Smooth Manifolds: Setup

Related lectures (31)

Page 2 of 4

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Delves into benign non-convexity, principal component analysis, low-rank matrix completion, and community detection in optimization.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers Hessians, symmetry, and examples related to vector fields, functions, and manifolds.

Explores how submanifolds can be deformed into linear patches using diffeomorphisms and the inverse function theorem.

Explores comparing tangent vectors and parallel transport on manifolds.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Explores convex functions, global minima, and their relationship with differentiability.