Random Matrix Theory Courses and Certifications

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
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Random Matrix Theory and its Applications - Lecture 2

Explore advanced concepts in random matrix theory, including linear algebra basics, operators, transformations, eigenvectors, and various matrix ensembles, with applications in statistical physics.

• YouTube
• 1 hour 28 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Shuffling Cards and Random Matrix Theory

Explore card shuffling and random matrix theory with Stanford's Persi Diaconis in this IMPA 70th anniversary conference talk on mathematical applications in everyday phenomena.

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

International Centre for Theoretical Sciences

Random Matrix Theory and its Applications - Lecture 4

Explore advanced concepts in Random Matrix Theory, including rotational invariance, correlation functions, spacing distributions, and applications to complex systems stability.

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications - Lecture 3

Explore advanced random matrix theory concepts, including complex quaternionic matrices, rotationally invariant ensembles, and applications to disordered systems in this in-depth lecture.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Random Matrix Theory and Its Applications - Lecture 5

Explore advanced random matrix theory concepts, including Gaussian ensembles, coarse-graining techniques, and the Wigner semi-circular law in this comprehensive lecture.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

BIMSA

Recent Progress in Random Matrix Theory

Explore recent advancements in random matrix theory, focusing on spectral statistics of normalized adjacency matrices in random d-regular graphs and their eigenvalue rigidity.

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

Centre de recherches mathématiques - CRM

Branching Processes in Random Matrix Theory and Analytic Number Theory

Explore branching processes in random matrix theory and analytic number theory, focusing on limiting distributions, log-correlated phenomena, and recent conjectures about maxima of characteristic polynomials and L-functions.

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

Schmid College, Chapman University

Linear Systems and Differential Equations in Random Matrix Theory

Explore linear systems and differential equations in random matrix theory, focusing on solving nonlinear equations using Hankel operators, Fredholm determinants, and tau functions.

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

Centre de recherches mathématiques - CRM

The Moduli Space of Twisted Laplacians and Random Matrix Theory

Explore the convergence of spectral number variance for twisted Laplacians to random matrix theory ensembles, extending Rudnick's work to break time-reversal symmetry and include Dirac operators.

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

ICTP-SAIFR

Random Matrix Theory Applications from Single to Many-Body Quantum Chaos - Class 2

Explore random matrix theory applications in quantum chaos, from single-particle to many-body systems, with insights from Thomas Guhr's advanced lecture series.

• YouTube
• 1 hour 42 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Using Random Matrix Theory to Analyze Power Law Signatures in scRNA-seq Data

Explore how Random Matrix Theory can be applied to analyze power law signatures in single-cell RNA sequencing data in this talk from the 10th Indian Statistical Physics Community Meeting.

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

Harvard CMSA

Integrability in Discrete Random Matrix Theory

Explore integrability in discrete random matrix theory, covering probabilistic results, Hall-Littlewood polynomial formulas, and new formulas for Hermitian and antisymmetric p-adic matrices with formal Hall-Littlewood processes.

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

Institute for Pure & Applied Mathematics (IPAM)

A New Approach to 1/N Expansion in Random Matrix Theory

Discover a simple method to control finite dimension regimes in random matrix theory using polynomial approximation, presented by Chi-Fang Chen at IPAM's workshop on Free Entropy Theory.

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

International Centre for Theoretical Sciences

Quantum Fluctuations of 2D Fermions and Random Matrix Theory

Explore quantum fluctuations in 2D fermionic systems through random matrix theory connections, bridging statistical physics and quantum mechanics.

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