ICTP Mathematics Courses

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

Static Black Hole Uniqueness Theorems - Lecture 2

Explore uniqueness theorems for static black holes, covering classical extensions, spacetime cross-sections, and proof techniques in this advanced mathematics lecture.

• YouTube
• 1 hour 14 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

Black Holes, Binary Systems, and Gravitational Waves - Comparable-Mass Binaries

Explore comparable-mass binary systems, post-Newtonian theory, and relaxed Einstein equations in the context of gravitational waves and black hole physics.

• YouTube
• 1 hour 15 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

Black Holes, Binary Systems, and Gravitational Waves - Kerr Black Hole

Explore Kerr black holes, binary systems, and gravitational waves with expert Nicolas Yunes. Delve into advanced concepts like Killing tensors and zero angular momentum observers in this comprehensive lecture.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Fractal Dimensions in Nature and Mathematics - 2019

Explore fractal dimensions in nature and math, from intuitive integer dimensions to non-integer fractals. Learn alternative definitions, simple examples, and applications in dynamical systems.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

New Complex Analytic Methods in the Theory of Minimal Surfaces - Franc Forstnerič

Explore recent developments in minimal surface theory using complex analytic methods, covering global theory, Calabi-Yau problem, and complex Gauss map applications.

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

Apparent Contours and Reconstruction of Solid Shapes

Explore 3D shape reconstruction from apparent contours in Computer Vision, covering topological challenges and the Appcontour program's role in this fascinating field.

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

Ergodicity in Smooth Dynamics 1

Explore ergodicity in smooth dynamics, covering introductory concepts, examples, proofs, and higher dimensions with experts Jana Rodriguez-Hertz and Amie Wilkinson.

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