Lectures related to Symplectic geometry

Non-linear dynamics

Explores practical applications in nonlinear dynamics, emphasizing symplectic integration methods and thin lens approximations for accurate computations in accelerator physics.

Symplectic Geometry

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

The Weil Representation: Part 2

Covers the Weil representation, Heisenberg group actions, and symplectic group concepts.

Symplectic Rigidity: Forms of Symplectic Rigidity

Explores symplectic rigidity, including rigidity, flexibility, and dynamical rigidity, with a focus on symplectic manifolds and Lagrangian submanifolds.

Essential Coexistence Phenomenon in Hamiltonian Dynamics

By Yakov Pesin delves into the essential coexistence phenomenon in Hamiltonian dynamics, exploring types I and II and providing examples and proofs.

Periodic Orbits of Hamiltonian Systems

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Weil Representation and Heis Operators

Covers the Weil representation, Heis operators, Stone-Neumann theorem, unitary operators, Lie algebra structure, and symplectic form.

Non-linear dynamics: phenomenology, tools and methods

Explores Hamiltonian and Lagrangian formulations, canonical variables, Lie operators, and their applications in beam dynamics and nonlinear systems.

Riemannian Trust Regions framework

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

Volume Growth of Positive Contactomorphisms

Covers the growth of positive contactomorphisms in Legendrian spheres and symplectic forms.

Gateways to the Moon and Local Floer Homology

Explores the problem of a falling stone hitting the moon, focusing on gateways to the moon and local Floer homology.

Embedded Submanifolds: Stiefel Manifold

Covers embedded submanifolds, Stiefel manifold, tangent spaces, and differential ranks.

Riemannian Geometry: Robot Motion Learning and Control

Delves into Riemannian geometry for robot motion learning and control, emphasizing geodesic synergies and the configuration space manifold.

Harmonic Oscillator: Numerical Stability Analysis

Explores the numerical stability of the harmonic oscillator and the importance of improving digital diagrams.

Periodic Orbits of Hamiltonian Systems

Explores periodic orbits in Hamiltonian systems and their stability under various conditions.

Canonical Transformations: Properties and Applications

Explores canonical transformations, their properties, and applications in Hamiltonian mechanics, emphasizing their role in simplifying the analysis of complex systems.

Canonical Transformations 2

Explores canonical transformations, symplectic matrices, and the concept of identity in matrix space.

Riemannian connections: Proof sketch

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.