Address:
Universidade Estadual de Maringá, Departamento de Matemática, sala 118. Avenida Colombo, 5790, Campus Universitário, 87020-900 Maringá, PR – Brazil.
Contact:
Research profiles:
About me
I am a Colombian mathematician specializing in Differential Geometry and Lie Theory, currently an adjunct professor in the Department of Mathematics at the State University of Maringá (Brazil). At the same institution, I belong to the research group in Lie theory. Additionally, I serve as Vice President of ICMAM Latin America, an international community promoting mathematical research and collaboration across developing countries.
Publications and Preprints
Preprints
Grajales, B. and Grama, L. A Geometric characterization of the center of a compact Lie algebra. Preprint.
Papers
Grajales, B., Saavedra, J. and Rondón, G. Riemannian Geometry of G2-type Real Flag Manifolds. Eur. J. Math. 11,59 (2025). https://doi.org/10.1007/s40879-025-00848-3.
Grajales, B., Grama, L. and Prado, R. F. Geodesics on adjoint orbits of SL(n,R). Commun. Contemp. Math. 27(1) (2025). https://doi.org/10.1142/S0219199724500019.
Grajales, B. and Grama, L. Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands. Ann. Mat. Pura Appl. 203(6) (2024): 2741- 2768. https://doi.org/10.1007/s10231-024-01464-w.
Cardona, D., Delgado, J. Grajales, B. and Ruzhansky, M. Control of the Cauchy problem on Hilbert spaces: A global approach via symbol criteria. Commun. Pure Appl. Anal. 22(11) (2023): 3295-3329. https://doi.org/10.3934/cpaa.2023113.
Grajales, B. and Grama, L. Invariant Einstein metrics on real flag manifolds with two or three isotropy summands. J. Geom. Phys. 176 (2022). https://doi.org/10.1016/j.geomphys.2022.104494.
Grajales, B., Grama, L. and Negreiros, C.J.C. Geodesic orbit spaces in real flag manifolds. Commun. Anal. Geom. 28(8) (2020): 1933-2003. https://dx.doi.org/10.4310/CAG.2020.v28.n8.a7.
Conference papers/chapter of books
Grajales, B. and Saavedra, J. A Note on Homogeneous Geometry of G2-Type Real Flag Manifolds. In: Ruzhansky, M., Torebek, B. (eds) Extended Abstracts MWCAPDE 2023. Trends in Mathematics(), vol 1. Birkhäuser, Cham (2024): 33-40. https://doi.org/10.1007/978-3-031-41665-1_4.
Grajales, B., López, E. and Hudson, M. Remarks on Gradient Yamabe Solitons. In: Ruzhansky, M., Van Bockstal, K. (eds) Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics(), vol 2. Birkhäuser, Cham (2024): 39-44. https://doi.org/10.1007/978-3-031-42539-4_5.
Books
Cardona, D. and Grajales, B. (Editors). Analysis and PDE in Latin America, ICMAM 2023-2024. To appear in Research Perspectives: Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, Cham. https://link.springer.com/book/9783031995569
Cardona, D. and Grajales, B. (Editors). Analysis and PDE in Latin America, ICMAM 2022. Research Perspectives: Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser, Cham (2024). https://doi.org/10.1007/978-3-031-73274-4.
Selected talks
A geometria dos estados quânticos, Seminários do Programa de Educação Tutorial em Matemática, Universidade Estadual de Maringá, July 4th, 2025.
Inhomogeneous Einstein metrics on complex projective spaces, Geometry Webinar AmSur/AmSul, May 23rd, 2025.
Geometria das variedades de codimensão um, Seminários do PMA, Universidade Estadual de Maringá, March 18th, 2025.
Geometry of compact cohomogeneity one manifolds, VI Jornadas Ecuatorianas de Matemática, Escuela Superior Politécnica de Chimborazo, Ecuador, November 25th-29th, 2024.
Einstein metrics on the complex projective space, Seminário da Pós-graduação, Universidade Federal de Viçosa, Brazil, September 4th , 2024.
Einstein metrics on cohomogeneity one manifolds, Primer Encuentro Colombiano de Geometría y Topología, Universidad Nacional de Colombia, Colombia, July 29th-August 2nd, 2024.
Equigeodesics on compact homogeneous spaces, VIII School and Workshop on Lie Theory, Universidade Estadual de Maringá, Brazil, December 6th-8th, 2023.
Autovalores do operador Laplaciano num grupo de Lie compacto simples, Seminários de Álgebra e Geometria, Universidade Federal Rural do Semi-Árido, Brazil, August 22nd, 2023.
The spectrum of the Laplace operator on compact simple Lie groups, Microlocal day #8, Ghent University, Belgium, February 17th, 2023.
Geometry on homogeneous spaces, Analysis & PDE Group Seminar, Ghent University, Belgium, December 23th, 2022.
An introduction to vector bundles, Ghent Geometric Analysis Seminar, Ghent University, Belgium, June 27th, 2022.
Geodesics on adjoint orbits of SL(n,R)/Pϕ, London-Ghent Microlocal Analysis Workshop, Imperial College London, United Kindom, Ghent University, Belgium, March 23th-24th, 2022.
Real flag manifolds of type G2, XI Semana da Matemática - UFCG 2021, Universidade Federal de Campina Grande, Brazil, November 24th-26th, 2021.
Aplicaciones de la Teoría de Lie a la geometría de variedades homogéneas, Encuentro Nororiental de Matemáticas 2020, Universidad de Pamplona, Colombia, November 18th-20th, 2020.
A brief survey on Riemannian manifolds with homogeneous geodesics, International Conference: Multidisciplinary Aspects in Mathematics and its Applications (ICMAM) 2020, Universidad del Valle, Colombia, October 29th-31st, 2020.
Geodesic Orbit Spaces in Real Flag Manifolds, VI School and Workshop on Lie Theory, Universidade de Brasília, Brazil, August 5th-8th, 2019.
Métricas de Einstein invariantes em variedades bandeira reais, Seminário UEM-UNICAMP, Universidade Estadual de Campinas, Brazil, July 17th-18th, 2019.
Geodesic orbit spaces in real flag manifolds of classical type, XXII Congreso Colombiano de Matemáticas, Universidad del Cauca, Colombia, June 10th-14th, 2019.
Teoría de Lie y espacios homogéneos, CONVImaTE, Universidad del Valle, Colombia, December 19th-20th, 2017.
Scientific events organized
ICMAM Satellite Conference on Differential Geometry 2025, online, September 25th-26th, 2025.
ICMAM Latin America 2024, Pontificia Universidad Javeriana (hybrid), Cali, Colombia, October 14th-18th, 2024.
ICMAM Latin America Satellite Conference on Analysis and PDE 2023, online, October 10th-14th, 2023.
Microlocal day #8, Ghent University, Belgium, February 17th, 2023.
International Conference: Multidisciplinary Aspects in Mathematics and its Applications (ICMAM) 2022, Latin America, online, October 25th-28th, 2022.
International Conference: Multidisciplinary Aspects in Mathematics and its Applications (ICMAM) 2020, Latin America, online, October 29th-31st, 2020.
CONVImaTe 2019, Universidad del Valle, Cali, Colombia, December, 2019.
Students
Artur Nogueira, Undergraduate, UEM (2025-), advisor.
Daniela Ishizaki, Undergraduate, UEM (2025-), advisor.
João Marcos Bernardelli, Undergraduate, UEM (2025-), advisor