Centre de recherches mathématiques - CRM Courses

Polynomial-Time Power-Sum Decomposition of Polynomials - Efficient Algorithms and Applications

Explore efficient algorithms for power-sum decomposition of polynomials, improving on prior work for tensor decomposition and Gaussian mixture identifiability. Gain insights into numerical linear algebra and noise-resilient techniques.

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

Tensor Decomposition Algorithms via Algebraic Complexity

Explorez les algorithmes de décomposition tensorielle et leur lien avec les circuits arithmétiques, en examinant les cas moyens et les pires scénarios pour les tenseurs de faible rang.

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

Tensor Rank and Bias of Multilinear Forms Over Finite Fields

Explorez les liens entre le rang tensoriel et le biais des formes multilinéaires sur les corps finis dans cette conférence mathématique approfondie.

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

On the Subrank of Generic Tensors

Explorez les limites supérieures et inférieures du sous-rang des applications bilinéaires et tenseurs d'ordre supérieur génériques. Découvrez les mesures des multiplications indépendantes réductibles.

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

An Equation of Diophantus - Introduction to Torsion and Ranks of Elliptic Curves

Explore Diophantus' equation and its impact on number theory, from ancient times to modern developments in elliptic curves and their torsion and ranks.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Large Coupling Limits of Integrable Spin Chains

Explore dynamics of integrable spin chains, focusing on XXZ chain and Hubbard model. Examine large coupling limits and emerging effective theories in various physical situations.

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

Full Likelihood Inference for Abundance from Capture-Recapture Data

Explore full likelihood inference for abundance estimation in capture-recapture experiments, focusing on semiparametric efficiency and the EM algorithm for improved accuracy and coverage.

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

Vertex Algebras and Quantum Groups with Big Center

Explore vertex algebras and quantum groups with large centers, focusing on semisimple Lie algebras and their connections to quantum geometric Langlands correspondence and logarithmic Kazhdan-Lusztig conjecture.

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

VOAs from Higher-Dimensional Quantum Field Theories - Lecture 3

Explorez les algèbres d'opérateurs vertex issues des théories quantiques des champs en dimensions supérieures et leurs liens avec d'autres domaines mathématiques.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Modular Tensor Categories, Quantum Groups and Vertex Algebras - Lecture 4

Explore connections between modular tensor categories, quantum groups, and vertex algebras. Delve into the logarithmic Kazhdan–Lusztig conjecture linking quantum groups and vertex algebras.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

VOAs from Higher-Dimensional Quantum Field Theories - Lecture 4

Explorez les algèbres d'opérateurs vertex issues des théories quantiques des champs en dimensions supérieures et leurs liens avec d'autres domaines mathématiques.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators

Explore Loop Braid Group, Loop Hecke Algebras, and charge conserving Yang-Baxter operators. Gain insights into recent mathematical developments in quantum symmetries and topological quantum field theories.

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

Extensions of Affine Algebra Vertex Operator Algebras

Explore extensions of affine algebra VOAs, focusing on V(g,k) for simple Lie algebras. Learn about finite-index extensions, simple currents, and quantum subgroups in module category classification.

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

Fermionic Forms in Logarithmic Vertex Operator Algebras and BPS Quivers

Explore connections between quantum groups, vertex algebras, and quiver representations. Uncover new insights into fermionic forms and their applications in representation theory and enumerative geometry.

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

Slot Decomposition of the Box-Ball System - Part I

Explorez la décomposition en fentes du système de boîtes à balles, un automate cellulaire de transport conservant les solitons. Découvrez les composantes solitoniques et leur évolution hiérarchique.

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