About me
I am a postdoctoral fellow at the Institute of Mathematics, Statistics and Scientific Computing, University of Campinas (Brazil). I am 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 Differential Geometry at the State University of Campinas, the Research Group in Mathematics at the University of Pamplona, and the ICMAM Latin America research group.

Publications and Preprints

Preprints

• Grajales, B., Saavedra, J., and Rondón, G. Riemannian Geometry of G_2-type Real Flag Manifolds. arXiv:2401.02805. 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. arXiv:2302.04139v1. https://doi.org/10.48550/arXiv.2302.04139.

Published/accepted for publication

• Grajales, B. and Grama, L. Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summands. To appear in Annali di Matematica Pura ed Applicata (1923 -). https://doi.org/10.48550/arXiv.2310.03935.

• Grajales, B. and Saavedra, J.  A Note on Homogeneous Geometry of G_2-Type Real Flag Manifolds. Extended Abstracts MWCAPDE 2023. MWCAPDE 2023. Trends in Mathematics(), vol 1. Birkhäuser, Cham, 2024, pp. 33-40. https://doi.org/10.1007/978-3-031-41665-1_4.

• Grajales, B., López, E., Hudson, M. Remarks on Gradient Yamabe Solitons. Extended Abstracts 2021/2022. APDEGS 2021. Trends in Mathematics(), vol 2. Birkhäuser, Cham, 2024, pp. 39-44. https://doi.org/10.1007/978-3-031-42539-4_5.

• Grajales, B., Grama, L., and Prado, R. F. Geodesics on adjoint orbits of SL(n,R). Commun. Contemp. Math. 2024. https://doi.org/10.1142/S0219199724500019.

• 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, pp. 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, pp. 1933 - 2003. https://dx.doi.org/10.4310/CAG.2020.v28.n8.a7.

Selected talks

• 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.

• Editor of Analysis and PDE in Latin America, ICMAM 2022 Latin America, to appear in Research Perspectives: Ghent Analysis and PDE Center, Birkhäuser, 2024 (with Duván Cardona).

• 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 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.

• CONVImaTe 2019.