Dr. Efrén Morales Amaya

  Curriculum Summary

 Efrén Morales Amaya

 Dr. Efrén Morales Amaya is a Full Professor C at the Faculty of Mathematics, Acapulco node, of the Autonomous University of Guerrero. He is a Mathematician from the Faculty of Sciences of the National Autonomous University of Mexico (UNAM, 1998). He entered directly from his undergraduate degree into the PhD program in Sciences, specializing in Basic Mathematics, at the Center for Research in Mathematics CIMAT A. C. in Guanajuato and in 1999 obtained his PhD degree. He completed a 2-year postdoctoral stay at the Institute of Mathematics of the UNAM, Cuernavaca Unit and, subsequently, a postdoctoral stay at University College London, London, United Kingdom, in 2001, where he collaborated with the famous British mathematician David George Larman. Both stays were funded by CONACyT. He started working at CIMAT in 2002, through a CONACYT repatriation chair, where he worked until 2005.

Dr. Morales's areas of expertise are Geometry (Discrete, Convex, and Differential) and Topology.

In 2000, he joined the National System of Researchers (SNI) of CONACYT-Mexico as a candidate for National Researcher. In 2004, he obtained Level I status and has held this status continuously ever since. Dr. Morales has held the Desirable Profile of the Program for the Improvement of Teaching Staff (PROMEP) of SEP-Mexico since 2008 and is the coordinator of the training faculty in Differential Geometry and Methods of Physics and Mathematics. Professor Morales has supervised 5 Master's theses and 7 Bachelor's theses.

He has been a referee for the Journal of Convex Analysis.

Dr. Morales is an evaluator for the Council for the Accreditation of Mathematics Educational Programs, A.C.

Dr. Morales has conducted several research stays and given scientific lectures at internationally renowned universities in cities in Spain, Hungary, Austria, the Czech Republic, the United States, Canada, England, Israel, Colombia, and Cuba.

 Chemnitz University of Technology, Germany; November-December 1996.

Vienna University of Technology, Austria; November-December 2004.

Alfréd Rényi Institute, Budapest, Hungary; September 2004.

University College London, United Kingdom; Sabbatical, January-December 2014.

Antonio Nariño University, Federmán, Bogotá, Colombia. July 2016.

University of Holguín, Holguín, Cuba. June 2018.

 Scientific conferences at international events.

[1998] Minimal fixing system of convex bodies. Julio 1998. Halifax, Nova Scotia, Canada.

[2000] Characterizations of the sphere and the ellipsoid. Festival of Geometry in honor of Victor Klee and Branko Grunbaum, 2000. Mar de Galilea. Israel. 

[2004] Variations of Classic Characterizations of Ellipsoids and a Short proof of the False Centre Theorem. Geometric Tomography, Alicante, España, octubre de 2004.

[2004] Variations of Classic Characterizations of Ellipsoids and a Short proof of the False Centre Theorem. Alfred Renyi's Institute of Mathematics. Budapest, Hungría. noviembre de 2004.

[2004] Characterizations of Ellipsoids, Universidad Técnica de Viena, Viena, Austria. diciembre de 2004. 

[2006] A generalization of Rogers's Theorem and a characterization of ellipsoid I, Banff International Research Station, Banff, Canada. marzo de 2006.

[2008] Shaken Rogers's Theorem for Homothetic Sections, Departamento de Matemáticas de University College London, Londres, Inglaterra, Febrero del 2008.

[2009] Characterization of Ellipsoids by Means of Parallel Translated Sections, Banff International Research Station, Banff, Canadá, enero de 2009.

[2010] Only solid spheres admit a false axis of revolution. Convexity and Combinatorics AMS Special Session November 6–7, 2010, Richmond, Virginia. EUA.

[2016] Sobre las simetrías de conjuntos convexos a partir de las simetrías de sus secciones transversales. Universidad Antonio Nariño; Bogotá, Colombia del 2016.

[2016] Sobre las simetrías de conjuntos convexos a partir de las simetrías de sus secciones transversales. Universidad de Holguín; Holguín, Cuba. Julio del 2016.

[2019] Characterizations of the sphere by means of visual cones: an alternative proof of Matsuura's theorem. Conference: Helly and Tverberg type Theorems. Octubre-2019. Casa Matemática Oaxaca,  Banff International Research Station for mathematical innovation and discovery BIRS. Oaxaca. México.

[2023] On Barker-Larman Conjecture relative to a convex body with centrally symmetric sections. Junio-2023. Casa Matemática Oaxaca,  Banff International Research Station for mathematical innovation and discovery BIRS. Oaxaca. México.

[2025]  “Characterizations of Special Convex Bodies in Terms of Support Cones", Analysis and Convex Geometry Week at UniAndes, Febrero 17-21, 2025 Bogotá, Colombia.

https://math.uniandes.edu.co/eventos/2025/Analysis&ConvexGeometry/#talks

 Dr. Morales has published 14 research articles in prestigious international peer-reviewed journals. Three more articles have been accepted for publication, and three are currently in the peer-review process.

