organization of multiple congresses and national and international schools) Gerardo has played a fundamental role in the scientific community both in Spain and abroad. He was a member of the American Physical Society (APS), of the European Physical Society (EPS), of the Cuban Society of Physics, of the Institute of Physics, of the Scientific Advisory Board of the European Physics Journal, President of the Spanish Section of the International Union of Pure and Applied Physics (2005-2011), member of the Group of Physics for the Development of the EPS and first president and founder of the Latin American Federation of Physics Societies (FeLaSoFi) in 2005. He was always passionate about the topics related to Latin America, and its outstanding contribution to Ibero-American science, was recognized as Doctor Honoris Causa by the University of Havana. He worked tirelessly to establish stronger links between the RSEF and the EPS. Thanks to him, the RSEF became an important partner of the EPS after a period of low Spanish profile. He was a member of the EPS Executive Committee from 2001 to 2006. Through FeLaSoFi, he opened communication channels with Latin America and started new activities in Physics for Development. Gerardo was a founding member of the EPS Forum Physics and Society to promote the dialogue between Physics and Society. Gerardo was elected EPS Fellow in 2007 and received the Gero Thomas Medal in 2015 for outstanding contributions to EPS; in particular, for its commitment to international scientific cooperation, outreach and education and Physics for development.
In the CSIC, together with the institutes’ addresses mentioned above and among many other commitments, he was a member of the Governing Board of the CSIC (2001-2004) and member of the CSIC’s Ethics Committee since 2011, occupying his vice-presidency from 2012 until his death. Regarding the RSEF, he received the “Novel de Física” prize from the RSEFyQ (1977) and the Gold Medal of the RSEF (1983), and created in 1988, being its first president, the Specialized Group of Atomic and Molecular Physics (GEFAM). Gerardo was president of the RSEF from 1997 to 2006. During his presidency, the RSEF experienced an amazing growth, in number of members, financial resources and impact on civil society. Among many other advances, we want to highlight his support for the creation of the Specialized Group of Women in Physics (GEMF), approved by the Governing Board of the RSEF in 2002. He was also responsible for the integration of the journal Anales de Física in the European Physics Journal. In 2003, the RSEF celebrated its centenary and Gerardo was the president of the Organizing Committee. In 2005, the World Year of Physics took place, coinciding with the centenary of Albert Einstein’s ‘annus mirabilis’, with Gerardo presiding over its Organizing Committee for Spain. Both events were important milestones for the RSEF and required a great commitment in public relations, agreements with financing agencies and in the explanation of the important role of Physics in our society. Gerardo was also a close associate of the BBVA Foundation, participating as a member of the jury in the first three editions (2008-10) of the Frontiers of Knowledge Awards in the category of Basic Sciences, and also in the jury of the Physics Awards RSEF-BBVA Foundation since 2008 as well as in the evaluation commissions of the Basic Sciences area of the Leonardo Scholarships. He was also an assiduous collaborator with the Areces Foundation, acting during the last ten years as a jury in the selection of its postgraduate scholarships in Physics and Mathematics and carrying out the follow-up and evaluation of the work done by the scholarship recipients abroad.
Beyond the responsibilities in the world of Physics, which without being exhaustive we have tried to review, we want to emphasize that Gerardo was a magnificent physicist, both in teaching and research. His concerns were, however, much broader: from Religion and Philosophy to Economics and Politics, through History, Music, Theater and Sport. The conversations with him, whatever the subject, were always a pleasant and inexhaustible source of knowledge. He was a true erudite. His death means without a doubt a great loss for his family, but also for Physics, particularly in Spain, Europe and Latin America. Those of us who had the privilege and honor of working closely with him were able to estimate and admire his great value, his leadership and work capacity, by transmitting his contagious enthusiasm and vigor, and by depositing ever and ever in us his whole confidence. Besides being a great teacher and priceless fellow, his friendship will always remain in our memory and our hearts. Rest in peace.
[1] Y. G. Smeyers, G. Delgado-Barrio, Anales de Química de la Real Sociedad Española de Física
y Química 68(1971) 25.
[2] Y .G. Smeyers, G. Delgado-Barrio, Int. J. Quantum Chem. 8(1974) 733.
[3] G. Delgado-Barrio, R. F. Prat, Phys. Rev. A 12(1975) 228.
