Hamiltonian Systems Courses and Certifications

International Mathematical Union

Structure-Preserving Model Order Reduction of Hamiltonian Systems

Explore structure-preserving model order reduction for Hamiltonian systems, focusing on symplectic geometry and reduced basis algorithms. Learn about extensions to nonlinear problems and applications in plasma physics.

• YouTube
• 45 minutes
• On-Demand
• Free Video

IPhT-TV

Hamiltonian Systems and Dubrovin-Frobenius Manifolds - Lecture 2

Explore Hamiltonian systems and Dubrovin–Frobenius manifolds in this advanced mathematics lecture, part of the TRSalento 2022 school series.

• YouTube
• 4 hours 1 minute
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Integrable Hamiltonian Systems from Poisson Reductions of Doubles: Quasi-Poisson Double Case - Part 3

Delve into advanced mathematical concepts of integrable Hamiltonian systems, focusing on Poisson reductions of doubles and their applications to SU(n) cases with quasi-Poisson structures.

• YouTube
• 1 hour
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Integrable Hamiltonian Systems from Poisson Reductions of Doubles: Ruijsenaars-Schneider Systems - Part 2

Delve into advanced mathematical concepts of Poisson reductions in Heisenberg doubles, exploring degenerate integrability and Ruijsenaars-Schneider systems with applications to many-body physics.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Integrable Hamiltonian Systems from Poisson Reductions of Doubles - Part 1

Delve into advanced mathematical concepts of integrable Hamiltonian systems, exploring Poisson reductions, classical doubles, and their applications in semisimple Lie groups and cotangent bundles.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Conference GSI

Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta Methods

Explore advanced numerical methods for simulating Hamiltonian systems using Mono Implicit Runge-Kutta techniques, enhancing accuracy and efficiency in scientific computations.

• YouTube
• 40 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Hamiltonian Structure of Rational Isomonodromic Deformation Systems and Mathematical Physics

Explore advanced mathematical physics through lectures on Hamiltonian systems, quantum field theory, integrable systems, and modern applications in quantum computing and cryptography.

• YouTube
• 3 days 59 minutes
• On-Demand
• Free Video

ICTP Mathematics

On the Stability and Instability of Elliptic Equilibria and Invariant Quasi-Periodic Tori of Real Analytic Hamiltonians

Explore the stability and instability of elliptic equilibria and invariant quasi-periodic tori in real analytic Hamiltonian systems with expert Bassam Fayad.

• YouTube
• 55 minutes
• On-Demand
• Free Video

BIMSA

On the Stability and Instability of Elliptic Equilibria and Invariant Quasi-Periodic Tori of Real Analytic Hamiltonians

Explore stability and instability of elliptic equilibria and invariant quasi-periodic tori in real analytic Hamiltonian systems with expert Bassam Fayad.

• YouTube
• 1 hour
• On-Demand
• Free Video

Institute for Advanced Study

Geometry and Integrability of Hamiltonian and Gradient Flows

Explore the connections between integrable Hamiltonian flows, gradient flows, and combinatorial geometry, focusing on the Toda lattice system and its relation to convex polytopes and total positivity theory.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Ross Dynamics Lab

Integrable and Non-Integrable Hamiltonian Systems - KAM Tori - Poincare Sections - Poisson Brackets

Explore integrable and non-integrable Hamiltonian systems, KAM theory, Poincaré sections, and Poisson brackets in this advanced dynamics lecture, offering insights into complex nonlinear systems and their behavior.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Ross Dynamics Lab

Center Manifolds for Hamiltonian Systems and PDEs - Lorenz System Bifurcation, Part 2

Explore center manifolds in Hamiltonian systems and PDEs, including Lorenz system bifurcation, unstable directions, and applications to flame front evolution and celestial mechanics.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Hamiltonian Structure of Rational Isomonodromic Deformation Systems

Explore Hamiltonian structure of rational isomonodromic deformation systems, focusing on applications in physics and integrability properties of nonlinear differential equations.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Conference GSI

Canonical Hamiltonian Systems in Symplectic Statistical Manifolds

Explore canonical Hamiltonian systems within symplectic statistical manifolds, delving into advanced mathematical concepts and their applications.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Ross Dynamics Lab

Hamiltonian Systems Introduction - Why Study Them?

Explore Hamiltonian systems and their advantages in mechanics. Learn about generalized momentum, canonical equations, and the transformation from Lagrangian to Hamiltonian formalism.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video