Spectral Theory Courses and Certifications

BIMSA

Optimal Estimates for Neumann Eigenvalues

Explore optimal estimates for Neumann eigenvalues, including award-winning research on maximizing second eigenvalues and recent findings on convex set bounds.

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

Centre de recherches mathématiques - CRM

The Method of Gauge Transform II

Explorez la méthode de transformation de jauge et son application aux problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

The Method of Gauge Transform - Periodic and Ergodic Spectral Problems

Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux, en mettant l'accent sur les aspects mathématiques avancés et les techniques analytiques.

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

Centre de recherches mathématiques - CRM

Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part II

Explorez la théorie quantitative globale des opérateurs quasipériodiques à une fréquence, en examinant la réductibilité et ses implications dans les problèmes spectraux.

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

Centre de recherches mathématiques - CRM

Quantitative Global Theory of One-Frequency Quasiperiodic Operators - Part I

Explore quantitative global theory of one-frequency quasiperiodic operators, covering dynamic approaches, prototypical models, and applications in spectral problems.

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

Centre de recherches mathématiques - CRM

The Method of Gauge Transform - Lecture 4

Explorez la méthode de transformation de jauge et ses applications dans les problèmes spectraux périodiques et ergodiques avec Jeffrey Galkowski de l'University College London.

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

Centre de recherches mathématiques - CRM

The Method of Gauge Transform - Lecture 3

Explore advanced mathematical concepts in periodic and ergodic spectral problems, focusing on the Gauge transform method.

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

Centre de recherches mathématiques - CRM

The Dry Ten Martini Problem for Sturmian Schrodinger Operators

Explore the Dry Ten Martini Problem for Sturmian Schrodinger operators, examining spectral gaps and integrated density of states. Delve into recent solutions and advancements in this mathematical challenge.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

BIMSA

Semiclassical Measures on Compact Hyperbolic Surfaces

Explore semiclassical measures on compact hyperbolic surfaces, focusing on eigenfunctions of the Laplacian operator and the quantum ergodicity theorem. Delve into fractal uncertainty principles and their implications.

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

Centre de recherches mathématiques - CRM

Polya's Conjecture for Euclidean Balls

Explore Polya's conjecture for Euclidean balls, examining its proof for arbitrary dimensions and implications in spectral geometry.

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

Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 1

Delve into spectral analysis of random graphs, exploring adjacency operators, Laplacian matrices, and Benjamini-Schramm topology. Examine convergence properties and quantum percolation in graph theory.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 4

Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology through rigorous mathematical frameworks and quantum percolation theory.

• YouTube
• 2 hours 1 minute
• On-Demand
• Free Video

Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 2

Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology with focus on spectral measures and quantum percolation theory.

• YouTube
• 2 hours
• On-Demand
• Free Video

Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 5

Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology through rigorous mathematical frameworks and quantum percolation theory.

• YouTube
• 2 hours 9 minutes
• On-Demand
• Free Video

Kyoto-U OCW - Unofficial

Spectrum of Random Graphs - Lecture 3

Delve into advanced spectral analysis of random graphs, exploring adjacency operators, Laplacian operators, and Benjamini-Schramm topology with focus on convergence properties and quantum percolation.

• YouTube
• 1 hour 56 minutes
• On-Demand
• Free Video