Curriculum Vitae

Updated: January 2020

PERSONAL

Name: Juan Pablo Rada Rincón.

Date of birth: October 18, 1959.

Office address: Instituto de Matemáticas, Universidad de Antioquia. Medellín, Colombia.

e-mail: pablo.rada@udea.edu.co

DEGREES

  1. PhD in Mathematics (Universidad de Murcia, 1996). Thesis: "Covers, envelopes and open problems on the inmersion of modules in free modules", supervised by Dr. Manuel Saorín.
  2. Master in Mathematics (Universidad de Los Andes, 1989). Thesis: "Boundary problems and Fourier series", supervised by Dr. Antonio Tineo.
  3. Bachelor in Mathematics (Universidad de Los Andes, 1983). Thesis: "On finite groups", supervised by Dr. Raj Markanda.

EXPERIENCE

  1. Professor at the Universidad de Antioquia (UdeA), Medellín-Colombia, since 2012.
  2. Professor at the Universidad Simón Bolívar (USB), Caracas-Venezuela, 2008-2012.
  3. Professor at the Universidad de Los Andes (ULA), Mérida-Venezuela, 1983-2008.
  4. Visiting Professor at the University of Kentucky (UK), Lexington-USA, 2001.

RESEARCH INTERESTS

  1. Spectral Graph Theory.
  2. Chemical Graph Theory.
  3. Algebra.

SUPERVISED THESES

  1. Enery of matrices, Florencia Cubría, Master's thesis, Universidad de la República, Uruguay, 2018.
  2. Extremal values of energy and trace norm of digraphs, Juan Daniel Monsalve, PhD thesis, Universidad de Antioquia, Colombia, 2017.
  3. Bounds for the trace norm of (0,1)-matrices and digraphs, Natalia Agudelo, PhD thesis, Universidad de Antioquia, Colombia, 2017.
  4. Extremal values of VDB topological indices over graphs, Tatiana Pérez, Master's thesis, Universidad de Antioquia, Colombia, 2014.
  5. Topological indices over starlike trees, Clara Betancur, Master's thesis, Universidad de Antioquia, Colombia, 2014.
  6. Vertex-degree-based topological indices over hexagonal systems with fixed number of vertices, Lilia Berrocal, Master's thesis, Universidad Simón Bolívar, Venezuela, 2014.
  7. Pre-envelopes of commutative rings, Rafael Parra, PhD thesis, Universidad de Los Andes, Venezuela, 2011.
  8. Cotorsion pairs and adjoint functors, Diego Bravo, PhD thesis, Universidad de Los Andes, Venezuela, 2010.
  9. Cotorsion pairs and the finitistic dimension conjecture, Marco Pérez, Master's thesis, Universidad Simón Bolívar, Venezuela, 2009.
  10. Quasi-preenvelopes of rings, Carlos Parra, Master's thesis, Universidad de Los Andes, Venezuela, 2009.
  11. Upper bounds for the energy of digraphs, Elías Gudiño, Master's thesis, Universidad Simón Bolívar, Venezuela, 2009.
  12. Projective envelopes of finitely generated modules, Rafael Parra, Master's thesis, Universidad de Los Andes, Venezuela, 2008.
  13. Nonderogatory digraphs, Diego Bravo, Master's thesis, Universidad de Los Andes, Venezuela, 2006.
  14. Star-like trees, Franklin Camacho, Master's thesis, Universidad de Oriente, Venezuela, 2006.
  15. Construction of equienergetic digraphs, Williams López, Master's thesis, Universidad de Los Andes, Venezuela, 2006.
  16. Energy of digraphs, Ismael Peña, Master's thesis, Universidad de Los Andes, Venezuela, 2006.
  17. Graphs with maximum energy, Derwis Rivas, Master's thesis, Universidad de Los Andes, Venezuela, 2006.

