Spectral Theory Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Random Matrices and Dynamics of Optimization in Very High Dimensions - Lecture 1

Explorez les algorithmes d'optimisation en haute dimension pour l'apprentissage automatique, en mettant l'accent sur la descente de gradient stochastique et les transitions spectrales des matrices aléatoires.

• YouTube
• 2 hours 3 minutes
• On-Demand
• Free Video

Simons Foundation

Delocalization of Eigenvectors of Random Matrices - A Survey (February 20, 2025)

Explore Terence Tao's comprehensive survey on eigenvector delocalization in random matrices, examining key mathematical principles and recent developments in this complex field.

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

Institut des Hautes Etudes Scientifiques (IHES)

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 4

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and diverse mathematical fields. Gain insights into curve roundness and its implications.

• YouTube
• 2 hours 5 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 2

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications.

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

Institut des Hautes Etudes Scientifiques (IHES)

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 1

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications across multiple fields.

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

NCCR SwissMAP

Random Matrices and Universality 1 - Master Class in Mathematical Physics 2019-2020

Dive into advanced mathematical physics through comprehensive study of random matrix theory and universality principles in this intensive 21-hour master class series.

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

Instituto de Matemática Pura e Aplicada

Fourier Analysis and Beyond I (2025)

Explore advanced Fourier analysis techniques and their applications across mathematical disciplines through expert mini-courses and research presentations from leading specialists.

• YouTube
• 12 hours 11 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Wigner Random Matrices and the Semicircle Law

Explore Wigner's semicircle law through eigenvalues, graph theory, and Catalan numbers in random matrix theory with proofs and spectral analysis techniques.

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

Fields Institute

Graduate Course on K-Theory and C*-Algebras

Master advanced mathematical concepts in K-Theory and C*-Algebras through comprehensive graduate-level lectures from the Fields Institute's operator algebras program.

• YouTube
• 1 day 5 hours 22 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Topics in High Dimensional Probability

Explore advanced mathematical concepts in high-dimensional probability through expert lectures on random matrices, geometric approaches, and complex stochastic models.

• YouTube
• 1 day 2 hours 52 minutes
• On-Demand
• Free Video

Fields Institute

Mini-course on Operators on Function Spaces - Part 2

Explore advanced concepts in function spaces, including multiplication operators, Toeplitz operators, and the unilateral shift, with applications in complex analysis and operator theory.

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

Fields Institute

Mini-course on Operators on Function Spaces - Part 1

Explore operators on function spaces, focusing on the Volterra operator's properties, spectrum, and related concepts in functional analysis.

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

ICTP Mathematics

Dynamics of Smooth Surface Diffeomorphisms - Spectral Gap and Stochastic Properties

Explore surface diffeomorphisms, spectral gaps, and stochastic properties in smooth dynamics. Gain insights into symbolic models, entropy continuity, and hyperbolic systems.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

International Mathematical Union

Fractal Uncertainty Principle and Quantum Chaos

Explore quantum chaos and fractal uncertainty principle in wave equations, with applications to eigenfunctions, Schrödinger equation, and hyperbolic surfaces. Gain insights beyond classical/quantum correspondence.

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

ICTP Mathematics

Marked Length Spectral Rigidity for Flat Metrics - C. Leininger

Explore marked length spectral rigidity in flat metrics with C. Leininger, delving into advanced mathematical concepts and their applications in geometry and topology.

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