Mathematics Colloquia and Seminars

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(Ehresmann Connections and the Cartan Viewpoint of Differential Geometry) Ehresmann connections are a more general and much more intuitive way to talk about parallel transport than affine connections. In this talk I'll talk about why covariant derivatives are natural in everyday life and how to transport elements of any smooth fiber space (not just tangent vectors) across a manifold (in a very intuitive way). I'll give brief introductions to affine connections, fiber bundles and principle G-bundles. If time permits, I'll discuss gauge theory and why these concepts are a centerpiece of today's understanding of physics i.e. why connections are "real objects" in our universe.