Geometrical and Topological Methods in Physics
Abstract:
We will give an introduction to foundational topics in topology and geometry which feature prominently in modern applications in physics. Topics to be discussed include homotopy theory, homology and cohomology as well as bundles. These will be applied to the theory of monopoles, instantons and anomalies. Special attention will furthermore be paid to geometrical and topological aspects of Kaluza-Klein reduction of higher-dimensional theories such as string theory. In all these topics emphasis will be put on an intuitive understanding of the basic mathematical concepts and their manifold and beautiful applications to physics. If time permits we will exemplify some computational aspects with the help of modern computer algebra. The course addresses students with interest in mathematical aspects of theoretical physics and some basic knowledge of differential geometry e.g. as covered in a good course on General Relativity.