Geometric Measure Theory Courses and Certifications

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

Applied Algebraic Topology Network

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.

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

Introduction to Projection Theory - Lecture 01

Discover the fundamental questions and goals of projection theory, focusing on the exceptional set problem in this introductory MIT mathematics lecture.

• YouTube
• 1 hour 18 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

Institut des Hautes Etudes Scientifiques (IHES)

Area-Minimizing Integral Currents: Singularities and Structure - Lecture

Explore area-minimizing integral currents, their singularities, and structure. Delve into dimension bounds, fractal properties, and recent progress towards proving key conjectures in geometric measure theory.

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

Institut des Hautes Etudes Scientifiques (IHES)

Self-Similar Solutions to Extension and Approximation Problems - Lecture

Explore self-similar solutions in extension and approximation problems, focusing on Lipschitz and Hölder maps with unique properties in higher dimensions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Union of Tubes and Kakeya Sets - 2/3

Explore advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R2 and R3, with key applications to the challenging Kakeya problem.

• YouTube
• 2 hours 46 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Union of Tubes and Kakeya Sets - 1/3

Discover advanced techniques like Cordoba argument and projection theory to prove volume bounds on tube unions in R2 and R3, with key applications to the challenging Kakeya problem.

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

IAS | PCMI Park City Mathematics Institute

Almgren's Center Manifold in a Simple Setting

Explore Almgren's center manifold theory through a simplified toy case, proving C³,α regularity for minimal surfaces using elementary methods without Schauder estimates.

• YouTube
• 4 hours 16 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Furstenberg Sets Estimates with Application to Restriction Theory

Explore advanced mathematical concepts connecting Kakeya sets, Hausdorff dimensions, and Fourier restriction theory through wave packet decompositions in this research seminar.

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

The Bourgain Projection Theorem Part 1 - Over the Real Numbers - Lecture 14

Explore Bourgain's projection theorem, a fundamental result in projection theory, focusing on its formulation and applications over the real numbers in advanced mathematical analysis.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Sharp Projection Theorems Part 1 - Introduction and Beck's Theorem - Lecture 22

Explore breakthrough projection theory techniques by Orponen-Shmerkin and Ren-Wang, learning to transform non-sharp bounds into sharp bounds through Beck's Theorem applications.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Sharp Projection Theorems Part 2 - AD Regular Case - Lecture 23

Explore Orponen and Shmerkin's sharp projection theorem for sets with self-similar spacing in this advanced mathematical analysis lecture.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

The Bourgain Projection Theorem, Part 2 - Lecture 15

Explore uniform sets and branching functions in the second part of the Bourgain Projection Theorem, advancing your understanding of projection theory through rigorous mathematical analysis.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Fundamental Methods of Projection Theory - Lecture 2

Explore two fundamental methods for studying projections: Kaufman and Falconer's double counting technique and Fourier analysis approach from the 1960s-70s.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video