Geometry of Control, Dynamical and Stochastic Systems (Geometry / Topology of Homogenous Spaces)

• Grant number: 23/04083-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2023
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Luiz Antonio Barrera San Martin
• Grantee: Brian David Grajales Triana
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/13481-0 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

The aim of this research proposal is to investigate the global behavior of invariant geometric flows ona special class of homogeneous spaces called real flag manifolds. This project is to be carried out at the IMECC (Unicamp) under the supervision of Luiz San Martin and Lino Grama. It will combine theirexpertise on differential geometry and Lie theory and geometric flows with the candidate's knowledgeof real flag manifolds. These problems mix algebraic tools from Lie theory and analytical techniques from geometric analysis and dynamical systems. This project has connections with the work of several other researchers from IMECC, mainly V. del Barco and E. Correa. It is also related to the research developed at the Analysis and PDE Center at Ghent University, especially with the work of M. Ruzhansky and D. Cardona.