Leonardo F. Cavenaghi is a Brazilian mathematician currently a postdoc at the State University of Campinas (Unicamp), funded by the São Paulo Research Foundation (FAPESP), associated with the group of geometry, Lie theory, and dynamics. He defended his Ph.D. in Mathematics at the University of São Paulo (USP) (2020) under the supervision of Llohann D. Sperança e Marcos Alexandrino. He was awarded the Gutierrez Prize' and the 'CAPES thesis prize' for writing the best Ph.D. thesis in mathematics defended in 2020. He returned to Brazil for his current position after working for a year as a postdoc at the University of Fribourg (Switzerland), sponsored by the Swiss National Foundation for Sciences.His current research address goes from theoretical physics with the analytic interface: T-duality and General Relativity to Elliptic Partial Differential Equations via symmetries, Riemannian Geometry, and dynamical systems. (Source: Lattes Curriculum)
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This postdoctoral research program lies in the area of Riemannian geometry with two main focus: in the subarea of positive/non-negative curvatures, we aim via the study of the geometry and dynamics of exotic spheres, to possibly find invariants and/or hints to the existence/obstruction to metrics with such curvature assumptions on exotic manifolds and manifolds with symmetries in the form…
A procedure commonly used to construct metrics of positive or non-negative sectional curvature is the Cheeger deformation. The aim of this project is to base a generalization of this deformation, tracing its parallel with geometric analysis, in order to obtain obstruction or/and sufficient conditions for positive/nonnegative sectional curvature on principal bundles and other families of m…
The objective of project is to formulate and prove the Hodge theorem. Discussed topics include differentiable manifolds, the de Rham cohomology, integration of forms, forms on manifolds, Laplace operators and a brief introduction to Kahler manifolds. (AU)
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