Solvability of locally integrable structures

• Grant number: 18/12273-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2018
• End date: October 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Paulo Leandro Dattori da Silva
• Grantee: Gabriel Cueva Candido Soares de Araújo
• Host 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
• Associated scholarship(s): 19/27084-6 - Two integrability problems in the theory of involutive structures, BE.EP.PD

Abstract

This research project deals with several notions of solvability associated to systems of complex vector fields, especially those systems which are locally integrable i.e. that admit a maximal number of linearly independent first integrals, as well as solvability of complex vector fields on manifolds of dimension N\geq3. We are interested in studying questions related to local solvability (in particular in the setting of some classes of ultradifferentiable functions e.g. Gevrey or, more generally, Denjoy-Carleman classes) as well as some global questions.

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ARAUJO, GABRIEL; BERGAMASCO, ADALBERTO P.; DA SILVA, PAULO DATTORI L.. Gevrey semiglobal solvability for a class of elliptic vector fields with degeneracies. Mathematische Nachrichten, v. N/A, p. 20-pg., 2023-05-20. (18/14316-3, 18/15046-0, 18/12273-5)

ARAUJO, G.; DA SILVA, P. L. DATTORI; VICTOR, B. DE LESSA. Global Analytic Solvability of Involutive Systems on Compact Manifolds. JOURNAL OF GEOMETRIC ANALYSIS, v. 33, n. 5, p. 30-pg., 2023-05-01. (18/14316-3, 18/12273-5, 21/03199-9)

ARAUJO, GABRIEL. Global regularity and solvability of left-invariant differential systems on compact Lie groups. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 56, n. 4, p. 631-665, DEC 2019. (18/12273-5)

ARAUJO, G.; DATTORI DA SILVA, P. L.; VICTOR, B. DE LESSA. Global analytic hypoellipticity of involutive systems on compact manifolds. MATHEMATISCHE ANNALEN, v. N/A, p. 26-pg., 2022-07-18. (18/14316-3, 21/03199-9, 18/12273-5)

ARAUJO, GABRIEL; FERRA, IGOR A.; RAGOGNETTE, LUIS F.. Global solvability and propagation of regularity of sums of squares on compact manifolds. JOURNAL D ANALYSE MATHEMATIQUE, v. 148, n. 1, p. 34-pg., 2022-08-25. (18/12273-5, 16/13620-5)