[4] G. Delgado-Barrio, J. A. Beswick, Chem. Phys. Lett. 48(1977) 358.
[5] J. Campos-Martínez, O. Roncero, S. Miret-Artés, P. Villarreal, G. Delgado-Barrio,
- Chem. Phys. 91(1989) 155.
[6] J. A. Beswick, G. Delgado-Barrio, J. Jortner, J. Chem. Phys. 70(1979) 3895.
[7] J. A. Beswick, G. Delgado-Barrio, J. Chem. Phys. 73(1980) 3653.
[8] O. Roncero, J. A. Beswick, N. Halberstadt, P. Villarreal, G. Delgado-Barrio,
- Chem. Phys. 92(1990) 3348.
[9] A. Rohrbacher, T. Ruchti, K. C. Janda, A. A. Buchachenko, M. I. Hernández, T.
González-Lezana, P. Villarreal, G. Delgado-Barrio, J. Chem. Phys. 110(1999) 256.
[10] P. Villarreal, S. Miret-Artés, O. Roncero, G. Delgado-Barrio, J.A. Beswick, N. Halberstadt,
- D. Coalson, J. Chem. Phys. 94(1991) 4230.
[11] G. Delgado-Barrio, P. Villarreal, P. Mareca, G. Albelda, J. Chem. Phys. 78(1983) 280.
[12] A. García-Vela, P. Villarreal, G. Delgado-Barrio, J. Chem. Phys. 92(1990) 6504.
[13] A. García-Vela, J. Rubayo-Soneira, G. Delgado-Barrio, P. Villarreal,
- Chem. Phys. 104(1996) 8405.
[14] G. A. Natanson, G. S. Ezra, G. Delgado-Barrio, R. S. Berry, J. Chem. Phys. 81(1984) 3400.
[15] D. M. Leitner, J. E. Hunter, G. A. Natanson, R. S. Berry, P. Villarreal, G. Delgado-Barrio,
- Chem. Phys. 94(1991) 5917.
[16] P. Villarreal, O. Roncero, G. Delgado-Barrio, J. Chem. Phys. 101(1994) 2217.
[17] F. A. Gianturco, A. Palma, P. Villarreal, G. Delgado-Barrio, Chem. Phys. Lett. 111(1984) 399.
[18] M. P. de Lara-Castells, P. Villarreal, G. Delgado-Barrio, S. Miret-Artés, E. Buonomo, F. A.
Gianturco, Chem. Phys. Lett. 242(1995) 336.
[19] T. G. Lezana, J. Rubayo-Soneria, S. Miret-Artés, F.A. Gianturco, G. Delgado-Barrio, P.
Villarreal, Phys. Rev. Lett. 82(1999) 1648.
[20] I. Baccarelli, F. A. Gianturco, T. González-Lezana, G. Delgado-Barrio, S. Miret-Artés, P.
Villarreal, Phys. Rep. 452(2007) 1.
[21] M. P. de Lara-Castells, R. V. Krems, A. A. Buchachenko, G. Delgado-Barrio, P. Villarreal,
- Chem. Phys. 115(2001) 10438.
[22] R. Prosmiti, C. Cunha, P. Villarreal, G. Delgado-Barrio, J. Chem. Phys. 116 (2002) 9249.
[23] L. García-Gutierrez, L. Delgado-Tellez, A. Valdés, R. Prosmiti, P. Villarreal, G. Delgado-
Barrio, J. Phys. Chem. A 113(2009) 5754.
[24] D. López-Durán, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, C. Di Paola, F. A.
Gianturco, J. Jellinek, Phys. Rev. Lett. 93(2004) 053401.
[25] M. P. de Lara-Castells, R. Prosmiti, G. Delgado-Barrio, D. López-Durán, P. Villarreal, F. A.
Gianturco, J. Jellinek, Phys. Rev. A 74(2006) 053201.
[26] M. P. de Lara-Castells, P. Villarreal, G. Delgado-Barrio, and A. O. Mitrushchenkov,
- Chem. Phys. 131(2009) 194101.
[27] N. F. Aguirre, P. Villarreal, G. Delgado-Barrio, A. O. Mitrushchenkov, M. P. de Lara-Castells,
Phys. Chem. Chem. Phys. 15(2013) 10126.
[28] R. Pérez de Tudela, D. López-Durán, T. González-Lezana, G. Delgado-Barrio, P. Villarreal, F.
