Regularity Theory Courses and Certifications

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

Hausdorff Center for Mathematics

Sobolev Regularity for Maximal Operators

Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.

• YouTube
• 43 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

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

ICTP Mathematics

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
• 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 - 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

ICTP Mathematics

Existence and Regularity Theories of Brakke Flow - Lecture 4

Explore advanced theories of Brakke flow, focusing on existence and regularity aspects in this in-depth lecture by Yoshihiro Tonegawa from Tokyo Institute of Technology.

• YouTube
• 1 hour 20 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

Hausdorff Center for Mathematics

Regularity of Free Boundaries in Obstacle Problems - Lecture II

Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.

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

Institute for Pure & Applied Mathematics (IPAM)

Dimers on a Riemann Surface and Compactified Free Field

Explore dimer models on Riemann surfaces, height function convergence, and connections to compactified free fields. Gain insights into probabilistic methods and discrete complex analysis in statistical mechanics.

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

Stony Brook Mathematics

Geometric Variational Problems: Regularity vs Singularity Formation

Explore techniques for existence, regularity, and singularity formation in geometric problems, focusing on harmonic maps, Yang-Mills connections, and nematic liquid crystals. Discover new gluing methods for parabolic flows.

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

Institut des Hautes Etudes Scientifiques (IHES)

Generic Regularity in Obstacle Problems

Explore the obstacle problem in elastic membranes, including classical results, free boundary regularity, and recent developments in this fundamental mathematical challenge.

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