PUBLICATIONS

  1. J. Monsalve, J. Rada, On the maximal energy among orientations of a tree, to appear in Kuwait Journal of Science.
  2. M. Bhat, S. Pirzada, J. Rada, On spectra and real energy of complex weighted digraphs, to appear in Linear Multilinear Algebra.
  3. R. Cruz, J. Rada, Extremal values of exponential vertex-degree-based topological indices over graphs, Kragujevac J. Math. 46 (1) (2022) 105-113.
  4. M. Khan, R. Farooq, J. Rada, Corrigendum to Complex adjacency matrix and energy of digraphs, Linear Multilinear Algebra 68 (1) (2020) 220-222.
  5. N. Agudelo, J. Monsalve, J. Rada, On the characterization of digraphs with given rank, Linear Algebra Appl. 587 (2020) 215-227.
  6. S. Bermudo, R. Higuita, J. Rada, Domination in hexagonal chains, Appl. Math. Comput. 369 (2020) 124817.
  7. R. Cruz, J. Monsalve, J. Rada, Maximal Augmented Zagreb index of trees with at most three branching vertices, IEEE Access, 7 (2019) 146652-146661.
  8. R. Cruz, J. Rada, The path and the star as extremal values of vertex-degree-based topological indices among trees, MATCH Commun. Math. Comput. Chem. 82 (3) (2019) 715-732.
  9. J. Rada, Exponential vertex-degree-based topological indices and discrimination, MATCH Commun. Math. Comput. Chem. 82 (1) (2019) 29-41.
  10. F. Li, Q. Ye, J. Rada, The Augmented Zagreb indices of fluoranthene-type benzenoid systems, Bull. Malays. Math. Sci. Soc. 42 (2019) 1119-1141.
  11. J. Monsalve, J. Rada, Oriented bipartite graphs with minimal trace norm, Linear Multilinear Algebra 67 (6) (2019) 1121-1131.
  12. J. Rada, S. Bermudo, Is every graph the extremal value of a vertex-degree-based topological index?, MATCH Commun. Math. Comput. Chem. 81 (2) (2019) 315-323.
  13. M. Bhat, J. Rada, Lower bounds for the energy of weighted digraphs, Linear Multilinear Algebra 67 (4) (2019) 743-755 .
  14. J. Monsalve, J. Rada, Y. Shi, Extremal values of energy over oriented bicyclic graphs, Appl. Math. Comput. 342 (2019) 26-34.
  15. R. Cruz, C. Marín, J. Rada, Vertex-degree-based topological indices over trees with two branching vertices, Kragujevac J. Math. 43 (3) (2019) 399-411.
  16. F. Li, H. Broersma, J. Rada, Y. Sun, Extremal benzenoid systems for two modified versions of the Randic index, Appl. Math. Comput. 337 (2018) 14-24.
  17. N. Agudelo, J. Rada, M. Rivera, Upper bound for the trace norm of the Laplacian matrix of a digraph and normally regular digraphs, Linear Algebra Appl. 552 (2018) 194-209.
  18. R. Cruz, C. Marín, J. Rada, Extremal values of Merrifield-Simmons index for trees with two branching vertices, Kragujevac J. Math. 42 (1) (2018) 97-106.
  19. M. Khan, R. Farooq, J. Rada, Complex adjacency matrix and energy of digraphs, Linear Multilinear Algebra 65 (11) (2017) 2170-2186.
  20. R. Cruz, F. Duque, J. Rada, Extremal values of the number of inlets and number of bay regions over pericondensed hexagonal systems, MATCH Commun. Math. Comput. Chem. 78 (2) (2017) 469-486.
  21. J. Rada, Extremal properties of hexagonal systems, MATCH Commun. Math. Comput. Chem. MCM 20. Bounds in chemical graph theory-Mainstreams, Univ. Kragujevac, Kragujevac (2017) 239-286.
