Differential complexes associated to locally integrable structures.

• Grant number: 20/15368-7
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): March 01, 2021
• Effective date (End): February 28, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Gerson Petronilho
• Grantee: Nicholas Braun Rodrigues
• Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 18/14316-3 - Geometric theory of PDE and multidimensional complex analysis, AP.TEM
• Associated scholarship(s): 22/01958-2 - Gevrey regularity of CR functions, BE.EP.PD

Abstract

Investigate the question of local solvability for differential complexes associated with locally integrable structures as well as the regularity of the solutions, and investigate the question of the regularity of Gevrey vectors in such structures. More specifically, study the local solvability in top-degree (where there is a natural conjecture) for complexes associated with hypo-analytical structures in the usual sense and in the sense of hyperfunctions, and investigate the regularity of Gevrey vectors in corank one locally integrable structures of tube type.