CV

Education

Universidade de Aveiro, Aveiro, PORTUGAL

  • Doutoramento (PhD), Departamento de Matemáticas, December 2010

Tesis Topic: A Study of Singular Integral Operators with Shift

Adviser: Professor Luis P. Castro

Area of Study: Operator Theory

Universidad de Los Andes, Mérida, VENEZUELA

  • Magister Scientiae (MSc), Departamento de Matemáticas, September 2005

Thesis Topic: Operadores de Composición Inducidos por Transformaciones Fraccionales Lineales de CN, recommended for publication with honors (Composition operators induced by linear fractional maps on CN)

Adviser: Professor José Giménez

Area of Study: Operator Theory

  • Licenciatura (BSc), Departamento de Matemáticas, October 2003

. Thesis Topic: Reflexividad en espacios de Banach, recommended for publication (Reflexivity on Banach spaces)

Adviser: Professor José Giménez

Area of Study: Geometry of Banach spaces

Awards Grants and Honors

  1. Pontificia Universidad Javeriana, Proposal ID 00004980, Research Project: Algunas Generalizaciones del Teorema de Jungck (Some Generalizations of the Jungck’s Theorem), 2012

  2. Pontificia Universidad Javeriana, Proposal ID 00004934, Research Project: Estabilidad Ecuaciones de Volterra con Retardo (Stability of Volterra Equations with Delay), 2011

  3. Pontificia Universidad Javeriana, Proposal ID 00004499, Research Project: Ecuaciones Singulares Integrales (Singular Integral Equations), 2011

  4. Premio Promoción al Investigador: Nivel I (Research Promoting Award: Level I), Fundación Venezolana de Promoción al Investigador - Ministerio de Ciencia y Tecnología Venezuela 2008. The PPI Programme is a government-sponsored system that classifies Venezuelan researchers in a five-level system according to their scientific achievements, from Level 0 to Level IV (maximum)

  5. Plan II Fellowship, Vicerectorado Acádemico, Universidad de Los Andes, Venezuela, 2008. (Researcher grant)

  6. Premio de Estímulo al Investigador PEI, (Research Stimulate Award, PEI), CDCHT-ULA, 2007. These awards are destined to Universidad de Los Andes research personnel

  7. PhD Scholarship studies, Fundação para a Ciência e a Tecnologia, Portugal, 2006

Professional Experience

Universidad Nacional, Bogotá, COLOMBIA

  • Associate Professor, January 2019 to Present

Universidad Nacional, Bogotá, COLOMBIA

  • Assistant Professor, August 2014 to Present

Pontificia Universidad Javeirana, Bogotá, COLOMBIA

  • Assistant Professor, February 2011 to February 2014

Universidad de Los Andes, Mérida, VENEZUELA

  • Teaching Assistant, January 2004 to December 2006

  • Junior Teaching Assistant, January 2001 to December 2003


Communications on Conferences

International Conferences

  1. Positive Solutions of a Nonlinear Second-Order Second Order Boundary Value Problem with Three-Point Integral Boundary Conditions, The 11th International Conference on Fixed Point Theory and its Applications, Galatasaray University, Istanbul, Turkey, July 2015.

  2. On the stability of a nonlinear Volterra integral equation, 9th ISAAC Congress, Pedagogical University of Cracow, Cracow, Poland, August 2013.

  3. Solubilidad de Ecuaciones Singulares Integrales con Rotación y Núcleo Degenerado en el Caso de Coeficientes que se Anulan en el Círculo Unitario (Solvability of Singular Integral Equations with Rotations and Degenerate Kernel on the Case of Coefficients vanishing at the Unit Circle), IV Congreso Latinoamericano de Matema ́ticos, Universidad de Córdoba, Córdoba, Argentina, August 2012.

  4. On the Solutions of a Singular Integral Equation with Shift and Continuous Coefficients, 22nd International Workshop on Operator Theory and Applications, IWOTA 2011, Universidad de Sevilla, Seville, Spain, July 2011.

  5. On the Invertibility of Paired Operators within Ordered Groups, 21st International Workshop on Operator Theory and Applications, IWOTA 2010, Technische Universitat, Berlin, Germany, July 2010.

  6. Splitting Property for Singular Integral Operators with a Weighted Shift, Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2010 World Congress, INPE, São José dos Campos, Brazil, June 2010.

