Juan Francisco Torres Lopera is a Researcher affiliated with the Faculty of Mathematics and Department of Mathematics . He earned his doctorate from the University of Santiago de Compostela in 1982 with a thesis on plain semisimple homogeneous spaces, Grassmannian structures, and transversally Grassmannian foliations. His research spans Differential Geometry , Topology , and Sub-Riemannian Geometry , with a focus on Heisenberg groups, Cartan structures, and geometric transformations. His recent work examines Sub-Riemannian cut locus and Carnot Groups , while earlier studies include Non-Kähler Manifolds and Homogeneous Spaces . Collaborations include Ignacio Bajo, Alberto Martín Méndez, and Yusupdjan Khakimdjanov. Key trends in his publications include Geodesic Analysis , Conformal Transformations , and Manifold Cohomology . He has contributed to journals such as Transactions of the American Mathematical Society and ESAIM: Control, Optimization and Calculus of Variations .