  22. D. Bravo, F. Cubría, J. Rada, Energy of matrices, Appl. Math. Comput. 312 (2017) 149-157.
  23. R. Cruz, C. Marín, J. Rada, Computing the Hosoya index of catacondensed hexagonal systems, MATCH Commun. Math. Comput. Chem. 77 (3) (2017) 749-764.
  24. J. Rada, Vertex-degree-based topological indices of hexagonal systems with equal number of edges, Appl. Math. Comput. 296 (2017) 270-276.
  25. J. Rada. Energy of digraphs, MATCH Commun. Math. Comput. Chem. MCM 17. Energy of Graphs-Theory and Applications. Univ. Kragujevac, Kragujevac (2016). 237-276.
  26. J.A. de la Peña, J. Rada, On the energy of symmetric matrices and Coulson's integral formula, Rev. Colombiana Mat. 50 (2) (2016) 173-186.
  27. J. Monsalve, J. Rada, Energy of strongly connected digraphs whose underlying graph is a cycle. Proyecciones 35 (4) (2016) 395-404.
  28. R. Cruz, F. Duque, J. Rada, Hexagonal systems with minimal number of inlets. MATCH Commun. Math. Comput. Chem. 76 (3) (2016) 707-722.
  29. N. Agudelo, J.A. de la Peña, J. Rada, Extremal values of the trace norm over oriented trees. Linear Algebra Appl. 505 (2016) 261-268.
  30. J. Rada, The zig-zag chain as an extremal value of VDB topological indices of polyomino chains. J. Combin. Math. Combin. Comput. 96 (2016) 103-111.
  31. R. Cruz, J. Rada, Extremal values of VDB topological indices over catacondensed polyomino systems. Appl. Math. Sci. 10 (10) (2016) 487-501.
  32. J. Monsalve, J. Rada, Bicyclic digraphs with maximal energy. Appl. Math. Comput. 280 (2016) 124-131.
  33. N. Agudelo, J. Rada, Lower bounds of Nikiforov´s energy over digraphs. Linear Algebra Appl. 496 (2016) 156-164.
  34. J. Rada, Ordering catacondensed hexagonal systems with respect to VDB topological indices. Rev. Mat. Teor. Apl. 23 (1) (2016) 277-289.
  35. R. Cruz, J. Rada, Extremal polyomino chains of VDB topological indices. Appl. Math. Sci. 9 (108) (2015) 5371-5388.
  36. C. Marín, J. Monsalve, J. Rada, Maximum and minimum energy trees with two and three branched vertices. MATCH Commun. Math. Comput. Chem. 74 (2) (2015) 285-306.
  37. R. Cruz, T. Pérez, J. Rada, Extremal values of vertex-degree-based topological indices over graphs. J. Appl. Math. Comput. 48 (1-2) (2015) 395-406.
  38. A. Olivieri, J. Rada, A.J. Ríos, Digraphs with few eigenvalues. Util. Math. 96 (2015), 89-99.
  39. C. Betancur, R. Cruz, J. Rada, Vertex-degree-based topological indices over starlike trees. Discrete Appl. Math. 185 (2015) 18-25.
  40. R. Cruz, I. Gutman, J. Rada, Topological indices of Kragujevac trees. Proyecciones 33 (4) (2014) 471-482.
  41. J. Rada, R. Cruz, Vertex-degree-based topological indices over graphs. MATCH Commun. Math. Comput. Chem. 72 (3) (2014) 603-616.
  42. J. Rada, The linear chain as an extremal value of VDB topological indices of polyomino chains. Appl. Math. Sci. 8 (103) (2014) 5133-5143.
  43. L. Berrocal, A. Olivieri, J. Rada, Extremal values of VDB topological indices over hexagonal systems with fixed number of vertices. Appl. Math. Comput. 243 (2014) 176-183.
  44. J. Rada, R. Cruz, I. Gutman, Benzenoid systems with extremal vertex-degree-based topological Indices. MATCH Commun. Math. Comput. Chem. 72 (1) (2014) 125-136.