Published Research Articles:

1.    Arocha, GL, Montejano, L, Morales, E (1996) A quick proof of Höbinger-Burton-Larman’s Theorem. Geom Dedicata 63: pp. 331-335.

2.    V. Boltyanski, E. Morales Amaya, Minimal fixing systems for convex bodies, Journal of Applied Analysis 1, 1 (1995), pp. 1–11.  

3.    V. G. Boltyanski, E. Morales Amaya: Cardinalities of Primitive Fixing Systems for Convex Bodies. Discrete & Computational Geometry 24(2-3): 209-218 (2000).

4.   L. Montejano and E. Morales, Characterizations of ellipsoids and polarity in convex bodies. Mathematika 50 (2003) 63-72.

5.    J. Jeronimo-Castro, L. Montejano and E. Morales. Shaken Rogers theorem for homothetic sections. Canadian Mathematical Bulletin, ISSN 0008-4395, Vol. 52 (3), 2009, Pags. 403-406.

6.    J. Jerónimo-Castro, L. Montejano, E. Morales-Amaya Only Solid Spheres Admit a False Axis of Revolution.  Journal of Convex Analysis  Volume 18 (2011) 505—511.

7.    L. Montejano and E. Morales, Variations of classic characterizations of ellipsoid and a short proof of the false centre theorem,  Mathematika 54 (2007), 37-42.

8.    L. Montejano and E. Morales, Shaken False Centre Theorem I, Mathematika 54 (2007), 43-48.

9.    D. Larman and E. Morales Amaya. On the false pole problem. Monatshefte für Mathematik 2007, Volume 151 (4), 271-286.

10.  D. Larman, L. Montejano and E. Morales: `Characterization of Ellipsoids by Means of Parallel Translated Sections'.  Mathematika (2010), 56: 363-378.

11. R. Abreu-Blaya, J. Bory-Reyes, E. Morales Amaya, J. M. Sigarreta Almira, Criteria for self-conjugateness of differential forms on bounded domains. Revista de la Unión Matemática Argentina Vol. 60 No. 1 (2019) Pags. 247-256. 

12. Morales-Amaya, E., Jerónimo-Castro, J. and Verdusco Hernández, D. J.. "A characterization of centrally symmetric convex bodies in terms of visual cones" Advances in Geometry, vol. 22, no. 4, 2022, pp. 481-486. https://doi.org/10.1515/advgeom-2022-0006

13. I. González-García, J. Jerónimo-Castro, E. Morales-Amaya, and D. J. Verdusco-Hernández. Sections and projections of nested convex bodies. Aequat Math. 96 (2022) 885-900. https://doi.org/10.1007/s00010-022-00884-4

14. I. González-García, J. Jerónimo-Castro, E. Morales-Amaya, and D. J. Verdusco-Hernández. A characterization of the ellipsoid through planar grazes. Mathematika Vol. 69 no. 1 (2022), pp. 100-105. https://doi.org/10.1112/mtk.12176

 15. Jerónimo-Castro, J., Jimenez-Lopez, F.G. & Morales-Amaya, E. Some Results About Equichordal Convex Bodies. Discrete Comput Geom 70, 1741–1750 (2023). https://doi.org/10.1007/s00454-023-00543-8

16. González-García, I., Jerónimo-Castro, J., Jiménez-Desantiago, V., & Morales-Amaya, E. (2024). Convex Bodies with Equipotential Circles. The American Mathematical Monthly, 132(3), 251–260. https://www.tandfonline.com/doi/full/10.1080/00029890.2024.2434439

  17. Morales-Amaya, E., Mondragón, G. & Jerónimo-Castro, J. On characteristic properties of the ellipsoid in terms of circumscribed cones of a convex body. Bol. Soc. Mat. Mex. 31, 57 (2025). https://doi.org/10.1007/s40590-025-00736-6

 18. Jerónimo-Castro, J., Morales-Amaya, E. & Verdusco-Hernández, D.J. Characterizations of the Sphere by Means of Point-Projections. Discrete Comput Geom 73, 887–895 (2025). https://doi.org/10.1007/s00454-024-00712-3

19. Alfonseca, M. Angeles, Cordier, M., Jerónimo-Castro, J. and Morales-Amaya, E.. "Characterization of the sphere and of bodies of revolution by means of Larman points" Advances in Geometry, vol. 24, no. 2, 2024, pp. 247-262 https://doi.org/10.1515/advgeom-2024-0007

20. Morales-Amaya, E. Convex bodies with pairs of sections associated by reflections. Beitr Algebra Geom (2025). https://doi.org/10.1007/s13366-025-00806-w