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The session explains how momentum accelerates gradient descent, presents the theory of nonlinear conjugate gradients on manifolds, compares several beta‑rule updates, discusses line‑search and preconditioner choices, and shows how to employ the Manopt library for Riemannian optimization without explicit Hessians.
Delves into the invariance of domain theorem, proving that a subset homeomorphic to an open subset is open itself, with implications for embeddings and homeomorphisms.
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.
Covers the concept of intervals in Rn using geometric balls and defines open and closed sets, interior points, boundaries, closures, bounded domains, and compact sets.
