General Manifolds and Topology

Related lectures (30)

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Explores the transition from embedded to general manifolds, upgrading foundational concepts and discussing mathematical reasons for both approaches.

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

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Introduces d-dimensional charts on manifolds and the concept of an atlas.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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