Mathematician María Amelia Salazar completed her undergraduate studies at the National University of Colombia and earned her master’s degree from the University of the Andes, also in Colombia. She earned her doctorate at Utrecht University in the Netherlands, followed by a visiting research position at the Mathematical Research (CRM) in Spain. She later embarked on research fellowships at the renowned Max-Planck Institute of Mathematics in Germany and the esteemed National Institute of Applied Mathematics in Rio de Janeiro.
Beyond her academic pursuits, Dr. Salazar is an active individual who values a balanced lifestyle. She regularly engages in physical activities such as running and swimming. A breakfast enthusiast, she starts her day with a wholesome meal prepared by her husband. Currently serving as an adjunct professor at the Fluminense Federal University, she also enjoys the company of her kitten, Félix, as part of her daily routine.”
Geometricians study objects and their symmetries, including the rotation of spheres. Lie groupoids, a powerful mathematical framework, emerge as a sophisticated tool for tackling these geometric problems by encapsulating both the objects and their symmetries in a unified language and preserving all the inherent algebraic and geometric structures. This enables us to examine seemingly disparate problems from a common perspective, revealing underlying connections and patterns. This information can be further refined using a concept known as the Lie algebroid, which serves as the “linear approximation” or “derivative” of the groupoid. Despite their seemingly simpler nature, Lie algebroids contain a wealth of information. he theory of Lie groupoids and Lie algebroids holds immense potential to amalgamate tools from geometry and algebra, yielding elegant and powerful results. Although this theory remains in its early stages of development, my project seeks to tackle fundamental questions at its core, with the potential to uncover applications in other realms of geometry and algebra.