Random Matrix Theory Courses and Certifications

Institute for Pure & Applied Mathematics (IPAM)

Random Matrix Theory Applications to Biology

Discover how Random Matrix Theory extracts biological signals from noisy single-cell RNA-seq data by leveraging spectral distributions and eigenvector properties.

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

Institute for Pure & Applied Mathematics (IPAM)

Free Entropy Theory and Random Matrices

Explore advanced connections between free probability theory, random matrices, and von Neumann algebras through expert lectures on entropy methods and spectral analysis.

• YouTube
• 18 hours 8 minutes
• On-Demand
• 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
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Lectures on Random Matrices

Dive into random matrix theory through expert lectures covering Wigner ensembles, free probability, KPZ equations, and applications in physics and statistics from leading researchers.

• YouTube
• 1 day 15 hours 42 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Research Problems on Random Matrices

Explore cutting-edge research problems in random matrix theory through expert presentations covering eigenvalue densities, dynamical methods, and applications to physics and statistics.

• YouTube
• 12 hours 34 minutes
• On-Demand
• Free Video

ICTP Mathematics

Determinantal Point Processes - Lecture 1

Explore determinantal point processes with Alexander Bufetov, delving into mathematical concepts and applications in random matrix theory.

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

ICTP Mathematics

Large Deviations for Traces of Wigner Matrices

Large deviations theory for traces of Wigner matrices, exploring typical behaviors, principles, and universality. Covers bounded and sub-Gaussian entries, mechanisms, and nonlinear aspects of random matrix theory.

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

ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - I

Explore random matrices, matrix models, and Dyson-Schwinger equations in this advanced mathematics lecture, focusing on integration techniques and unique solutions.

• YouTube
• 1 hour
• 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

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

ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - Lecture 5

Explore advanced concepts in random matrix theory, focusing on Dyson-Schwinger equations and their applications in mathematical physics and probability theory.

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

ICTP Mathematics

The Point Processes at Turning Points of Large Lozenge Tilings

Explore the fascinating world of point processes in large lozenge tilings, focusing on turning points and their mathematical implications.

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

ICTP Mathematics

Random Matrices and the Uses of Dyson-Schwinger Equations - Lecture 4

Explore advanced concepts in random matrix theory, focusing on Dyson-Schwinger equations and their applications in mathematical physics and probability theory.

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

ICTP Mathematics

Noise Sensitivity of the Top Eigenvector of a Wigner Matrix

Explore the noise sensitivity of Wigner matrices' top eigenvectors, delving into random matrix theory and its applications in mathematical physics and data analysis.

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

ICTP Mathematics

Determinantal Point Processes - Lecture 3

Explore advanced concepts in determinantal point processes, focusing on mathematical theory and applications in random matrix theory and point processes.

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