  45. R. Cruz, H. Giraldo, J. Rada, An upper bound for the energy of radial digraphs. Linear Algebra Appl. 442 (2014) 75-81.
  46. I. Gutman, R. Cruz, J. Rada, The Wiener index of Eulerian graphs. Discrete Appl. Math. 162 (2014) 247-250.
  47. R. Cruz, H. Giraldo, J. Rada, Extremal values of vertex-degree topological indices over hexagonal systems. MATCH Commun. Math. Comput. Chem. 70 (2) (2013) 501-512.
  48. R. Cruz, I. Gutman, J. Rada, On benzenoid systems with minimal number of inlets. J. Serb. Chem. Soc. 78 (9) (2013) 1351–1357.
  49. J. Rada, I. Gutman, R. Cruz, The energy of directed hexagonal systems. Linear Algebra Appl. 439 (7) (2013) 1825-1833.
  50. S. Pirzada, M. Bhat, I. Gutman, J. Rada, On the energy of digraphs. Bull. IMVI 3 (1) (2013) 69-76.
  51. J. Rada, R. Cruz, I. Gutman, Vertex-degree-based topological indices of catacondensed hexagonal systems. Chem. Phys. Lett. 572 (2013) 154-157.
  52. R. Cruz, I. Gutman, J. Rada, Convex Hexagonal Systems and Their Topological Indices, MATCH Commun. Math. Comput. Chem. 68 (1) (2012) 97-108.
  53. D. Bravo, E. Enochs, A. Iacob, O. Jenda, J. Rada, Cotorsion pairs in C(RMod), Rocky Mountain J. Math. 42 (6) (2012) 1787-1802.
  54. J. Rada, Bounds for the energy of normal digraphs. Linear Multilinear Algebra 60 (3) (2012) 323-332.
  55. C. Parra, R. Parra, J. Rada, Almost preenvelopes of commutative rings. Int. J. Algebra 6 (12) (2012) 595-603.
  56. R. Parra, J. Rada, Projective envelopes of finitely generated modules. Algebra Colloq. 18 (Spec 1) (2011) 801-806.
  57. E. Gudiño, J. Rada, A lower bound for the spectral radius of a digraph. Linear Algebra Appl. 433 (2010) 233-240.
  58. J. Rada, Lower bounds for the energy of digraphs. Linear Algebra Appl. 432 (2010) 2174-2180.
  59. F. Camacho, J. Rada, On the characteristic polynomial of starlike trees. Util. Math. 80 (2009) 245-261.
  60. J. Rada, The McClelland inequality for the energy of digraphs. Linear Algebra Appl. 430 (2009) 800-804.
  61. J. Rada, Nonderogatory directed windmills. Rev. Colombiana Mat. 42 (1) (2008) 61-66.
  62. I. Peña, J. Rada, Energy of digraphs, Linear Multilinear Algebra 56 (5) (2008) 565-579.
  63. J.A. de la Peña, I. Gutman, J. Rada, Retarded regular graphs are regular or semiregular. Linear Multilinear Algebra 56 (5) (2008) 507-509.
  64. J.A. de la Peña, I. Gutman, J. Rada, Estimating the Estrada Index. Linear Algebra Appl. 427 (1) (2007) 70-76.
  65. D. Bravo, J. Rada, Non-derogatory unicyclic digraphs. Int. J. Math. Math. Sci. Volume 2007 (2007), Article ID 46851, 8 pp.
  66. W. López, J. Rada, Equienergetic digraphs. Int. J. Pure Appl. Math. 36 (3) (2007) 361-372.
  67. D. Bravo, J. Rada, Coalescence of difans and diwheels. Bull. Malays. Math. Sci. Soc. 30 (1) (2007) 49-56.
  68. I. Gutman, S. Firoozabadi, J.A. de la Peña, J. Rada, On the energy of regular graphs. MATCH Commun. Math. Comput. Chem. 57 (2) (2007) 435-442.
  69. J.A. de la Peña, J. Rada, On the multiplicities of eigenvalues of a graph. Acta Math. Hungar. 114 (1-2) (2007) 91-101.
  70. B. Zhou, I. Gutman, J.A. de la Peña, J. Rada, L. Mendoza, On spectral moments and energy of graphs. MATCH Commun. Math. Comput. Chem. 57 (1) (2007) 183-191.
