Integrable Systems Courses and Certifications

Centre de recherches mathématiques - CRM

The Open Toda Chain with External Forcing

Explore the open Toda chain with external forcing, examining stretching and compressing effects. Learn about complete integrability and Juergen Moser's observation in this mathematical analysis.

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

Centre de recherches mathématiques - CRM

Diagonalization of Heun-Askey-Wilson Operator Leonard Pairs and Algebraic Bethe Ansatz

Explore diagonalization of Heun-Askey-Wilson operators using Leonard pairs and algebraic Bethe ansatz. Delve into eigenstates, Bethe equations, T-Q relations, and connections to Askey-Wilson polynomials.

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

Centre de recherches mathématiques - CRM

Duality, Onsager Algebra and Ising-Type Structures in Root-of-Unity Six-Vertex Models

Explore duality, Onsager algebra, and Ising-type structures in root-of-unity six-vertex models. Uncover connections between quantum group representations and symmetries in integrable systems.

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

Centre de recherches mathématiques - CRM

Spacetime Correlations of the Classical Toda Chain in Thermal Equilibrium

Explore spacetime correlations in the classical Toda chain, comparing molecular dynamics simulations with Landau-Lifshitz theory predictions based on generalized hydrodynamics.

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

Centre de recherches mathématiques - CRM

Generalised Hydrodynamics for Classical Particle Systems

Explore generalised hydrodynamics in classical particle systems, focusing on asymptotic coordinates mapping and its applications in integrable systems like box-ball and Toda.

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

Centre de recherches mathématiques - CRM

Integrability of Box-Ball Systems and Randomized Box-Ball Systems - Part 1

Explorez l'intégrabilité des systèmes de boîtes à boules et leurs versions aléatoires. Découvrez les liens avec la théorie des cristaux, l'ansatz de Bethe et l'ultradiscrétisation dans ce domaine fascinant des mathématiques.

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

Centre de recherches mathématiques - CRM

Box-Ball Systems: Reviews and Recent Developments - Lecture 1

Explore box-ball systems' integrability, combinatorial Yang-Baxter equation, and generalizations. Delve into Kirillov-Reshetikhin crystals and recent developments in boundary conditions.

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

Centre de recherches mathématiques - CRM

Direct and Inverse Scattering for the Ultradiscrete KdV Equation

Explore direct and inverse scattering methods for solving the ultradiscrete KdV equation, including the Takahashi-Satsuma Box & Ball system, using Darboux transformations and eigenfunctions.

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

Centre de recherches mathématiques - CRM

Viewpoints Brought by the Box and Ball System

Explore the box and ball system's evolution from cellular automaton to integrable system, examining its applications in traffic flow, pattern formation, and chaos through ultradiscretization and max-plus representations.

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

Kyoto-U OCW - Unofficial

Vertex Operator Algebras and Integrable Systems - Lecture 2

Delve into advanced mathematical concepts of vertex operator algebras, screening methods, W-algebras, and their applications in geometric Langlands theory and integrable systems with Boris Feigin.

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

International Centre for Theoretical Sciences

Stationary Measures for Integrable Probabilistic Systems

Explore advanced mathematical concepts in integrable probabilistic systems, focusing on stationary measures, discrete models, and their applications in theoretical physics and mathematics.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Total Positivity, Directed Networks and Integrable Cluster Dynamics - Lecture 1

Explore advanced mathematical concepts in discrete integrable systems, focusing on difference equations, cluster algebras, and their connections to theoretical physics and probability theory.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

A New Compact Formula for the Symmetric Macdonald Polynomials via the ASEP

Explore discrete integrable systems through mini-courses and workshops, covering difference equations, cluster algebras, and probabilistic models in theoretical physics and mathematics.

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

International Centre for Theoretical Sciences

Skew RSK Dynamics in Discrete Integrable Systems

Delve into discrete integrable systems, exploring soliton solutions, cluster algebras, and probabilistic models through advanced mathematical physics and theoretical applications.

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

International Centre for Theoretical Sciences

The Boundary-driven q-Hahn Process

Delve into discrete integrable systems, exploring difference equations, cluster algebras, and probabilistic models through advanced mathematical physics and theoretical applications.

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