General Manifolds: A First Look

Related lectures (31)

Page 3 of 4

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Explores gradient descent with memory, momentum methods, conjugate gradients, and nonlinear CG on manifolds.

Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Explores flow projection on stable and unstable manifolds using dual basis and Gram-Schmidt, with practical error quantification.

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

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.