Differential Geometry Courses and Certifications

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Global Homotopies for HKR Theorems in Differential Geometry

Delve into advanced differential geometry concepts through an exploration of HKR theorems, global homotopies, and their applications in deformation theory and symbol calculus.

• YouTube
• 55 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Online Course

Professor Leonard

Calculus 3 - TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation

Explore TNB Frames, curvature, and torsion in vector calculus. Learn to compute Frenet-Serret frames, find osculating circles and planes, and perform vector encapsulation for 2D functions.

• YouTube
• 2 hours 37 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Differential Calculus for Curves - Lagrange's Algebraic Approach - Lecture 4

Explore Lagrange's algebraic approach to differential calculus, focusing on polynomial functions and Taylor approximations. Learn about tangent lines, conics, and sub-derivatives without limits or real numbers.

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

ICTP Mathematics

Extrinsic Curvature Flows - Analysis and Geometry at the Interface

Explore advanced mathematical techniques in extrinsic curvature flows, covering mean curvature flow, singularities, Brakke flow theory, and applications to geometry and physics.

• YouTube
• 1 day 18 hours 51 minutes
• Self-Paced
• Free Video

Mathemaniac

The Clever Way Curvature is Described in Math - Gaussian and Mean Curvatures

Explore Gaussian and mean curvatures in differential geometry, focusing on the shape operator to understand surface curvature and its applications in minimal surfaces.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Geometry for Higher Spin Gravity - Conformal Structures, PDEs, and Q-manifolds

Explore advanced mathematical frameworks connecting higher-spin gravity, conformal geometry, and quantum field theory through expert lectures on Cartan geometries, holography, and PDEs.

• YouTube
• 2 days 15 hours 48 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Seminar in Analysis and Geometry

Explore advanced topics in analysis and geometry through expert seminars covering fluid dynamics, differential equations, manifold theory, and geometric structures.

• YouTube
• 23 hours 18 minutes
• Self-Paced
• Free Video

World Science Festival

Curvature and Parallel Motion

Explore Einstein's theory of gravity through curvature mathematics. Brian Greene introduces key concepts and equations, offering insights into the universe's fundamental nature.

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

Institut des Hautes Etudes Scientifiques (IHES)

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 2

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Loewner Energy at the Crossroad of Random Conformal Geometry - Lecture 1

Explore the Loewner energy's role in random conformal geometry, connecting SLE, Weil-Petersson quasicircles, and various mathematical branches. Gain insights into curve roundness and its implications across multiple fields.

• YouTube
• 1 hour 52 minutes
• Self-Paced
• Free Video

Broad Institute

Single-Cell Spatiotemporal Modeling - From RNA Velocity to Spatial Transcriptomics

Explore single-cell spatiotemporal modeling with dynamo framework and Stereo-seq technology. Uncover insights into cellular states, transitions, and spatial dynamics in developmental biology and neuroscience.

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

International Centre for Theoretical Sciences

The Mathematics of Soap Bubbles

Explore the fascinating mathematical principles behind soap bubbles' perfect spherical shape and discover connections to physics, integrable systems, and ongoing research.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Infinite-Dimensional Geometry - Theory and Applications

Explore infinite-dimensional geometry from abstract theory to medical applications through 5 weeks of mini-courses covering manifolds, dynamical systems, shape analysis, and real-world uses.

• YouTube
• 2 days 18 hours 49 minutes
• Self-Paced
• Free Video