Global analysis: a study on solvability and hypoellipticity

• Grant number: 25/08642-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: March 01, 2026
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gabriel Cueva Candido Soares de Araújo
• Grantee: Gabriel Cueva Candido Soares de Araújo
• Visiting researcher: Luis Fernando Ragognette
• Visiting researcher institution: Instituto De Ciências Exatas/Icex/Ufmg , Brazil
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

We present here the plan of activities for the Visiting Researcher Luis Fernando Ragognette to ICMC-USP. This project aims to study the global solvability and global hypoellipticity in compact manifolds for operators invariant by the action of a Lie group and also for the system of vector fields associated to a locally integrable structure. Both problems will be developed in collaboration with the Proponent Researcher Gabriel Araujo. One of the problems is a continuation of the previous works and aims to study solvability and hypoellipticity of operators under the action of a Lie group and, in particular, we want to generalize results obtained before for operators of the type sum of squares. The second problem is related with systems of operators which are defined by the action of the exterior derivative in the quotient of fiber bundles and these systems are many times understood via the cohomology groups of the associated differential complex.We also describe other activities that will be done by the visiting reseacher, among them we have one minicourse, some lectures in the seminars of the proponents group and the organization of a congress. (AU)