This lecture introduces the concept of geodesic convexity on Riemannian manifolds, defining convex sets and geodesically convex sets. It explores the properties of geodesically convex functions and their relation to convexity.
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Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.