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.

## Differential Geometry and Fiber Bundles

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