Low-dimensional topology

Related lectures (10)

Covers 3-dimensional Anosov flows, exponential mixing, transfer operators, and equilibrium measures.

Explores shell components in transcendental parameter planes and attracting cycles.

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Explores divergence theory, surface integrals, and volume computation using spherical coordinates and parametrizations.

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

Explores classifications of flow based on stability, fluctuations, compressibility, and viscosity.

Explores intermittency corrections to the K41 theory in turbulence and the breakdown of self-similarity.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

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