- Gianturco, E. Yurtsever, J. Phys. Chem. A 115(2011) 6892.
[29] R. Rodríguez-Cantano, D. López-Durán, R. Pérez de Tudela, T. Gonzalez-Lezana, G. Delgado-
Barrio, P. Villarreal, F. A. Gianturco, Comput. Theor. Chem. 990(2012) 106.
[30] R. Rodríguez-Cantano, R. Pérez de Tudela, D. López-Durán, T. González-Lezana, F. A.
Gianturco, G. Delgado-Barrio, P. Villarreal, Eur. Phys. J. D 67(2013) 119.
[31] A. Castillo-García, T. González-Lezana, G. Delgado-Barrio, P. Villarreal,
Eur. Phys. J. D 72(2018) 102.
[32] R. Prosmiti, P. Villarreal, G. Delgado-Barrio, J. Phys. Chem. A 107(2003) 4768.
[33] C. Sanz-Sanz, O. Roncero, A. Valdés, R. Prosmiti, G. Delgado-Barrio, P. Villarreal, P.
Barragán, A. Aguado, Phys. Rev. A 84(2011) 060502(R).
[34] R. Pérez de Tudela, P. Barragán, R. Prosmiti, P. Villarreal, G. Delgado-Barrio,
- Phys. Chem. A 115(2011) 2483.
[35] J. S. Medina, R. Prosmiti, P. Villarreal, G. Delgado-Barrio, G. Winter, B. González, J. V.
Alemán, C. Collado, Chem. Phys. 388(2011) 9.
[36] A. Vitek, D. J. Arismendi-Arrieta, R. Rodríguez-Cantano, R. Prosmiti, P. Villarreal, R. Kalus,
- Delgado-Barrio, Phys. Chem. Chem. Phys. 17(2015) 8792.
[37] M. Sánchez, R. Prosmiti, G. Delgado-Barrio, J. Mol. Model. 20(2014) 2320.
Carmela Valdemoro López, Full Professor at the Institute of Fundamental Physics (IFF, CSIC) from 1988 to 2002 (Doctor ad Honorem from 2002 to 2013), and a pioneer of reduced density matrices-based methodologies for electronic structure, passed away on Thursday October 26, 2017, in company of her family. Carmela Valdemoro was an enthusiastic, creative, generous, and encouraging researcher right to the end, having inspired generations of scientists.
Carmela Valdemoro López was born in Spain and obtained a B.Sc. degree in Chemistry from the Universidad Complutense de Madrid (UCM, Spain) in 1956. She was awarded a graduate student fellowship, which she took up at Consejo Superior de Investigaciones Científicas (CSIC) from 1956 to 1959. She then moved to the Institut de Biologie Physico-Chimique (Paris), where she joined the group of Professor Bernard Pullman, who was her Ph.D. supervisor, and performed research on quantum biochemistry. Carmela Valdemoro received her PhD Degree in Chemistry in 1962 at the Universidad Complutense de Madrid. Later on, she spent two years at the Institute of Theoretical Physics in Naples. During 1964-1965, she was hired as a researcher by the Consejo Superior de Investigaciones Científicas in Valladolid (Spain). In 1966, she was awarded a position as research associate in the Department of Chemistry at the University of Alberta (Canada). In 1967, she joined the University of Sheffield (UK) as an assistant lecturer, and became a full lecturer a year after (1968-1971).
In 1971, Carmela Valdemoro returned to Spain as an assistant professor of the Department of Chemistry at the Universidad Autonoma de Madrid (UAM). She then joined the Consejo Superior Superior de Investigaciones Científicas (Instituto de Matemáticas y Física Fundamental) as Tenured Researcher in 1973, having been promoted to full professor in 1988, and awarding the degree of Ad Honorem Doctor at CSIC from 2002 to 2013. Over the course of her career, Carmela Valdemoro published about 100 scientific papers, with pioneering contributions in the field of reduced density matrices-based methods for electronic structure. Thus, in 1986, Professor Carmela Valdemoro applied a matrix-contracting mapping (see, e.g., Ref. 1) to the matrix representation of the Schrödinger equation in the N-electron space, obtaining the well-known second-order Contracted Schrödinger equation. The next keystone was provided by her paper written in 1991 [2], in which she proposed a method for approximating higher-order reduced density matrices in terms of the first order one. An extension of the method allowed her and her colleagues to achieve an approximate solution to the second-order Contracted Schrödinger equation three years later, in 1994 [3]. From 1994 to 2013, Professor Valdemoro and her collaborators continued to work in the family of equations obtained by applying the matrix-contracting mapping to the Schrödinger, Liouville, and hipervirial equations, with her latest contribution published in 2013 [4]. Among many other appointments, she mentored four PhD students and was a member of the Board of Directors of the International Society for Theoretical Chemical Physics.