  71. J. Rada, Randic decomposition of catacondensed systems. Util. Math. 68 (2005) 155-164.
  72. J. Rada, C. Uzcátegui, Randic ordering of chemical trees. Discrete Appl. Math. 302 (1-3) (2005) 232-250.
  73. J. A. de la Peña, L. Mendoza, J. Rada, Comparing momenta and p-electron energy of benzenoid molecules. Discrete Math. 302 (1-3) (2005) 77-84.
  74. O. Araujo, M. Estrada, D. Morales, J. Rada, Higher order matching polynomial of a graph. Int. J. Math. Math. Sci. 2005:10 (2005) 1565-1576.
  75. E. Enochs, J. Rada, Abelian groups which have trivial absolute coGalois group. Czechoslovak Math. J. 55 (2) (2005) 433-437.
  76. J. Rada, Variation of the Wiener index under tree transformations. Discrete Appl. Math. 148 (2) (2005) 135-146.
  77. J. Rada, Energy ordering of catacondensed hexagonal systems. Discrete Appl. Math. 145 (3) (2005) 437-443.
  78. J. Rada, Hexagonal systems with extremal connectivity index. MATCH Commun. Math. Comput. Chem. 52 (2004) 167-182.
  79. J. Rada, Second Order Randic Index of Benzenoid Systems. Ars Combin. 72 (2004) 77-88.
  80. J. Rada, A. Tineo, Upper and lower bounds for the energy of bipartite graphs. J. Math. Anal. Appl. 289 (2) (2004) 446-455.
  81. J. Rada, A. Tineo, Polygonal chains with minimal energy. Linear Algebra Appl. 372 (2003) 333-344.
  82. J. Rada, O. Araujo, A recursive formula for the Randic index of a tree, MATCH Commun. Math. Comput. Chem. 49 (2003) 15-21.
  83. J. Rada, C. Uzcátegui, Randic Structure of a Graph, Discrete Appl. Math. 128 (2-3) (2003) 447-463.
  84. J. Rada, Characteristic polynomial of catacondensed systems, Linear Algebra Appl. 367 (C) (2003) 243-253.
  85. J. Rada, Bounds for the Randic Index of Catacondensed Systems, Util. Math. 62 (2002) 155-162.
  86. J. Rada, O. Araujo, Higher order connectivity index of starlike trees, Discrete Appl. Math. 119 (3) (2002) 287-295.
  87. O. Araujo, J. Rada, Vertex and Edge Type Relations of Randic Index for Chemical Trees, Ars Combin. 62 (2002) 65-78.
  88. I. Gutman, O. Araujo, J. Rada, Matchings in Starlike Trees, Appl. Math. Lett. 14 (2001) 843-848.
  89. J. Rada, O. Araujo, I. Gutman, Randic index of benzenoid systems and phenylenes, Croat. Chem. Acta 74 (2001) 225-235.
  90. I. Gutman, O. Araujo, J. Rada, An identity for Randic's connectivity index and its applications, ACH-Models Chem. 137 (2000) 653-658.
  91. O. Araujo, J. Rada, Randic index and lexicographic order, J. Math. Chem. 27 (3) (2000) 201-212.
  92. I. Gutman, J. Rada, O. Araujo, The Wiener index of starlike trees and a related partial order, MATCH Commun. Math. Comput. Chem. 42 (2000) 145-154.
  93. J. Rada, M. Saorín, A. del Valle, Reflective Subcategories, Glasg. Math. J. 42 (2000) 97-113.
  94. J. Rada, M. Saorín, On two open problems about embedding of modules in free modules, Comm. Algebra 27 (1) (1999) 105-118.
  95. J. Rada, M. Saorín, Rings characterized by pre-envelopes and pre-covers of modules, Comm. Algebra 26 (3) (1998) 899-912.
  96. J. Rada, M. Saorín, On semiregular rings whose finitely generated modules embeds in free modules, Canad. Math. Bull. 40 (2) (1997) 221-230.

