Centre de recherches mathématiques - CRM Courses

Critical Well-Posedness for the Derivative Nonlinear Schrödinger Equation on the Line

Explore critical well-posedness for the derivative nonlinear Schrödinger equation on the line, focusing on recent advancements in resolving the problem in critical space.

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

Branching Processes in Random Matrix Theory and Analytic Number Theory

Explore branching processes in random matrix theory and analytic number theory, focusing on limiting distributions, log-correlated phenomena, and recent conjectures about maxima of characteristic polynomials and L-functions.

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

Higher Auslander Algebras and Higher Representation Finite Algebras

Explore higher Auslander algebras, their construction methods, and connections to representation theory. Gain insights into recent developments and applications in algebra and representation theory.

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

Higher Order KR-Modules, Imaginary Modules and Monoidal Categorification

Explore connections between cluster algebras, quantum affine algebras, imaginary modules, and representation theory of general linear groups over non-archimedean fields.

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

Categorification at Roots of Unity

Explorez la catégorification des groupes quantiques aux racines de l'unité, en examinant les algèbres p-DG et les représentations catégoriques pour sl(2).

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

Categorifying Connections in Fusion Categories and Subfactors

Traduisez les idées principales de la théorie des paragroupes d'Ocneanu en langage catégorique tensoriel. Explorez les liens entre catégories de fusion et sous-facteurs.

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

Embeddings of Kac-Moody Affine Grassmannian Slices

Explorez les développements récents dans la théorie des représentations géométriques, en se concentrant sur les tranches de Grassmanniennes affines de type Kac-Moody et leur construction via les branches de Coulomb.

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

Weyl Algebras for Quantum Homogeneous Spaces and Applications

Explore quantum analogues of differential operators on symmetric spaces, examining Capelli operators and their connection to Macdonald polynomials in representation theory.

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

T-Shift on Reduced Plabic Graphs and Legendrian Weaves

Explorez les T-shifts sur les graphes plabiques réduits et les tissages légendrien pour interpréter topologiquement la structure de cluster des strates positroïdes du grassmannien.

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

Newton-Okounkov Bodies and Minimal Models for Cluster Varieties

Explore Newton-Okounkov bodies construction for line bundles on cluster variety minimal models, with applications to Grassmannians and flag varieties. Examine connections to representation theory polytopes.

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

The Deep Locus of Cluster Varieties

Explore the deep locus of cluster varieties, focusing on finite types with full rank and specific infinite types. Gain insights into applications for homological mirror symmetry of Grassmannians.

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

Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie III

Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.

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

Plongements du Disque de Poincaré dans l'Espace Ambiant - Partie I

Découvrez la construction explicite d'un plongement isométrique C^1 du disque de Poincaré, explorant ses propriétés surprenantes et son importance en géométrie hyperbolique.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

Parabolic Hilbert Schemes and Rational Cherednik Algebras

Explore connections between symmetric group representations, rational Cherednik algebras, and parabolic Hilbert schemes. Gain insights into geometric constructions of irreducible modules using combinatorics and torus fixed points.

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

Belavin-Drinfeld Quantum Groups - Survey and Future Directions

Explore Belavin-Drinfeld quantum groups, their deformations, and connections to semi-simple algebraic Poisson groups. Survey current knowledge, conjectures, and future research directions in this field.

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