Centre de recherches mathématiques - CRM Courses

The Origin of Trigonometric K-matrices in Quantum Systems - Part II

Explore the universal K-matrix and its role in quantum integrable systems with boundaries. Gain insights into trigonometric K-matrices and their applications in boundary quantum algebras.

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

Exact Results in Non-Equilibrium Statistical Mechanics - Part II

Explore advanced concepts in non-equilibrium statistical mechanics, including Work Identities, Fluctuation Theorem, and Macroscopic Fluctuation Theory. Learn how integrability techniques yield exact solutions.

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

Exact Results in Non-Equilibrium Statistical Mechanics - Part I

Explore recent advancements in non-equilibrium statistical mechanics, including Work Identities, Fluctuation Theorem, and Macroscopic Fluctuation Theory. Learn how integrability techniques yield exact solutions.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

The Origin of Trigonometric K-matrices - Part I

Explore the mathematical foundations of quantum integrability with boundaries, focusing on K-matrices and their universal properties in relation to quantum affine algebras and reflection equations.

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

How Lagrangian States Evolve into Random Waves

Explore the evolution of Lagrangian states into random waves in quantum chaos, focusing on Berry's conjecture and its implications for high-energy limits on negatively curved manifolds.

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

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

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

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

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

Explore integrability and randomization in box-ball systems. Delve into crystals, Bethe ansatz, ultradiscretization, and analytical results from TBA and GHD. Gain insights into density plateaux and current correlations.

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

Some Results for Hard Rods of Inhomogeneous Size

Explore results for hard rods of varying sizes in particle systems. Analyze hydrodynamic equations, Cauchy problems, and effective velocities in comparison to soliton gas models.

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

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

Invariant Measures for KPZ Systems with Boundaries

Explore invariant measures for KPZ systems with boundaries in this mathematical workshop presentation by Ivan Corwin.

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

Polynuclear Growth and the Toda Lattice

Explore polynuclear growth models in KPZ universality, examining integrable Markov processes and determinantal formulas governed by the non-Abelian 2D Toda lattice.

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

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

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