ICTP Mathematics Courses

Virtual Topological Invariants of Moduli Spaces of Sheaves on Surfaces

Explore virtual topological invariants of moduli spaces, focusing on sheaves on surfaces. Learn about ischemic points, Euler numbers, and perfect obstruction theory.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Invariants of Manifolds From 6 Dimensions

Explore invariants of 6-dimensional manifolds, covering vector spaces, complex numbers, and vertex operator algebras. Delve into state field correspondence and multi-dimensional environments.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Wroten Type Coding for Kleinian Groups

Explore Kleinian groups through Wroten type coding, covering motivation, concepts, inversion conditions, and generalizations in this mathematical deep dive.

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

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
• Self-Paced
• Free Video

Soliton Quantization and Random Partitions

Explore soliton quantization and random partitions in Benjamin Ono equations, focusing on one-phase solutions, simulations, and Hamiltonian structures in dispersive wave theory.

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

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
• Self-Paced
• Free Video

Asymptotics for the Lower Tail of the KPZ Equation

Exploration of asymptotic behavior in the KPZ equation's lower tail, covering motivation, proofs, and generalizations for advanced mathematics researchers.

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

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
• Self-Paced
• Free Video

Asymptotics of Orthogonal Polynomial Ensembles via Integrable Methods

Explore statistical properties of random matrices and point processes, focusing on asymptotics of orthogonal polynomial ensembles and their applications in various fields of mathematics and physics.

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

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
• Self-Paced
• Free Video

Determinantal Point Processes - II

Exploration of determinantal point processes, covering theorems, Young graphs, Markov chains, and related mathematical concepts with applications in random matrix theory.

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

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
• Self-Paced
• Free Video