This project deals with questions regarding solvability and regularity for some classes of Partial Differential Equations. In the class of involutive systems, we want to study, with emphasis on hypocomplex structures, the top-degree solvability for the associated differential complex. Our goal is to extend techniques already obtained by the candidate in his doctoral thesis  to other classes of ultradifferentiable functions.In the context of vector fields, we are interested on systems of vector fields introduced in a paper by Meziani in 2017 . We are particularly interested in studying solvability and regularity of the solutions in the context of ultradifferentiable classes, as well as extending the results obtained by Meziani on the torus to the context of compact Lie groups in general. M.R. Jahnke, Top-degree solvability for hypocomplex structures and the cohomology of left-invariant structures on compact Lie groups. Ph.D. Thesus, University of São Paulo, 2018.: A. Meziani, Normalization and solvability of vector fields near trapped orbits. Transactions of the American Mathematical Society, 369(5):3325-3354, 2017.
News published in Agência FAPESP Newsletter about the scholarship: