Centre de recherches mathématiques - CRM Courses

Exponentially Many Graphs Are Determined by Their Spectrum

Explore discrete analogues of Kac's question on "hearing the shape of a drum" and learn about graphs determined by their spectrum in this mathematical seminar.

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

Why p-adic Numbers Are Better Than Real for Representation Theory

Explore p-adic numbers and their application in representation theory, focusing on SL(2) group and nilpotent orbits in Lie algebra.

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

Hamiltonian Geometry of Fluids

Explore Hamiltonian geometry of fluids, covering Arnold's group-theoretic approach, compressible fluids, optimal mass transport, and Newton's equations on diffeomorphism groups and probability densities.

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

Spectral Multiplicity and Nodal Domains of Torus-Invariant Metrics

Explore spectral multiplicity and nodal domains of torus-invariant metrics, examining Uhlenbeck's theorem, symmetry impacts, and unique nodal set properties for non-invariant eigenfunctions.

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

Peijel's Nodal Domain Theorem in Spaces with Synthetic Ricci Curvature Lower Bounds

Explore Peijel's Nodal Domain Theorem in synthetic Ricci curvature spaces, extending classical results to non-Riemannian settings and broader Euclidean domains.

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

Dirac Eigenvalue Optimization and Harmonic Maps

Explore Dirac eigenvalue optimization, comparing it to Laplace eigenvalues and examining critical metrics' correspondence with harmonic maps to complex projective spaces.

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

Learning Causal Models via Algebraic Constraints

Explorez les modèles causaux linéaires et leurs graphes dirigés. Découvrez des méthodes algébriques pour identifier les relations causales à partir de données observationnelles, même avec des cycles ou variables cachées.

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

The Local Langlands Program and Characteristic p

Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.

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

Model-Based Optimization with Convex-Composite Optimization

Explore convex-composite optimization framework for complex problems. Learn to balance model complexity with computational efficiency and analyze post-optimal stability in various applications.

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

Point Counting over Finite Fields and the Cohomology of Moduli Spaces of Curves

Explore algebraic geometry through point counting over finite fields and cohomology of moduli spaces of curves, resolving longstanding questions and confirming Langlands program predictions.

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

Integrable Billiards and Rigidity - Lecture 1

Explore integrable billiards and the Birkhoff-Poritsky conjecture, focusing on Hopf-type rigidity and its extension to Twist symplectic maps and billiards.

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

Hamiltonian Structure of Rational Isomonodromic Deformation Systems

Explore Hamiltonian structure of rational isomonodromic deformation systems, focusing on applications in physics and integrability properties of nonlinear differential equations.

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

Mathematical Tools for the Detection and Analysis of Local Singularities - Lecture 3

Explorez les outils mathématiques pour détecter et analyser les singularités locales dans divers domaines, en utilisant des bases d'ondelettes et de Wilson pour la classification et l'analyse multifractale.

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

Local Singularities of Functions: Cusps, Chirps, and Oscillating Singularities - Part II

Explorez les singularités locales des fonctions, leurs types et applications. Apprenez les méthodes d'analyse harmonique pour détecter et caractériser ces comportements dans divers domaines scientifiques.

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

On the Hunt for Chirps - Part I

Explorez les méthodes d'analyse harmonique pour détecter et classifier les comportements oscillatoires spécifiques dans les signaux, avec applications en turbulence, ondes gravitationnelles et données physiologiques.

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