Curriculum Vitae of Juan Gerardo Alcázar

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1 Curriculum Vitae of Juan Gerardo Alcázar Personal Information: Date and Place of birth: 25th September 1970, Madrid (Spain) Contact Address: Faculty of Sciences, Department of Mathematics, Ctra. Madrid- Barcelona Km 33,600. E-28871, Alcala de Henares (Madrid) Address: Web Page: alcazar Marital Status: married; one daughter. Education: Bachelor in Mathematics, Universidad Complutense de Madrid (1995) Ph.D. in Mathematics, Universidad de Alcala (2007). Thesis: Effective Algorithms for the Study of the Topology of Algebraic Varieties, and Applications. Advisor: J. Rafael Sendra Pons (Calification: Sobresaliente Cum Laude) Research Interests: Constructive (Real) Algebraic Geometry, Topology of Algebraic Varieties (computational approach), Offset Varieties, Computer Algebra, CAGD (Computer Aided Geometric Design). Professional Experience: High School (Secondary School): Mathematics Teacher at several Spanish high-schools between 1996 and Chair of the Mathematics Department at Leonardo da Vinci High School Institute (Puertollano, Ciudad Real, Spain) between 2001 and Civil servant, belonging to the Cuerpo de Profesores de Enseñanza Secundaria, especialidad Matematicas, de la Comunidad de Castilla-la-Mancha (Spain) from 1998; currently on leave of absence. University: Adjunct Professor at the Mathematics Department of the Universidad de Alcala ( ). Assistant Professor at the Universidad de Alcala (2007-now).

2 Vice-Chair of the Mathematics Department of Universidad de Alcala (Dic now). Courses lectured: Calculus and Numeric Methods (Faculty of Informatics) Calculus (Faculty of Engineering) Complex Analysis and Differential Equations (Faculty of Engineering) Data Analysis (Faculty of Environmental Sciences) Complements of Mathematics (Master on Secondary School Teaching) Statistics (Faculty of Environmental Sciences) Math Refreshing Course (Faculty of Biology, Fac. of Chemistry, Fac. of Engineering) Awards: Extraordinary Doctoral Prize, Universidad de Alcala, Prize Innovation Groups of the Universidad de Alcala Publications in Refereed Journals (reverse cronological order): 1. Alcazar J.G., Diaz-Toca G.M. (2010), Topology of 2D and 3D Rational Curves, Computer Aided Geometric Design 27 (7): pp Alcazar J.G. (2009), On the Shape of Families of Rational Algebraic Curves Depending on One Parameter, Computer Aided Geometric Design, vol. 27, issue 2, pp Alcazar J.G. (2009), Good Local Behavior of Offsets to Implicit Algebraic Curves, Mathematics in Computer Science, vol. 2, n 4, pp Alcazar J.G. (2008), Good Global Behavior of Offsets to Plane Algebraic Curves, Journal of Symbolic Computation, vol. 43, pp Alcazar J.G. (2008), Good Local Behavior of Offsets to Regularly Parametrized Surfaces, Journal of Symbolic Computation vol. 43 (December), pp Alcazar J.G., Sendra J.R. (2007) Local Shape of Offsets to Rational Algebraic Curves, Journal of Symbolic Computation, vol. 42, pp Alcazar J.G., Schicho J., Sendra J.R.(2007) A delineability-based method for Computing Critical Sets of Algebraic Surfaces, Journal of Symbolic Computation, vol 42 (June), pp Alcazar J.G., Sendra J.R. (2005) Computation of the Topology of Real Algebraic Space Curves, Journal of Symbolic Computation 39, pp Publications in (refereed) Conference Proceedings: 1. Alcazar J.G. (2011), Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter, Proc. CASC (Conference on Algebra in Sci-

