Concept
Diffeomorphism
Related lectures (28)
Conformal Field Theory: Stress Tensor & Ward Identities
Explores the invariance of quantum/statistical field theory under conformal transformations and the stress tensor properties.
Smooth sets and functions: Example - atlas for a circleMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.
Local FramesMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers the concept of local frames, their construction, and limitations.
Local Inversion Theorem
Explores the local inversion theorem, demonstrating uniqueness of solutions and continuity of functions.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Small Scale Stability: Equilibrium Point
Covers small scale stability at equilibrium points in dynamical systems for engineers.
Small Scale Stability: Equilibrium Point
Discusses stability analysis of equilibrium points in dynamical systems.
Gradients on Riemannian submanifolds, local frames
Discusses gradients on Riemannian submanifolds and the construction of local frames.
Advanced analysis II: local inversion theorem
Covers the local inversion theorem and uniqueness of solutions in a ball around a point.
Cohomology Operations: Cup Products and Bockstein
Explores cup products, Bockstein homomorphisms, and Steenrod algebra in cohomology.