ICTP Mathematics Courses

Introduction to Ergodic Theory 1

Explore measure theory fundamentals, sigma algebras, and Lebesgue measure construction in this comprehensive introduction to ergodic theory.

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

Rotations of the Circle and Renormalization

Explore circle rotations, renormalization, and dynamical systems with Corinna Ulcigrai. Learn key concepts, proofs, and applications in this advanced mathematics lecture.

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

Collisions in Plasmas - The Landau Equation - Part IV

Explore plasma collisions through the Landau equation, covering entropy structure, factorization theorems, and computational aspects of this advanced mathematical topic.

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

Entropy Method for Hypocoercive BGK and Fokker-Planck Equations

Explore entropy methods for hypocoercive equations, focusing on BGK and Fokker-Planck models. Learn about decay rates, auxiliary functionals, and regularization techniques in non-symmetric systems.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Metric Currents, Isoperimetric Inequalities, and Compactness

Explore metric currents, isoperimetric inequalities, and compactness in geometric measure theory. Gain insights from expert S. Wenger on nonpositive sectional curvature and growth types in metric spaces.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2

Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.

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

Regularity Theory for Area-Minimizing Currents

Explore advanced concepts in geometric measure theory, including zero forms, currents, and rectifiability theorems, with applications to area-minimizing problems in mathematics.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Regularity Theory for Area-Minimizing Currents

Explore advanced concepts in geometric measure theory, including currents, boundaries, and regularity theory for area-minimizing surfaces, with applications to optimal transport problems.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

Motion by Curvature of Networks in the Plane - Lecture 4

Explore motion by curvature of planar networks, covering collapse, parametrization, evolution equations, special cases, singularities, and localization. Gain insights into this advanced mathematical topic.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Phase-Field Models for Motion by Mean Curvature - Lecture 2

Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 5

Explore singularities in mean curvature flow of convex hypersurfaces, covering max inequality, weak solutions, surgeries, and Type 2 singularities with intuitive explanations.

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

Existence and Regularity Theories of Brakke Flow

Explore existence and regularity theories of Brakke flow, covering initial configuration, linear and alpha regularity, dispersed irregularity, and the Monotonicity Formula for minimal surfaces.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Existence and Regularity Theories of Brakke Flow

Explore theories of Brakke flow, including existence and regularity, with expert Yoshihiro Tonegawa. Delve into key concepts like geometric metatheory, approximate tangent space, and multiplicity functions.

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

Introduction to Quantum Computation - Antonello Scardicchio

Learn the basics of quantum computation, its potential for problem-solving, and current technological advancements in this field. Explore algorithms, complexity classes, and real-world applications.

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

Quantum Fields, Strings, and Black Holes: A Primer for Non Experts, Part I - Atish Dabholkar

Explore quantum black holes, string theory, and their connections to number theory and geometry. Gain insights into fundamental physics concepts, suitable for mathematicians and physics students.

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