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Positive curvatures, exotic manifolds and Riemannian foliations

Grant number: 22/09603-9
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): October 01, 2022
Effective date (End): September 30, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Lino Anderson da Silva Grama
Grantee:Leonardo Francisco Cavenaghi
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


This postdoctoral research program lies in the area of Riemannian geometry with two main focus: in the subarea of positive/non-negative curvatures, we aim via the study of the geometry and dynamics of exotic spheres, to possibly find invariants and/or hints to the existence/obstruction to metrics with such curvature assumptions on exotic manifolds and manifolds with symmetries in the form of group actions and/or singular Riemannian foliations; in the subarea of homogeneous or locally symmetric spaces, we seek to classify Riemannian foliations on these manifolds. Proofs of concept of the expected success of this research are explicitly given through all the text.

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