Geometry of foliations via foliated Brownian motion

• Grant number: 22/00284-8
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2022
• End date: October 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Andrey Jhen Shan Chen
• 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
• Associated scholarship(s): 23/08713-8 - Stochastic PDEs: from singularity to large scale behavior, BE.EP.DD

Abstract

Study dynamics and geometry in foliated spaces via stochastic calculus in foliation. In this context, relate: stability in the sense of Lyapunov exponents of a brownian clad motion, foliated approximation, relation with curvature, geometric entropy and dynamic entropy. (AU)