ICTP Mathematics Courses

Invariants States in Stochastically Forced Boussinesq Equations

Explore stochastic forcing in Boussinesq equations, covering existence, uniqueness, stability, and numerical simulations for fluid dynamics and convection phenomena.

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

Solving the 4NLS with White Noise Initial Data

Explore white noise initial data in solving 4NLS, covering Hamiltonian PDE, globalization arguments, and limit equations. Gain insights into complex mathematical concepts and proofs.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Stabilization of Nonlinear Systems by Oscillating Controls with Application

Explore nonlinear system stabilization using oscillating controls, with applications in nonholonomic and fluid dynamics. Covers control design, Lie brackets, and energy cascades.

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

Control Theory and Large Deviation Principles for PDEs

Explore control theory and large deviation principles for PDEs, covering IID cases, contraction principles, rate functions, and applications to random forces and controllability.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Quaternionic Brownian Windings

Explore quaternionic Brownian windings, Lévy area formula, and stochastic processes in complex projective and hyperbolic spaces. Gain insights into asymptotic behavior and skew-product decompositions.

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

A Controllability Approach to SDEs Driven by Degenerate Noises and Applications to Networks of Oscillators

Explore stochastic differential equations with degenerate noise, focusing on controllability and applications to oscillator networks. Gain insights into exponential mixing and solid controllability.

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

The Cosmic Censorship Conjectures in General Relativity - Lecture 4

Explore cosmic censorship conjectures in general relativity, covering singularities, wave equations, and Penrose diagrams. Gain insights from expert Mihalis Dafermos on this advanced topic in theoretical physics.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Static Black Hole Uniqueness Theorems - Lecture 3

Explore asymptotic flatness, positive mass theorem, and scalar curvature in static black hole uniqueness theorems with expert Carla Cederbaum.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

The Cosmic Censorship Conjectures in General Relativity - Lecture 3

Explore cosmic censorship conjectures in general relativity, focusing on global high publicity, null infinity, and the Hawking pass, with expert Mihalis Dafermos.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Introduction to the AdS-CFT Conjecture from a General Relativity Perspective - Lecture 3

Explore the AdS-CFT conjecture from a general relativity perspective, covering supergravity, universal sectors, and Hawking temperature in this advanced physics lecture.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

The Cosmic Censorship Conjectures in General Relativity - Lecture 2

Explore strong and weak cosmic censorship conjectures in general relativity, examining singular behavior, spacelike singularities, and spherical symmetry through Penrose diagrams.

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

Black Hole Thermodynamics - Lecture 3

Explore black hole thermodynamics, focusing on stationary black holes, their laws, and stability, with insights from General Relativity and expert Robert Wald.

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

Some Geometric Properties of Spacetime - Lecture 3

Explore geometric properties of spacetime, including minimal hypersurfaces, stability, and boundary integrals. Gain insights into linear and nonlinear models in this advanced mathematics lecture.

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

Some Geometric Properties of Spacetime - Lecture 2

Explore geometric properties of spacetime, including theorems on topology, dihedral angles, and scalar curvature, with insights on the positive mass theorem and Gauss-Bonnet theorem.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Some Geometric Properties of Spacetime

Explore geometric properties of spacetime, including constraint equations, scalar curvature, cone angles, and the positive mass theorem. Gain insights into fundamental concepts in geometry and gravity.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video