Regularity Theory Courses and Certifications

ICTP Mathematics

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
• On-Demand
• Free Video

Institute for Advanced Study

Fluid Equations - Regularity and Kolmogorov’s Turbulence Theory

Explore fluid dynamics, Navier-Stokes equations, and Kolmogorov's turbulence theory. Gain insights into regularity results and mathematical confirmations of phenomenological theories.

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

ICTP Mathematics

Regularity Theory for Area-Minimizing Currents - Lecture 5

Explore advanced concepts in geometric measure theory, focusing on regularity theory for area-minimizing currents. Gain insights from experts De Lellis and Spadaro in this in-depth lecture.

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

Hausdorff Center for Mathematics

Edgard Pimentel - Regularity Theory for Nonlinear PDEs

Explore recent developments in regularity theory for nonlinear PDEs, covering compactness, stability, and scaling arguments. Learn about fully nonlinear PDEs, Isaacs equation, and free boundary problems.

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

ICTP Mathematics

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
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 3

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 5 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Part 1

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 1 hour 55 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Quantum Field Theory on Low-Regularity Spacetimes

Explore quantum field theory on low-regularity spacetimes, focusing on massless scalar fields, Cauchy problems, Green operators, and physical states in a mathematically rigorous framework.

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

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 4

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 10 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Regularity Theory of Kinetic Equations with Rough Coefficients - Lecture 2

Delve into the extension of De Giorgi-Nash-Moser theory to hypoelliptic PDEs in kinetic theory, focusing on Kolmogorov equations with rough coefficients and connections to control theory and hypocoercivity.

• YouTube
• 2 hours 1 minute
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Evolution of Interfaces - Trimester Program

Explore advanced mathematical theories on interface evolution, covering De Giorgi-Almgren theory, Brakke's mean curvature flow, convex integration, and cutting-edge research in PDEs and fluid dynamics.

• YouTube
• 1 day 11 hours 40 minutes
• On-Demand
• Free Video

ICTP Mathematics

Geometric Measure Theory and Optimal Transport

Explore advanced mathematical concepts connecting geometric measure theory with optimal transport through expert lectures on regularity theory, Monge-Ampère equations, and stability results.

• YouTube
• 1 day 7 hours 45 minutes
• On-Demand
• Free Video

ICTP Mathematics

Partial Differential Equations - Lecture 22

Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

ICTP Mathematics

Partial Differential Equations - Lecture 16

Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

ICTP Mathematics

Partial Differential Equations - Lecture 10

Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.

• YouTube
• 1 hour 33 minutes
• On-Demand
• Free Video