Centre de recherches mathématiques - CRM Courses

Complexity of Submanifolds and Colding-Minicozzi Entropy

Explore Colding-Minicozzi entropy's role in analyzing submanifold complexity and its applications to mean curvature flow singularities and hypersurface simplicity.

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

A Journey from Statistical Mechanics to Number Theory

Explore connections between statistical mechanics and number theory, focusing on the Riemann zeta function and its relation to phase transitions in disordered systems.

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

R-matrices for the Category O of Quantum Loop Algebras

Explore R-matrices for quantum loop algebras' category O, examining a functor relating Uq(g) and Uh(g) categories, and analyzing resulting R-matrices' properties and factorization.

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

Reducible but Indecomposable Representations in Mathematical Physics

Explore representation theory in non-unitary physical systems, focusing on reducible but indecomposable representations and their importance in statistical loop models and CFT.

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

K-tilings of the Aztec Diamond

Explore K-tilings of the Aztec diamond, a fascinating mathematical concept in integrable systems and exactly solvable models.

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

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

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

Universal K-matrix and Fused K-operators in Quantum Affine Algebras

Explore universal K-matrices and fused K-operators in quantum algebras. Delve into the construction of transfer matrices and their applications to open spin-chains.

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

Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part II

Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial crystal definitions in statistical mechanics and representation theory.

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

New Solutions to the Tetrahedron Equation Associated with Quantized Six-Vertex Models

Explore new solutions to the tetrahedron equation RLLL = LLLR, focusing on quantized six-vertex models and their connections to q-oscillator and q-Weyl algebras.

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

Crystal Bases in Statistical Mechanics, Representation Theory and Combinatorics - Part I

Explore crystal base theory applications in symmetric functions and cyclic sieving through combinatorial definitions, enhancing understanding of statistical mechanics and representation theory.

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

The Origin of Trigonometric K-matrices - Part III

Explore the universal K-matrix in quantum integrable systems with boundaries, focusing on its role in generating trigonometric K-matrices for finite-dimensional representations.

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

Exact Results in Non-Equilibrium Statistical Mechanics - Part IV

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

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

Cluster Algebras and Hyperbolic Geometry

Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.

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

Exact Results in Non-Equilibrium Statistical Mechanics - Part III

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

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video