Differential Geometry and Fiber Bundles

13/01/2012 | PSIminar Talk, Perimeter Institute for Theoretical Physics

Can we capture our geometrical picture of the world in a precise mathematical language? Proximity, directions on a manifold, length – How can we do calculus on these structures? I am going to talk about the following aspects, but I am open for further questions:
– Topology: How to describe neighborhoods and holes.
– Homeomorphism: How to deform something in a continuous way.
– Standard topology of R^n: How to define its topology.
– Manifold: Which ingredients our definitions need.
– Fiberbundles: How generalize the idea of a graph.
– Tensors: How to define them coordinate independent.
– Frame bundles: How to use the Minkowski metric everywhere.
The content is also meant as a preparation for following talks on Quantum Gravity, Hopf fibration, Principal bundles and Homology/Cohomology.