Harmonic Maps Courses and Certifications

Banach Center

Singularities of Minimizing Harmonic Maps

Explore singularities of minimizing harmonic maps, delving into mathematical concepts and theories with expert insights from Michał Miśkiewicz.

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

BIMSA

Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps

Explore sharp rectifiability results for singular sets of minimizing harmonic maps, with uniform Minkowski bounds and integrability. Analyze quantitative stratification and dimension-reduction techniques.

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

BIMSA

Harmonic Maps with Free Boundary: Regularity, Singularity Formation and Geometric Applications

Explore harmonic maps with free boundary, covering existence, regularity, and parabolic blow-up. Examine elliptic and parabolic problems, recent advances in regularity theory, and geometric applications to the Steklov problem.

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

University of Chicago Department of Mathematics

Nonlinear Harmonic Maps and the Energy Identity

Dive into nonlinear harmonic maps, exploring singularity formation and defect measures. Gain insights into the Energy Identity conjecture and its recent proof in this advanced mathematics lecture.

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

Institut des Hautes Etudes Scientifiques (IHES)

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 1/4

Explore harmonic maps from 2D surfaces to high-dimensional spheres through unitary representations, rigidity phenomena, random matrix theory, and PSL2(R) representation theory.

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

BIMSA

Regularity of Harmonic Maps Between Singular Spaces

Explore advanced mathematical analysis of harmonic maps and their regularity properties when dealing with singular geometric spaces and complex boundary conditions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 4/4

Explore rigidity phenomena of harmonic maps from 2D surfaces to high-dimensional spheres using random matrix theory and PSL2(R) representation theory in geometric analysis.

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

Institut des Hautes Etudes Scientifiques (IHES)

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 3/4

Explore rigidity phenomena of harmonic maps from 2D surfaces to high-dimensional spheres using representation theory and random matrix techniques in geometric analysis.

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

Institut des Hautes Etudes Scientifiques (IHES)

Harmonic Maps in High-Dimensional Spheres, Representations and Random Matrices - 2/4

Explore harmonic maps from 2D surfaces to high-dimensional spheres using unitary representations, random matrix theory, and PSL2(R) representation theory in geometric analysis.

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

International Centre for Theoretical Sciences

Harmonic Maps and Framed PSL(2,C)-Representations

Explore the intricate connections between harmonic maps and framed PSL(2,C)-representations in this advanced mathematical lecture on minimal surface theory.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Loop Groups and Harmonic Maps - Lecture 2

Explore advanced connections between loop groups and harmonic maps in minimal surface theory through rigorous mathematical analysis and geometric perspectives.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Asymptotics of High Energy Harmonic Maps from Riemann Surfaces - Lecture 3

Explore advanced mathematical analysis of harmonic maps from Riemann surfaces, focusing on high-energy asymptotic behavior in this specialized geometry lecture.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Loop Groups and Harmonic Maps - Lecture 1

Explore loop groups and their connection to harmonic maps in this foundational lecture on minimal surface theory and geometric analysis.

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

International Centre for Theoretical Sciences

Asymptotics of High Energy Harmonic Maps from Riemann Surfaces - Lecture 2

Explore advanced mathematical analysis of harmonic maps from Riemann surfaces, focusing on high-energy asymptotic behavior and geometric properties in this specialized lecture.

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

International Centre for Theoretical Sciences

Asymptotics of High Energy Harmonic Maps from Riemann Surfaces - Lecture 1

Explore asymptotic behavior of high-energy harmonic maps from Riemann surfaces in this advanced mathematical analysis lecture by Mike Wolf.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video