Differential Geometry Courses and Certifications

Sloppy Models, Differential Geometry, and Why Science Works

Explore how complex systems can be modeled despite parameter uncertainties, using differential geometry to understand 'sloppiness' and its implications for scientific comprehension and prediction.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Geometry of Curves and Surfaces

Explore the intrinsic geometry of curves and surfaces in this comprehensive introduction to differential geometry, covering curvature, Frenet-Serret formulas, Gauss maps, and the Gauss-Bonnet theorem.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Intrinsic Volumes on Pseudo-Riemannian Manifolds

Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.

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

Institute for Pure & Applied Mathematics (IPAM)

The Log-Minkowski Problem - IPAM at UCLA

Explore the log-Minkowski problem and recent progress in convex geometry, including uniqueness of self-similar solutions and isomorphic resolution, with applications to centro-affine differential geometry.

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

ICTP Mathematics

Finding Solitons in Differential Geometry

Explore solitons in differential geometry, their role in discovering distinguished geometric structures, and applications in various mathematical contexts including Lie groups and algebras.

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

Open Data Science

Physics-Inspired Learning on Graph - Michael Bronstein, PhD

Explore physics-inspired continuous learning models for graphs, challenging traditional message-passing paradigms. Discover new approaches using differential geometry, algebraic topology, and differential equations to revolutionize graph machine learning.

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

Insights into Mathematics

Curvature for the General Paraboloid - Differential Geometry - NJ Wildberger

Novel approach to surface curvature using projective geometry and linear algebra. Explores paraboloid curvature through characteristic polynomials, offering insights for higher-dimensional generalizations.

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

Insights into Mathematics

Classification of 2-Manifolds and Euler Characteristic - Differential Geometry

Explore the classification of compact, oriented 2-manifolds and their Euler characteristics through combinatorial methods, cut-and-paste operations, and topological invariants in differential geometry.

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

Insights into Mathematics

Paraboloids and Associated Quadratic Forms - Differential Geometry

Explore paraboloids and quadratic forms in differential geometry, covering diagonalization, eigenvalues, and Dupin's indicatrix. Learn key concepts for understanding surface curvature.

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

Insights into Mathematics

Manifolds, Classification of Surfaces and Euler Characteristic - Differential Geometry

Informal introduction to manifolds, focusing on 2D surfaces. Explores charts, orientation, and classification using Euler characteristic. Highlights key concepts in differential geometry.

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

Insights into Mathematics

Geometric and Algebraic Aspects of Space Curves - Differential Geometry

Explore geometric and algebraic aspects of space curves, including tangent vectors, normal planes, curvature, torsion, and associated surfaces. Learn about Monge's contributions and invariant properties.

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

Insights into Mathematics

Curvature, Turning Numbers and Winding Numbers - Differential Geometry

Explores advanced concepts in planar curvature, including turning numbers, winding numbers, and parametric curves. Connects to complex analysis and circular motion, offering insights into differential geometry.

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