  7. On the Kernel Dimension of Singular Integral Operators with Weighted Shifts, Second International Conference on Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2010, Sozopol, Bulgaria, June 2010.

  8. Explicit Solutions of a Singular Integral Equation with Carlerman Shift, Advanced School on Integral Equations, IST-Universidade Técnica, Lisbon, Portugal, April 2010.

  9. A Polynomial Collocation Method to Compute the Kernel Dimension of Singular Integral Operators with Reflection, International Conference on Modern Mathematical Methods in Science and Technology, M3ST’09, Poros, Greece, September 2009.

  10. Bounds for the Kernel Dimension of Singular Integral Operators with Carleman Shift, 7th ISAAC Congress, Imperial College, London, England, July 2009.

  11. Singular Integral Operators with Flip Having Different Classes of Coefficients: Reduction and Fredholm Property, The Tenth International Conference on Integral Methods in Science and Engineering, IMSE08, Universidad de Cantabria, Santander, Spain, July 2008.

  12. Fredholm Property of Singular Integral Operators with Flip on a Weighted Lebesgue Space, Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA08, Università degli studi di Genova, Genova, Italy, June 2008.

  13. Similarity Transformation Methods for Singular Integral Operators with Reflec- tion on Weighted Lebesgue Spaces, Great Plain on Operator Theory Sympo- sium, GPOTS 2007, University of Nebraska, Lincoln, USA, May 2007.

National Conferences

  1. Ecuaciones integrales de Volterra en espacios de Lebesgue con exponente variable (Volterra integral equations on variable Lebesgue spaces), XXII Congreso Colombiano de Matemáticas, Universidad del Cauca, Popayán, June 2019.

  2. Soluciones no negativas de un sistema de Vlasov-Mawell singularmente perturbado (Non negative solutions of a singular Vlasov-Mawell system), V taller de análisis no lineal, Universidad Nacional de Colombia, Bogotá, June 2019.

  3. Problemas de Frontera y Ecuaciones Singulares Integrales en Espacios de Banach de Funciones Medibles (Boundary Value Problems and Singular Integral Equations in Banach Function Spaces of Measurable Functions), XXI Congreso Colombiano de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, July 2017.

  4. Representaciones en Coeficientes Continuos para Operadores Singulares Integrales con Desplazamiento (Continuous Representation Coefficients for Singular Integral Operators with Shift), XVII Congreso Colombiano de Matemáticas, Universidad Industrial de Santander, Bucaramanga, Colombia, July 2011.

  5. Un Estudio de Las Dilataciones no Isotrópicas de la Bola Unitaria de CN (A Study of the non Isotropic Dilations on the Unit Ball of CN), XIX Jornadas de la Asociación Matemática Venezolana, Universidad de Oriente, Cumaná, Venezuela, April 2006.

  6. Un Modelo de Transformación Fraccional Lineal en CN (A Model of Linear Fractional Maps on CN), XVIII Jornadas de la Asociación Matemática Venezolana, Universidad Central de Venezuela, Caracas, Venezuela, March 2005.

  7. Rango Numérico de Operadores de Composición (Numerical Range of Compo- sition Operators), XVII Jornadas de la Asociación Matemática Venezolana, Universidad de Los Andes, Trujillo, Venezuela, March 2004.


Courses

  1. Espacios de Lebesgue con Exponente Variable, un Espacio de Banach de Funciones Medibles (Spanish, Lebesgue Spaces with Variable Exponent. A Banach Function Spaces), XXVII Escuela Venezolana de Matemáticas EMALCA- VENEZUELA 2014, September 2014.

Seminars

  1. On the Existence of Solutions of the Limit Problem for theMagnetically Non-insulated Diode, Functional Analysis and Applications Group, University of Averio, Aveiro, Portugal, April 2022.

  2. Un modelo límite de (no) aislamiento magnetico para un diodo plano al vacío (A limit model of magnetic non-insulated vacum diode), Seminario de Ciencias Básicas, Universidad ECCI, Bogotá, Colombia, April 2022.

  3. Ecuaciones Singulares Integrales con Rotación y Núcleo Degenerado: Coeficientes que se anulan en puntos aislados (Singular Integral Equations with rotation and degenerate kernel: Coefficients vanishing in isolated points), Coloquio de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, June 2015.

  4. El Principio de Contracción de Banach y Algunas Generalizaciones (The Banach Contraction Principle and some Generalizations), Coloquio de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia, November 2014.

