Nonlocal Partial Differential Equations Courses and Certifications

ICTP Mathematics

Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability

Explore advanced mathematical techniques in nonlocal partial differential equations with applications spanning plasma physics, geometry, and probability theory.

• YouTube
• 1 day 14 hours 4 minutes
• On-Demand
• Free Video

ICTP Mathematics

The De Giorgi Conjecture for the Half-Laplacian in Dimension 4 - I

Explore the De Giorgi conjecture for the half-Laplacian in dimension 4, presented by A. Figalli from ETH Zürich. Delve into advanced mathematical concepts in nonlocal partial differential equations and their applications.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

ICTP Mathematics

Quantization of Measures - A Gradient Flow Approach

Explore gradient flow techniques for measure quantization, examining applications in geometry, physics, and probability theory.

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

ICTP Mathematics

The De Giorgi Conjecture for the Half-Laplacian in Dimension 4 - II

Explore advanced mathematical concepts in nonlocal PDEs, focusing on the De Giorgi conjecture for the half-Laplacian in dimension 4, presented by A. Figalli from ETH Zürich.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

ICTP Mathematics

Fractional Poincare Inequalities on Manifolds With Finite Total Q-Curvature

Explore fractional Poincare inequalities on manifolds, focusing on finite total Q-curvature. Advanced mathematical concepts for geometry and physics enthusiasts.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

ICTP Mathematics

Global Regularity of Solutions to the 4-Species Quadratic Diffusion-Reaction System

Explore advanced mathematical concepts in nonlocal partial differential equations, focusing on global regularity solutions for a 4-species quadratic diffusion-reaction system across all spatial dimensions.

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

ICTP Mathematics

Collisions in Plasmas: The Landau Equation - Part 5

Explore plasma collisions through the Landau equation, delving into advanced mathematical concepts and their applications in physics and probability theory.

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

ICTP Mathematics

Construction of Weak Solutions for the Landau Equation by Approximations of Solutions to

Explore the construction of weak solutions for the Landau equation through approximations of Boltzmann equation solutions in grazing collision limit scenarios.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - I

Explore the regularity of the Boltzmann equation in bounded domains, focusing on advanced mathematical concepts and applications in geometry, physics, and probability theory.

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

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - II

Explore advanced mathematical concepts in nonlocal PDEs, focusing on the Boltzmann equation's regularity in bounded domains. Gain insights from expert Tonon, D. in this in-depth lecture.

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

ICTP Mathematics

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
• On-Demand
• Free Video