Differential Geometry
The geometry of curved spaces: smooth manifolds, tangent spaces, curvature, geodesics, connections, and Riemannian metrics. Where calculus meets geometry on arbitrary surfaces.
Course Overview
Textbook |
do Carmo, Differential Geometry of Curves and Surfaces (intro) / Lee, Introduction to Smooth Manifolds (advanced) |
Chapters |
TBD |
Sections |
TBD |
Prerequisites |
|
Target |
General relativity, gauge theory, geometric deep learning |
Status |
Planned |
Chapters will be scaffolded when this course becomes active.
Why This Course
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General relativity — spacetime IS a Riemannian manifold
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Machine learning — geometric deep learning operates on manifolds
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Computer vision — shape analysis, 3D reconstruction
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Robotics — Lie groups for robot kinematics
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Physics — gauge theory, fiber bundles, Yang-Mills equations