Introduction to the applications of algebraic topology in physics

• Grant number: 16/06553-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2016
• End date: May 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Murilo Barbosa Alves
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 14/03721-3 - Differential homology and cohomology, gerbes and applications, AP.JP

Abstract

In the previous project, the candidate Murilo studied the rigorous geometrical foundations of analytical mechanics, in particular about the Lagrangian and Hamiltonian formulation of classical mechanics. With the project under submission we would like to keep on studying the foundations of classical physics, investigating the applications of algebraic topology to electromagnetism. Moreover, we will deal with some modern developments of such a topic, about the Aharonov-Bohm effect and the semi-classical description of D-branes in string theory. (AU)