Symplectic geometry

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Related lectures (32)

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Symmetry Property: Riemannian Connection in Geometry

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

Symplectic Groups

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Riemannian Hessians: Connections and Symmetry

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Curves with Poritsky Property and Liouville Nets

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

Harmonic Oscillator: Numerical Stability Analysis

Explores numerical methods for the harmonic oscillator, focusing on stability and convergence in solving oscillatory systems.

Linear Beam Dynamics

Explores particle accelerator dynamics, transfer maps, Hamiltonian equations, and phase space conservation.

Topological Polyhedron: Creating a Pavilion in TopSolid

Demonstrates creating a pavilion using a topological cube in TopSolid, emphasizing geometric accuracy and practical modeling techniques.

Canonical Transformations: Symplectic Group and Properties

Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.

Model Selection and Local Geometry

Explores model selection challenges in causal models and the impact of local geometry on statistical inference.

Geometry: Euclidean Propositions and Architectural Foundations

Explores Euclid's first proposition and its architectural implications, emphasizing the enduring relevance of classical geometric principles in contemporary architectural practice.

Continuum Mechanics: Conservation Laws, Tensor Objects, and Fluid Dynamics

Covers conservation laws, tensor objects, and fluid dynamics in Continuum Mechanics.

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