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Vector fields, sums of squares and Bers-Vekua equations: existence and regularity of solutions

Grant number: 21/03199-9
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): May 01, 2021
Effective date (End): April 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Adalberto Panobianco Bergamasco
Grantee:Bruno de Lessa Victor
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM

Abstract

This project mainly consists of two research areas we intend to deal with: the first one relates to global analysis on the torus in the ultradifferentiable setting; we are particularly interested in global solvability and hypoellipticity (in the Denjoy-Carleman frame) for complex vector fields and operators given by sums of squares of vector fields. The second part is concerned with infinitesimal bendings of two-dimensional surfaces with nonnegative Gaussian curvature and its connection with solvability of Bers-Vekua equations for planar complex vector fields with singularities.

News published in Agência FAPESP Newsletter about the scholarship: