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Tensors, manifolds and differential geometry: applications in mechanics and relativity

Grant number: 14/15527-7
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): October 01, 2014
Effective date (End): September 30, 2015
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal researcher:Maurício Richartz
Grantee:Thiago Assumpção
Home Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil
Associated research grant:13/09357-9 - Physics and geometry of spacetime, AP.TEM

Abstract

A detailed and mathematically rigorous analysis of fundamental concepts of Mathematical Physics is proposed, including applications in Relativity and Mechanics. The research proposal initially includes the study of multilinear algebra, tensors and basic topology. Subsequently, Differential Geometry will be the main focus - differentiable manifolds, tangent spaces, curvatures, differential forms, integration and Stokes theorem will be studied. In the project's last stage, the student will conduct an introductory study of General Relativity and Hamiltonian formalism of Classical Mechanics, applying the previously developed concepts. At the end of the project, the student is expected to have a solid background on Differential Geometry which will allow him, in the future, to continue his studies in Physics or Mathematics.

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