Hamiltonian Dynamics Courses and Certifications

Fields Institute

Hamiltonian Geometry and Dynamics Behind Compressible Fluids

Explore Hamiltonian geometry and dynamics in relation to compressible fluids, delving into mathematical concepts and physical applications in fluid mechanics.

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

Inside Livermore Lab

A Physics-Based Reduced Order Model Capturing the Topology of Dynamical Manifolds

Explore a transformational approach to dynamics using the Heisenberg Scattering Transformation, applied to create fast surrogate models for 2D pulsed power liner implosions in MagLIF.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

NPTEL;  IIT Madras

Topics in Nonlinear Dynamics

Explore nonlinear dynamics through critical points, Hamiltonian systems, bifurcations, limit cycles, discrete-time dynamics, and stochastic processes. Gain insights into complex system behaviors and analysis techniques.

• YouTube
• 1 day 5 hours
• On-Demand
• Free Video

NPTEL;  IIT Madras

Topics in Nonlinear Dynamics

This is a basic course in classical mechanics at the senior undergraduate/ master's level. It covers the standard topics in this subject, including the Lagrangian and Hamiltonian formalisms. It also places the subject in the broader context of classical…

• YouTube
• 1 day 5 hours
• On-Demand
• Free Video

Ross Dynamics Lab

Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds

Explore stability of periodic orbits using Floquet theory. Learn about monodromy matrices, Floquet multipliers, and invariant manifolds in Hamiltonian systems. Understand the foundations of chaos in dynamical systems.

• YouTube
• 1 hour 13 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

Simons Institute

A Theory of Trotter Error

Explores advanced theory of Trotter error in quantum simulation, providing tighter error bounds and improved algorithms for various quantum systems and observables.

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

Institute for Advanced Study

Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg

Explore Hamiltonian Floer complexes on surfaces, connecting dynamics to Floer chain structure. Discover a new symplectic norm and geometric interpretations of chain complexes using transverse foliations.

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

Joint Mathematics Meetings

Symmetry and Asymmetry in Dynamics

Explore symmetry and asymmetry in dynamics, examining dynamical symmetry groups, Hamiltonian dynamics, and rigidity theorems. Gain insights into mathematical concepts and their applications.

• YouTube
• 55 minutes
• On-Demand
• Conference Talk

IMSA

Gromov-Hausdorff Convergence of Filtered A Infinity Categories

Explore Floer homology's dependence on Hamiltonian isotopy, its multiplicative structure, and connections to homological Mirror symmetry in formal deformation theory.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Asymmetry in Dynamics

Explore symmetries in dynamical systems and progress on Smale's conjecture about generic smooth systems having only trivial symmetries. Delve into complex analytic, Hamiltonian, and smooth dynamics.

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

Institute for Pure & Applied Mathematics (IPAM)

Introduction to Modelling Gravitational Waves from Compact Binaries

Explore gravitational wave modeling techniques for compact binary systems, covering inspiral, merger, and ringdown phases. Learn about semi-analytic models crucial for detection and analysis.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

PCS Institute for Basic Science

A New Interpretation of Laser Instabilities

Explore a novel mathematical approach to laser instabilities, uncovering their nearly Hamiltonian nature and the challenges in adiabatic elimination of atomic polarization.

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

Isaac Newton Institute for Mathematical Sciences

Hamiltonian Monte Carlo and Geometric Integration

Explore Hamiltonian Monte Carlo sampling algorithm, its applications, and underlying concepts from statistical physics, geometric integration, Bayesian statistics, and Hamiltonian dynamics.

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

Simons Institute

Using Chaos to Characterize a Programmable Analog Quantum Simulator

Explore chaos in analog quantum simulators, uncovering random behavior, estimating fidelity, and learning noise models for large-scale entangled states using Rydberg atom arrays.

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