Brian Grajales
Address:
Universidade Estadual de Maringá, Departamento de Matemática, sala 118. Avenida Colombo, 5790, Campus Universitário, 87020-900 Maringá, PR – Brazil.
Contact:
Online research profiles:
About me
I am Colombian mathematician interested in Differential Geometry and Lie Theory, particularly in studying Riemannian Geometry on homogeneous spaces. I am currently a member of the research group in Lie Theory at the State University of Maringá, the Research Group in Mathematics at the University of Pamplona, and the ICMAM Latin America research group.
Publications and Preprints
Preprints
Grajales, B. and Grama, L. A Geometric characterization of the center of a compact Lie algebra. Preprint.
Mora, J. A., Grajales, B., Terra Cunha, M. and Grama, L. Characterizing optimal-speed unitary time evolution of pure and quasi-pure quantum states. https://doi.org/10.48550/arXiv.2408.07794.
Grajales, B., Saavedra, J. and Rondón, G. Riemannian Geometry of G_2-type Real Flag Manifolds. https://doi.org/10.48550/arXiv.2401.02805.
Cardona, D., Grajales, B. and Ruzhansky, M. On the sharpness of Strichartz estimates and spectrum of compact Lie groups. https://doi.org/10.48550/arXiv.2302.04139.
Papers
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
Grajales, B. and Saavedra, J. A Note on Homogeneous Geometry of G_2-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 2022 Latin America. 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
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 G_2, 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.
Other professional activities
President of the ICMAM (2022-2024).
Life member of the ISAAC.
Visiting researcher at the Analysis and PDE Center (Ghent University), from December 21st, 2022 to February 20th, 2023.
Here is a list of some events I was part of the organizing committee.
ICMAM Latin America 2024, October 14th-18th, 2024.
ICMAM Latin America Satellite Conference on Analysis and PDE 2023, October 10th-14th, 2023.
Microlocal day #8, February 17th, 2023.
International Conference: Multidisciplinary Aspects in Mathematics and its Applications (ICMAM) 2022, Latin America, October 25th-28th, 2022.
International Conference: Multidisciplinary Aspects in Mathematics and its Applications (ICMAM) 2020, Latin America, October 29th-31st, 2020.