Geometical methods for phyiscs created by Ibere Kuntz and Christopher Fritz, University of Sussex.
Ibere Kuntz is a PhD student interested in many branches of theoretical and mathematical physics, specially in the application of geometrical and topological methods to physics. He is currently working with modifications on General Relativity.
Christopher Fritz is a PhD student interested in theoretical physics.
This course is divided in two parts. The first part will cover basically differential topology and differential geometry, including smooth manifolds, differentiable maps and curves, tangent/cotangent spaces, tangent map, flows and Lie derivatives, (pseudo) Riemannian geometry, connections, geodesics, curvature, homotopy groups. Examples from physics always will be given after a new mathematical concept has been introduced. The second part of the course is devoted to the applications. Here the machinery from the first part will be mainly used in the context of General relativity and of topological defects in condensed matter systems. I will assume no prior knowledge besides elementary physics, calculus and linear algebra, although basic group theory may be desirable but not essential. This means this course is perfect for postgraduate students.