Differential complexes associated to locally integrable structures.

• Grant number: 20/15368-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2021
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gerson Petronilho
• Grantee: Nicholas Braun Rodrigues
• Host 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.

Scientific publications

(4)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

RODRIGUES, N. BRAUN; CORDARO, PAULO D.; PETRONILHO, GERSON. Hypoellipticity for certain systems of complex vector fields. Journal of Differential Equations, v. 375, p. 13-pg., 2023-12-05. (18/14316-3, 20/15368-7)

JAHNKE, MAX REINHOLD; RODRIGUES, NICHOLAS BRAUN. A class of globally analytic hypoelliptic operators on compact Lie groups. JOURNAL OF GEOMETRIC ANALYSIS, v. 35, n. 9, p. 16-pg., 2025-07-10. (20/15368-7)

RODRIGUES, NICHOLAS BRAUN; DA SILVA JR, ANTONIO VICTOR. Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Spaces. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 31, n. 1, p. 30-pg., 2025-02-01. (20/15368-7)

RODRIGUES, NICHOLAS BRAUN. Smooth and Gevrey microlocal hypoellipticity for a class of hypocomplex tube structures. JOURNAL OF FUNCTIONAL ANALYSIS, v. 290, n. 2, p. 29-pg., 2026-01-15. (20/15368-7)