3 entific Computing) 2011, Kassel (Germany). Lecture Notes in Computer Science, Springer (to appear). 2. Alcazar J.G. (2011), The Shape of Conchoids to Algebraic Curves, Proc. XII Conference on Curves and Surfaces, Avignon (France). Lecture Notes in Computer Science, Springer (to appear) 3. Alcazar J.G., Diaz-Toca G.M. (2010), Topology of 2D and 3D Rational Curves, Proc. Encuentros de Algebra Computacional y Aplicaciones (EACA 2010), Santiago de Compostela, Spain, July Alcazar J.G., Local Shape of Generalized Offsets to Real Plane Algebraic Curves, Proc. EACA 2008 (Granada, Spain), pp , September Alcazar J.G., Schicho J., Sendra J.R., Shape of Level Curves: Determination and Some Applications, Proc. EACA 2006 (Sevilla, Spain), pp , September Chapters of Books: 1. Alcazar J.G. (2010), Applications of Level Curves to Some Problems on Algebraic Surfaces, Contribuciones Cientificas en Honor de Mirian Andres, Universidad de La Rioja (Spain) 2. Alcazar J.G., Marva M., Orden D., San Segundo F. (2011), Software Tools Used in Math Refreshing Courses at the University of Alcalá, Spain, chapter to be included in the book Teaching Mathematics Online: Emergent Technologies and Methodologies, IGI Global Pub. Co. as part of the Advances in Distance Education Technologies Series (to appear) Other Publications (Research): 1. Alcazar J.G., Sendra J.R. (2007) Local Shape of Offsets to Rational Algebraic Curves, Technical Report SFB (RICAM, Austria). 2. Alcazar J.G., Schicho J., Sendra J.R. (2007) Computation of the Topology Types of the Level Curves of Real Algebraic Surfaces, Technical Report RICAM. 3. Alcazar J.G., Sendra J.R. (2005) Computation of the Topology of Algebraic Space Curves, RISC-Linz Report Series N Other Publications (Education): 1. Alcazar J.G., Marva M., Orden D. (2009), Realizar Encuestas Docentes es Facil si Usted Sabe Como, Proceedings of VI Jornadas Internacionales de Innovacion Universitaria, Universidad Europea de Madrid, September Alcazar J.G., Marva M. (2009), Tutorizacion Virtual de Asignaturas de Matematicas mediante Moodle, Proceedings of II Jornadas de Innovacion Docente en Tecnologias de la Informacion y Telecomunicaciones (ID+TIC 2009), Faculty of Engineering, Universidad de Alcala, April Posters:

4 1. Alcazar J.G. (2010) Computing the Topology Types Arising in Families of Algebraic Curves, NILS Mobility Project, Universidad Complutense, Madrid, Enero Talks Given: Congresses (research): 1. Alcazar J.G. (2011), Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter, CASC (Conference on Algebra in Scientific Computing) 2011, Kassel (Germany), September Accepted for presentation. 2. Alcazar J.G. (2010), On the Shape of Conchoids to Algebraic Plane Curves, Seventh International Conference on Curves and Surfaces, July 2010, Avignon (France). 3. Alcazar J.G. (2010), Topology of 2D and 3D Rational Curves, Encuentros de Algebra Computacional y Aplicaciones (EACA 2010), Santiago de Compostela (Spain), July Alcazar J.G. (2009), Estudio Algoritmico de las Propiedades Topologicas de Familias de Curvas, Congreso de la Real Sociedad Matematica Española, Oviedo (Spain), February Alcazar J.G. (2008), Local Shape of Generalized Offsets to Real Plane Algebraic Curves, EACA 2008 (Granada, Spain), September Alcazar J.G. (2008), Local Shape of Classical and Generalized Offsets to Plane Algebraic Curves, Sixth Internacional Conference on Mathematical Methods for Curves and Surfaces, Tornsberg (Norway), July Alcazar J.G. (2007) Local and Global Results on the Shape of Offsets, Workshop on Computer Algebra in Geometric Modeling and Industry, Castro Urdiales (Spain), December Alcazar J.G., Schicho J., Sendra J.R. (2006), Shape of Level Curves: Determination and Some Applications, EACA 2006 (Sevilla, Spain), September Congresses (education): 1. Alcazar J.G., Marva M., Tutorizacion Virtual de Asignaturas de Matematicas mediante Moodle, II Jornadas de Innovacion Docente en Tecnologias de la Informacion y Telecomunicaciones (ID+TIC 2009), Faculty of Engineering, Universidad de Alcala, April Seminars, etc. (research): 1. Alcazar J.G. (2011), Shapes in one-parameter families of algebraic objects, Seminar of the Algorithms and Complexity Department, Max- Planck Institute fur Informatikk, Saarbrucken (Germany), May Alcazar J.G. (2010), Computing the shapes arising in one-parameter families of algebraic curves and surfaces, Seminar of Geometry, Center of