PUBLISHED BOOKS

  1. J. Rada, Introducción al Álgebra Lineal. Consejo de Publicaciones de la Universidad de Los Andes, 2011.
  2. J. Rada and A. Ríos. Introducción a la Teoría Espectral de Digrafos. Ediciones IVIC, 2011.

MEMBER OF THE EDITORIAL BOARD FOR

  1. MATCH-Communications in Mathematical and in Computer Chemistry.
  2. Kragujevac Journal of Mathematics.
  3. International Journal of Graph Theory and its Applications.
  4. Mathematical Aspects of Topological Indices.

REVIEWER FOR

  1. Mathematical Reviews, USA.

TALKS GIVEN IN CONFERENCES AND SEMINARS

  1. "Energy of graphs". Primer encuentro Sur Occidental de matemática y matemáticas aplicadas. Universidad del Valle, Cali, Colombia, 2019.
  2. "Oriented bipartite graphs with minimal trace norm". Encuentro de Sociedades Matemáticas de Colombia y México, Universidad del Norte, Barranquilla, Colombia, 2018.
  3. "Trace norm of directed graphs". Centro de Estudios de Matemáticas, Universidad Industrial de Santander, Bucaramanga, Colombia, 2017.
  4. "Generalizations of graph energy". Center of Combinatorics Seminar in University of Nankai, Tianjin, China, 2017.
  5. "Generalizations of graph energy". 1er Workshop en Algebra, Medellín, Colombia, 2017.
  6. "Introduction to spectral digraph theory". 7 Encuentro Regional de Matemáticas, Medellín, Colombia, 2015.
  7. "Bounds of Nikiforov's energy for digraphs". Seminario de Álgebra del IMERL, Montevideo, Uruguay, 2015.
  8. "Bounds of Nikiforov's energy for digraphs". Seminario de Álgebra del CIMAT, Guanajuato, México, 2015.
  9. "Generalization of the energy of graphs to directed graphs". International Conference in Homological Algebra, Lexington, USA, 2015.
  10. "Maximum and minimum energy trees with two branched vertices". 2da. Escuela Colombiana de Matemáticas, Medellín, Colombia, 2014.
  11. "Energy of directed hexagonal systems". ICAMI 2013, San Andrés, Colombia, 2013.
  12. "Interaction between algebra and graph theory". ASOVAC, Universidad Central de Venezuela, Maracay, 2011.
  13. "Topological indices over hexagonal systems". Rafa Fest, Bucaramanga, Colombia, 2011.
  14. "Introduction to the spectral theory of digraphs". EMALCA, Mérida, Venezuela, 2011.
  15. "Bounds for the low energy of digraphs". Banff International Research Station, Banff, Canada, 2011.
  16. ''Lower bounds of the spectral radius of a digraph''. XXIII Jornadas de Matemáticas Venezolanas; Caracas, Venezuela, 2010.
  17. ''Projective envelopes of finitely generated modules''. XXII Jornadas de Matemáticas Venezolanas; San Cristóbal, Venezuela, 2009.
  18. "Envelopes and covers of modules". EMALCA, Mérida, Venezuela, 2008.
  19. ''The McClelland inequality for the energy of digraphs''. Workshop on Spectral Graph Theory; Río de Janeiro, Brasil, 2008.
  20. ''Non-derogatory directed windmills''. XXI Jornadas de Matemáticas Venezolanas; Barquisimeto, Venezuela, 2008.
  21. ''Retarded regular graphs''. XX Jornadas de Matemáticas Venezolanas; Caracas, Venezuela, 2007.
  22. ''A generalization of the energy to digraphs''. Third International Conference on Applied Mathematics, Plovdiv, Bulgaria, 2006.
  23. ''Multiplicity of the eigenvalues of a graph''. XIX Jornadas de Matemáticas Venezolanas; Cumaná, Venezuela, 2006.
  24. "Energy of hexagonal systems", Seminario de Representaciones de Álgebras, UNAM, DF, México, 2006.
  25. "Generalization of the energy to digraphs", Joint Meeting of the Canadian and Mexican Mathematical Societies, Guanajuato, México, 2006.
  26. "Energy of hexagonal systems", Seminario de Representaciones de Álgebras, UNAM, DF, México, 2005.
  27. "Extremal values of the energy and the connectivity index over hexagonal systems". Universidad de Antioquia, Medellín, 2004.
  28. "Randic index of benzenoid systems + Abelian groups which have trivial absolute cogalois group", Seminario de Representaciones de Álgebras, UNAM, DF, México, 2001.
  29. ''Randic index of benzenoid systems and phenylenes''. The Harry Wiener International Memorial Conference on the Role of Topology in Chemistry; Athens, USA, 2001.
  30. ''Generalized Randic index sequence''. Workshop in Mathematical Chemistry; Duluth, USA, 2000.
  31. ''Reflective subcategories''. Some Trends in Algebra; Praga, Czech Republic, 1999.
  32. "Duplication of the cube". Olimpíadas Matemáticas Venezolanas; San Antonio de los Altos, Venezuela, 1998.
  33. ''Envelopes and covers of modules in arbitrary classes''. XI Jornadas de Matemáticas Venezolanas; Cumaná, Venezuela, 1998.
  34. ''Rings characterized by envelopes and covers of their modules''. Euroconference in Ring Theory; Murcia, Spain, 1998.
  35. "Rings characterized by envelopes and covers". Seminario de Álgebra, Bucarest, Rumania, 1998.
  36. ''Open problems on the inmersion of f.g. modules in free modules''. X Jornadas de Matemáticas Venezolanas; Caracas, Venezuela, 1997.
  37. ''Inmersion of cyclic and f.g. modules in free modules''. Primeras Jornadas Españolas en Teoría de Anillos; Murcia, Spain, 1996.
  38. ''Rings whose modules embed in projectives''. Some trends in Algebra; Praga, Czech Republic, 1995.

