Manifold

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Related lectures (31)

Page 3 of 4

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

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

Covariant derivatives along curves

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

Manifolds and Tangent Space

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

Manopt: Optimization Toolbox for Manifolds

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Smooth maps and differentials: Differentials

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

Group Theory in Physics

Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.

Momentum methods and nonlinear CG

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

Differentiating Vector Fields: Definition

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

Diophantine Approximation on Manifolds: Lower Bounds

Covers Diophantine approximation on manifolds with a focus on lower bounds.