Spectral Theory Courses and Certifications

BunG Seminar

Shtukas and Excursions in Categorical Spectral Theory - Talk 42

Delve into advanced mathematical concepts exploring the relationship between excursion operators, shtuka cohomologies, and categorical spectral action through categorical traces.

• YouTube
• 2 hours 17 minutes
• Self-Paced
• Free Video

Discover AI

The New Geometry of Intelligence - Spectral Superposition Theory of Feature Geometry

Discover how spectral superposition theory reveals the geometric structure underlying AI feature representations and intelligence mechanisms.

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

Ryan O'Donnell

Spectral Graph Theory - Eigenvalues at CMU - Lecture 15a of CS Theory Toolkit

Explore eigenvalues of the Laplacian and Markov operator in spectral graph theory, including associated formulas and their applications in theoretical computer science research.

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

Ryan O'Donnell

Spectral Graph Theory - Minimizing/Maximizing the Quadratic Form

Explore spectral graph theory, focusing on minimizing and maximizing quadratic forms, with connections to graph components and bipartiteness in this graduate-level lecture.

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

Ryan O'Donnell

Spectral Graph Theory - The Quadratic Form

Explores spectral graph theory, focusing on the quadratic form associated with undirected graphs. Covers basic setup and provides examples for graduate-level computer science research.

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

International Centre for Theoretical Sciences

Spectral Graph Theory - Lecture 1

Explore spectral graph theory, covering self-adjoint matrices, Rayleigh equalities, graph isomorphism, Cayley graphs, and automorphism groups. Gain insights into complex systems and network analysis.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Paul G. Allen School

Theory Seminar - Spectral Independence in High-Dimensional Expanders, Kuikui Liu

Explore spectral independence in high-dimensional expanders and its application to the hardcore model, including rapid mixing of Glauber dynamics for generating random independent sets.

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

Society for Industrial and Applied Mathematics

Spectral Problems in Inverse Scattering Theory - 21st IMAGINE OneWorld SIAM-IS Seminar

Explore scattering theory's spectral problems, focusing on poles, non-scattering frequencies, and transmission eigenvalues. Learn how these relate to scattering operators and material properties in inhomogeneous media.

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

Materials Cloud

Koopmans Compliance: Towards a Functional Theory of the Spectral Density - Lecture 4.2

Explore Koopmans compliance and its role in developing a functional theory of spectral density, advancing understanding of Hubbard and Koopmans functionals in quantum systems.

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

BIMSA

An ℓp Theory of PCA and Spectral Clustering

Explore an advanced $\ell_p$ theory of PCA, improving upon vanilla PCA for heteroscedastic noises and yielding optimal bounds for spectral clustering and community detection.

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

IISc Bangalore;  NPTEL

C* Algebras and Spectral Theorem

Explore C* algebras, Gelfand-Naimark theorem, and projection valued measures to prove the spectral theorem for bounded normal operators. Ideal for advanced mathematics students and researchers.

• Swayam
• 8 weeks
• Self-Paced
• Free Online Course

NCCR SwissMAP

Quantum Mechanics for Mathematicians - Master Class in Mathematical Physics 2019-2020

Master quantum mechanics through rigorous mathematical foundations and advanced theoretical frameworks in this comprehensive 20-hour physics masterclass.

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

ICTP Mathematics

Random Matrix Theory and Point Processes

Explore advanced mathematical concepts in random matrix theory, determinantal point processes, and their applications in dynamical systems through expert lectures and research seminars.

• YouTube
• 1 day 32 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Universality for Random Matrix Ensembles of Wigner Type

Dive into advanced random matrix theory with Terry Tao, exploring universality phenomena in Wigner-type ensembles through rigorous mathematical analysis and proofs.

• YouTube
• 4 hours 8 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video