  5. Estabilidad de una Ecuación de Volterra (Stability of a Volterra Equation), Encuentro Javeriano de Matemáticas 2012, Pontificia Universidad Javeriana, Bogotá, Colombia, September 2012.

  6. Números de Aproximación e Invertibilidad Generalizada de un Operador Singular Integral con Involución (Aproximation Numbers and Generalized Invertibility of a Singular Integral Operator with Involution), Coloquio de Matemáticas, Universidad de Los Andes, Bogotá, Colombia, April 2012.

  7. Sobre la Aplicabilidad de Métodos Numéricos para Operadores Singulares Iintegrales con Desplazamiento (On the Applicability of Numerical Methods for Singular Integral Operators with Shift ), Seminario de Ana ́lisis PUJ-UN-UNIANDES, Universidad Nacional, Bogotá, Colombia, January 2012.

  8. Una Representación para Métodos de Aproximación de Operadores Singulares Integrales con Desplazamiento (An Approximation Methods Representation for Singular Integral Operators with Shift ), Seminario del Centro Interdisciplinario de Lógica y Álgebra, Universidad de Los Andes, Mérida, Venezuela, January 2012.

  9. La Propiedad de Fredholm para Operadores Singulares Integrales con Reflexión en Espacios de Lebesgue Ponderados (The Fredholm Property for Singular Integral Operators with Reflection on Weighted Lebesgue Spaces), Encuentro Javeriano de Matemáticas, Pontificia Universidad Javeriana, Bogotá, Colombia, September 2011.

  10. Cotas para la Dimensión del Núcleo de Operadores Singulares Integrales con Desplazamiento de Tipo Carleman (Bounds for the Dimension of the Kernel of Singular Integral Operators with Carleman shift), Coloquio de Matemáticas, Pontificia Universidad Javeriana, Bogotá, Colombia, August 2011.

  11. Fredholm Criteria for Singular Integral Operators with Carleman Shift in the Framework of Different Subclasses of Essentially Bounded Coefficients, Functional Analysis and Applications Seminar, Universidade de Aveiro, Aveiro, Portugal, February 2010.

  12. Kernel Dimension and Moore-Penrose Inverse of Singular Integral Operators with Flip Through a Numerical Analysis Approach, Functional Analysis and Applications Seminar, Universidade de Aveiro, Aveiro, Portugal, March 2009.

  13. Soluciones a una ecuación integral con desplazamiento (Solutions of an Integral Equation with Shift), Charla Análisis Functional ULA, Universidad de Los Andes, Mérida, Venezuela, November 2008.

  14. On the Solvability of Singular Integral Equations with Reflection on the Unit Circle, Functional Analysis and Applications Seminar, Universidade de Aveiro, Aveiro, Portugal, September 2008.

  15. A Fredholm Criterion for Singular Integral Operators with Reflection Via Similarity Transformation Methods, Functional Analysis and Applications Seminar, Universidade de Aveiro, Aveiro, Portugal, October 2007.

  16. Existencia de Medidas de Haar en Grupos Compactos (On the Existence of Haar Measures on Compact Groups), Charla Análisis Functional ULA, Universidad de Los Andes, Mérida, Venezuela, July 2006.

  17. Operadores Discontinuos y Teoremas de Punto Fijo (Discontinuous Operators ad Fixed Point Theorems), Charla Análisis Functional ULA, Universidad de Los Andes, Mérida, Venezuela, March 2006.

  18. Transformaciones Fraccionales Lineales en Dominios de CN (Linear Fractional Maps on Domains of CN), Charla Análisis Functional ULA, Universidad de Los Andes, Mérida, Venezuela, March 2004.

  19. RangoNumérico de Matrices (Numerical Range of Matrices), Jornadas de Charlas ULA-UCV, Universidad Central de Venezuela, Caracas, Venezuela, April 2004.

  20. Operadores de Composición en el Espacio de Hardy (Composition Operators on the Hardy Space), Charla Análisis Functional ULA, Universidad de Los Andes, Mérida, Venezuela, March 2004.


Editorial

  1. Invited editor in the volume “Nonlinear Operator Theory and Its Applications”, Journal of Function Spaces, Hindawi, 2017.

  2. Editor in “Results of Nonlinear Analysis-An international Peer Review Journal”, 2018.