Centre de recherches mathématiques - CRM Courses

A Tour of the Mathematics of Music and Sound

Explore the mathematical foundations of music and sound, from instrument acoustics to harmonic theory, with live demonstrations and spectrogram analysis.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Mathematics that Resonates - Eigenvalues and Eigenvectors in Acoustics, Engineering, and Quantum Mechanics

Explore how eigenvalues and eigenvectors explain resonances in cello tones, microwaves, car noise reduction, and fusion reactors through surprising mathematical connections.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Boundary Integral Methods, Eigenvalues and Computational Spectral Geometry

Explore boundary integral methods for computing eigenpairs of elliptic operators with high accuracy and efficiency, covering smooth and polygonal domains in spectral geometry.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Foliations of Bubblesheet Singularities: A Spectral Geometric Approach

Explore the concept of foliations in differential geometry, focusing on bubblesheet singularities through a spectral geometric approach and the new Quasi-Parallel Mean Curvature condition.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

A Study of Stochastic and Noisy Oracles in Unconstrained Continuous Optimization

Explore stochastic and noisy oracles in continuous optimization, covering inexact computations, derivative-free methods, and their effects on algorithmic behavior.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Recent Applications of Model Theory to Algebraic Dynamics

Explore recent applications of model theory to algebraic dynamics, including joint work on birational classification problems and connections to algebraic differential equations.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Comparing Dirichlet and Neumann Laplace Spectra

Explore the relationship between Dirichlet and Neumann eigenvalues of the Laplacian, examining isoperimetric ratios and boundary conditions across convex bodies, polygons, and manifolds.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

The Geometric Size of the Fundamental Gap

Explore advanced spectral geometry through the fundamental gap conjecture, examining sharp inequalities for Dirichlet Laplacian eigenvalues and their geometric quantification.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Quantum Fields, Gravity, and Mathematics

Explore the fascinating connection between quantum field theory, gravity, and mathematics, discovering how space-time emerges from quantum entanglement and Einstein's relativity relates to chaos theory.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Tuiles de Wang Apériodiques Associées aux Nombres Métalliques

Explore la théorie des pavages apériodiques et leur lien avec les nombres métalliques, allant au-delà du nombre d'or vers de nouvelles familles de pavages.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Quantum Groups, Vertex Algebras, and Geometric Invariants

Explore quantum groups and vertex algebras to construct invariants of knots and 3D manifolds, plus discover geometric invariants from logarithmic conformal field theories.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Extensions of Vertex Operator Algebras and Applications to Integrable Systems II

Explore advanced vertex operator algebra extensions and their connections to quantum groups, integrable systems, and the geometric Langlands program through tensor category techniques.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Extensions of Vertex Operator Algebras and Applications to Integrable Systems I

Explore vertex operator algebra extensions and their deformations, connecting quantum groups, tensor categories, and integrable systems with applications to critical level algebras.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Spectral Optimization in Exterior Domains - Robin and Steklov Problems

Explore spectral optimization in exterior domains, focusing on Robin and Steklov problems with applications to diffusion processes and geometric inequalities in mathematical analysis.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Combinatorics of Causal Set Theory

Explore how causal set theory applies combinatorics to quantum gravity, examining spacetime as locally finite posets and discovering new mathematical perspectives.

• YouTube
• 59 minutes
• Self-Paced
• Free Video