Random Matrix Theory Courses and Certifications

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

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

International Mathematical Union

Weingarten Calculus and Its Applications

Explore Weingarten calculus and its applications in compact groups, quantum probability, and random matrix theory, with insights on theoretical properties and recent developments.

• YouTube
• 46 minutes
• 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

Asymptotics of the Averaged Characteristic Polynomial for Ginibre Ensemble

Explore asymptotics of averaged characteristic polynomials in Ginibre Ensemble, covering Coulomb gas, Szego curves, orthogonal polynomials, and partition functions in random matrix theory.

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

ICTP Mathematics

Determinantal Point Processes - V

Explore determinantal point processes, covering conditional measures, sign processes, gamma kernels, Palm measures, and infinite determinantal measures in this advanced mathematics lecture.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

ICTP Mathematics

Absolute Continuity of Limiting Spectral Distributions of Toeplitz and Hankel Random Matrices

Explore limiting spectral distributions of Toeplitz and Hankel matrices, focusing on absolute continuity and its implications for random matrix theory.

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

ICTP Mathematics

Eigenvalue Distribution for Non Linear Models of Random Matrices

Explore eigenvalue distribution in non-linear random matrix models, covering motivation, limits, batch normalization, and moment methods with speaker Sandrine PECHE.

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

ICTP Mathematics

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

Explore advanced topics in random matrix theory, including Dyson-Schwinger equations, operator algebra, and central limit theorems, with applications in mathematical physics.

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

ICTP Mathematics

Edge Universality for Non-Hermitian Random Matrices

Explore edge universality in non-Hermitian random matrices, covering eigenvalues, circular law, universality conjectures, and proof techniques for spectral universality and Girko's Hermitization.

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

ICTP Mathematics

Variational Problems and Spectral Curves for the Hermitian Matrix Model with External Source

Explore variational problems and spectral curves in hermitian matrix models with external sources, focusing on finite N spectral curves and their applications in 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

International Mathematical Union

Quantitative Invertibility of Non-Hermitian Random Matrices

Explore quantitative invertibility of non-Hermitian random matrices with Konstantin Tikhomirov in this mathematical lecture on advanced linear algebra concepts.

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