Curvature Courses and Certifications

Hausdorff Center for Mathematics

Curvature of the Determinant Line Bundle for Noncommutative Tori

Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Motion by Curvature of Networks in the Plane - Lecture 4

Explore motion by curvature of planar networks, covering collapse, parametrization, evolution equations, special cases, singularities, and localization. Gain insights into this advanced mathematical topic.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Phase-Field Models for Motion by Mean Curvature - Lecture 2

Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 5

Explore singularities in mean curvature flow of convex hypersurfaces, covering max inequality, weak solutions, surgeries, and Type 2 singularities with intuitive explanations.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Euclidean and Lorentz-Minkowski 3-Space - Lecture 1

Explore zero mean curvature surfaces in Euclidean and Lorentz-Minkowski spaces, covering fundamental concepts, variations, stability, and examples of minimal surfaces with diverse properties and geometries.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Society for Industrial and Applied Mathematics

Mean Curvature Flow, Neural Networks, and Applications

Explore mean curvature flow's applications in image processing, data science, and biology. Learn how neural networks can approximate interface evolutions for non-oriented surfaces, with applications to Steiner and Plateau problems.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Conference Talk

Schmid College, Chapman University

Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants

Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Width, Scalar Curvature and Macroscopic Scalar Curvature

Explore the interplay between positive scalar curvature and macroscopic scalar curvature, examining Urysohn width and closed geodesics in PSC and PMSC spaces.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Another Aspect of Gromov's Conjectures on Scalar Curvature

Explore Gromov's scalar curvature conjectures through general relativity, examining partial solutions via the positive mass theorem.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Variational Methods for Scalar Curvature and Other Curvature Problems

Explore geometric variational problems and their applications to curvature conditions, focusing on Schoen-Yau's approach and recent extensions.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Positive Mass Theorem and Positive Scalar Curvature with Singularities

Explore recent developments in positive mass theorem and scalar curvature, focusing on singular metrics and isolated conical singularities in mathematical physics.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Nonnegative Ricci Curvature, Nilpotency, and Hausdorff Dimension

Explore nonnegative Ricci curvature, nilpotency, and Hausdorff dimension in relation to universal covers, minimal representing loops, and asymptotic cones of manifolds.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Global Effects of Positive Scalar Curvature in Geometry

Explorez les effets globaux de la courbure scalaire positive, y compris le problème de remplissage de Gromov et les théorèmes de type Llarull sur les variétés complètes.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Spaces with Ricci Curvature Lower Bounds

Explore recent findings on spaces with nonnegative Ricci curvature, including singular set dimensions, fractal-like Weyl's laws, and nonproper Busemann functions in manifolds.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Ricci Curvature, Fundamental Group and the Milnor Conjecture - Part 2

Explore advanced concepts in topology and geometry, focusing on counterexamples to the Milnor conjecture and their construction using mapping class groups and asymptotic cones.

• YouTube
• 57 minutes
• Self-Paced
• Free Video