Geometric and Dynamical aspects of Rough Path Theory with jumps.

• Grant number: 24/21223-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2025
• End date: March 31, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: João Pedro Shimizu Rodrigues
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications, AP.TEM

Abstract

The project intends to bring up an international level mathematician on stochastics and rough path theory. The initial stage of the process require familiarization with the analysis involved in these equations, with differential geometry an processes on fibre bundles. Within this area the thesis of the project is a response to the following problems (giving emphasis on the first or the last depending on the development of the research): 1) Aspects of the dynamics of rough paths with jumps and 2)Lévy processes in Riemannian manifolds (AU)