INVITATIONS

  1. Center of Combinatorics at University of Nankai, Tianjin, China, 2017.
  2. Instituto de Matemáticas y Estadística IMERL, Montevideo, Uruguay, 2015.
  3. Centro de Investigación en Matemáticas, A.C. (CIMAT), Guanajuato, México, 2015.
  4. Fronteras de la Ciencia, ASOVAC , Maracay, Venezuela, 2011.
  5. Rafa Fest, Bucaramanga, Colombia, 2011.
  6. Latin American and Caribbean School of Mathematics, Merida, Venezuela, 2011.
  7. Banff International Research Station, Banff, Canada, 2011.
  8. University of Kentucky, USA, 2010.
  9. Latin American and Caribbean School of Mathematics, Merida, Venezuela, 2008.
  10. Instituto de Matemáticas de la UNAM, México, 2006.
  11. Instituto de Matemáticas de la UNAM, México, 2005.
  12. Universidad de Antioquia, Medellín, Colombia, 2004.
  13. Instituto de Matemáticas de la UNAM, México, 2001.
  14. University of Kentucky, USA, 2001.
  15. Olimpíada Matemática Venezolana, Caracas, 1998.
  16. University of Bucharest, Romania, 1998.
  17. Universidad de Murcia, Spain, 1998.