We will miss her dearly, as a creative researcher, inspiring teacher, guide, and friend. An overview of her scientific contributions will be posted here.
Maria del Mar Reguero de la Poza (Universitat Rovira i Virgili, Spain)
Carlos Pérez del Valle (Universtité Grenoble Alpes, France), co-supervised with Professor Juan J. Novoa (Universitat de Barcelona, Spain)
María Pilar de Lara-Castells (IFF-CSIC, Spain), co-supervised with Professor Pablo Villarreal-Herrán (IFF-CSIC, Spain)
Diego R. Alcoba (Universidad de Buenos Aires, Argentina).
Prof. Pedro Félix González Díaz was born the 2nd of July of 1947 in Larache (Spanish protectorate in Morocco until 1956). He was proud of both his african origin and his andalusian heritage. He always showed an enormous creative thinking, which he was able to capture not only through scientific research but also by drawing, writing poetry and theatre plays, acting and discussing. He was truly “a sage of the Renaissance”. In addition, he was a very kind and warm person, always open to talk to anybody wanting to approach him, and his humanity was simply bottomless since everybody, every human being, was important for him. For these reasons he will always remain in our memory and in our hearts.
Pedro graduated in Chemistry at the University of Granada in 1970 and completed his PhD in Science at the Complutense University of Madrid in 1974. He joined the Institute of Optics of CSIC in 1975. There, he founded several laboratories to study aspects of the structure and dynamics of molecules using spectroscopy. He applied also those techniques to the study of components with medical and biological interests. Meanwhile, he started to investigate in different fields of theoretical physics in a self-taught way. He first explored problems in quantum mechanics and quantum optics and then moved towards general relativity. It is worth mentioning that in 1983 he deduced an entropy-area bound for closed gravitating systems, known nowadays as the holographic bound, that is a key factor for the study of several problems in theoretical physics, and whose authorship is often wrongly attributed to Bekenstein. In 1992 he moved to our Institute, focusing his attention on classical and quantum cosmology. Finally, in 2000 he started a very productive decade during which he studied different questions based on the recently discovered acceleration of the universe, leading to the hypothesis of the dark energy that he explored, and he was also very actively involved in novel approaches to study the multiverse.
His productivity was huge, only in the field of general relativity he published 130 articles, 90 of them as single author. An interesting remark about his scientific creativity and originality is that for many years he was very interested in some problems of biology (especially protein folding) and their possible connections with cosmology.
We would like to highlight his educational commitment, with the supervision of a dozen of PhD students. Despite his overwhelming character, or may be because of it, he knew how to boost the abilities of his trainees, strengthening their independence as researchers. Also, his outreach labour was prominent, specially aimed to combine the scientific knowledge with his other passions: poetry, theatre and nature. These gave rise to the foundation of the theatre group “Francisca Cortés Guillén” and the scientific-cultural association “Ecological Station of Biocosmology”, both in Medellín (Badajoz, Spain), where he annually organized workshops of science and theatre.
His personal life was difficult in his early thirties as he suffered the terrible loss of his young wife through a rare illness, leaving a three-year old daughter, Tania, behind. Some years later he remarried and had a son, Daniel.
“Los poetas verdaderos tienen pasaporte para viajar por el tiempo, hacia delante o hacia atrás, y visitar todas las épocas pasadas y futuras, siguiendo posiblemente los mismos cánones que las partículas más elementales y los campos de fuerza …” (Pedro F. González).
Magna Santos Greve
Priscila García Fernández
Irene Cifuentes
Carmen Sigüenza
Guillermo Mena Marugán
Luis Garay Elizondo
Mariam Bouhmadi López
Carlos Barceló Serón (co-supervisor)
José A. Jiménez Madrid (co-supervisor)
Prado Martín Moruno
Alberto Rozas Fernández
Salvador Robles Pérez
Ana Alonso Serrano (co-supervisor)