5 Mathematics for Applications, Oslo (Norway), September Alcazar J.G., (2008) Determinacion algoritmica de los tipos topologicos presentes en una familia de curvas algebraicas planas, y aplicaciones, Seminar of Algebraic Geometry, Department of Algebra, Faculty of Mathematics, Universidad Complutense de Madrid, May Alcazar J.G., Sendra J.R. (2007), Computation of the Topology of a Family of Algebraic Curves depending on a parameter, applications, and an emphasis on offset curves, talk given at RICAM (Johann Radon Institute for Computacional and Applied Mathematics, Linz, Austria). August Seminars, etc. (education): 1. Alcazar J.G. (2010), Introduction to Moodle, within the seminar Moodle, Wiris, Geogebra lectured by the group LibreTics at the Universidad de Alcala (open to all the people teaching at UAH) Research Stays: 1. Max-Planck Institute for Informatikk, Saarbrucken (Germany), Algorithms and Complexity Department, 11 weeks, March-May Center of Mathematics for Applications, Oslo (Norway), five weeks, August- September 2010 (thanks to a grant in the frame of NILS Mobility Project). 3. RICAM (Johann Radonn Institute for Computer and Applied Mathematics), Linz, Austria. One week (August 2007). Participation in Research Projects: 1. Project title: Variedades Parametricas: algoritmos y aplicaciones, Spanish Ministerio de Ciencia y Tecnologia, MTM C03-01, Main Researcher: Juan Rafael Sendra 2. Project title: Curvas y Superficies: Computacion Hibrida y Aplicaciones, Spanish Ministerio de Educacion y Ciencia, CAM-UAH2005/051, Main Researcher: Juan Rafael Sendra 3. Project title: Resolucion Simbolico Numerica de Problemas para Curvas y Superficies Reales, Spanish Ministerio de Educacion y Ciencia, ref. MTM C02-01, Main Researcher: Juan Rafael Sendra 4. Project title: Curvas y Superficies: fundamentos, algoritmos y aplicaciones, Spanish Ministerio de Ciencia y Tecnologia, BMF C02-01, Main Researcher: Juan Rafael Sendra Patents, Registered Software, etc. 1. Critical (2010). Maple program for computing the topology types arising in a family of rational curves depending on a parameter. Author: Juan G. Alcazar, Copyright UAH (Univ. Alcala de Henares)

6 2. Toppara2D (2011). Maple program to compute the graph of a planar curve defined by means of a rational parametrization. Authors: Juan G. Alcazar, Gema Maria Diaz Toca. Copyright UAH (Univ. Alcala de Henares) and UM (Univ. Murcia). 3. Toppara3D (2011). Maple program to compute the graph of a space curve defined by means of a rational parametrization. Authors: Juan G. Alcazar, Gema Maria Diaz Toca. Copyright UAH (Univ. Alcala de Henares) and UM (Univ. Murcia). Languages Spoken: English language, correctly written, fluently spoken. Other Research Merits: Reviewer Mathematical Reviews (2007-now), American Mathematical Society. Reviewer Zentralblatt Math (2007-now), European Mathematical Society. Member of the network on Symbolic Computation EACA (financed by spanish Ministerio de Educacion y Ciencia a traves del proyecto MTM E). Referee for: MACIS 2007 (Second International Conference on Mathematical Aspects of Computer and Information Sciences. Paris, France, December 5-7, 2007) and ISAAC (International Symposium on Algorithms and Computation) Referee for different papers submitted to the following journals: Journal of Symbolic Computation, Computer Aided Geometric Design. Other Education Merits: Member of the innovation group in Mathematics teaching Innovamatuah (Universidad de Alcala, ), and of the innovation group LibreTics (2009-now) Head of the innovation group in Mathematics teaching LibreTics (Universidad de Alcala, ). Participation in the following projects on innovation in Mathematics teaching: 1. Curso cero de Matematicas en Biologicas con apoyo del aula virtual, Innovation Project, Universidad de Alcala ( ). 2. Implantacion de Moodle en asignaturas de Matematicas, Innovation Project, Universidad de Alcala ( ) 3. Calculo con Geogebra y Wiris, Innovation Project, Universidad de Alcala ( ). 4. Curso cero de Matematicas con Geogebra y Wiris, Innovation Project, Universidad de Alcala ( ).

7 Other Interests: Literature, Cinema, Art

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