Integrable Systems Courses and Certifications

International Mathematical Union

Algebraic-Geometrical Methods in the Theory of Integrable Systems

Explore algebraic-geometrical methods in integrable systems theory with renowned mathematician Igor Krichever, delving into advanced mathematical concepts and their applications.

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

IMSA

Products of Matrices, Non-Abelian Hodge Theory, Integrable Systems, and Theories of Class S

Explore connections between Deligne-Simpson problem and Hitchin systems, delving into SCF Theories of Class S and 3D mirror symmetry in this advanced mathematics lecture.

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

International Centre for Theoretical Sciences

The Computational Theory of Riemann-Hilbert Problems - Lecture 4

Explores computational approaches to Riemann-Hilbert problems, covering Cauchy integrals, Sobolev spaces, and applications to nonlinear equations like Schrödinger and KdV, with code demonstrations and numerical solution techniques.

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

International Centre for Theoretical Sciences

Forced Integrable Systems - The Case of Sine-Gordon Equation by Vasudeva Murthy

Explore forced integrable systems, focusing on the sine-Gordon equation. Examine its applications in tectonic stress transfer and crack dynamics, with insights on boundary conditions and numerical methods.

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

International Centre for Theoretical Sciences

Basic Lectures on Bethe Ansatz - Pedagogical Lecture 2

Comprehensive lecture on Bethe Ansatz, covering integrable models, spin excitations, prethermalization, and algebraic approaches. Explores key equations, Fourier space, and the 6-vertex model for advanced physics students.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Finite-Size Effects in Integrable Systems - Lecture 3

Explore finite-size effects, revivals, and conservation laws in integrable systems. Gain insights into macro states, thermodynamic entropy, and the string hypothesis for interacting models.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Fields Institute

Gelfand-Cetlin Analogues in Integrable Systems

Explore Gelfand-Cetlin analogues in integrable systems with Lisa Jeffrey, delving into advanced mathematical concepts and their applications in toric topology.

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

Fields Institute

Lifting Torus Actions to Integrable Systems

Explore the mathematical concept of lifting torus actions to integrable systems, delving into advanced topics in Hamiltonian geometry and dynamical systems.

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

Institute for Pure & Applied Mathematics (IPAM)

Compact Formula for Symmetric Macdonald Polynomials via ASEP and TAZRP

Explore connections between particle models and Macdonald polynomials, unveiling a new compact tableau formula with applications in probability and integrable systems.

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

Institute for Pure & Applied Mathematics (IPAM)

The Squish Map and the SL_2 Double-Dimer Model

Explore measure-preserving maps between dimer models on hexagon lattices, connecting single and double-dimer models for insights into partition functions and plane partition enumeration.

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

IPhT-TV

Introduction to Quantum Integrability - Lecture 3 of 5

Explore quantum integrability concepts, focusing on advanced topics and theoretical foundations in this comprehensive lecture series.

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

Dublin Institute for Advanced Studies DIAS

A Range Three Elliptic Deformation of the Hubbard Model

Explore a systematic method for constructing integrable Lindblad systems and discover a new range 3 integrable deformation of the Hubbard model in both Hermitian and Lindbladian formulations.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

M-Seminar, Kansas State University

Solitons in Infinite Relativistic Toda System

Explore infinite relativistic Toda systems, soliton solutions, and action-angle variables in this advanced mathematical seminar on integrable systems and cluster varieties.

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

BIMSA

Integrable Systems and Representation Theory: Between Geometry, Algebra and Analysis

Explore integrable systems in Hamiltonian mechanics, quantum systems, and statistical mechanics. Examine connections to representation theory and gauge theory quantization.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Log-Canonical Coordinates on Poisson-Lie Groups

Explore log-canonical coordinates on Poisson-Lie groups and their role in cluster structures. Discover a construction method for log-canonical charts using R-matrices from Belavin-Drinfeld classification.

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