Differential Geometry Courses and Certifications

NPTEL;  IIT Madras

Basic Algebraic Geometry - Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity

Explore algebraic geometry fundamentals, including varieties, morphisms, local rings, function fields, and nonsingularity. Gain insights into Zariski topology, affine and projective spaces, and geometric calculus.

• YouTube
• 1 day 13 hours
• Self-Paced
• Free Video

World Science Festival

Steven Weinberg and the Quest to Explain the World

Explore Nobel laureate Steven Weinberg's groundbreaking contributions to physics, including electroweak theory, with Brian Greene and John Preskill in this tribute to a scientific visionary.

• YouTube
• 57 minutes
• Self-Paced
• Conference Talk

The Royal Institution

The Extraordinary Theorems of John Nash

Explore John Nash's revolutionary contributions to game theory and geometric analysis with Fields Medal winner Cédric Villani, delving into the world of mathematical genius and groundbreaking theorems.

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

Professor Leonard

Calculus 3 - Cylinders and Surfaces in 3-D

Comprehensive guide to identifying and hand-sketching 3D geometric shapes, including cylinders, ellipsoids, hyperboloids, cones, paraboloids, and hyperbolic paraboloids in calculus.

• YouTube
• 2 hours 32 minutes
• Self-Paced
• Free Video

Richard Behiel

Introduction to Fiber Bundles and the Hopf Fibration

Explore the fascinating world of fiber bundles and Hopf fibration, discovering their mathematical beauty and applications in quantum mechanics and theoretical physics.

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

Institute for Advanced Study

Symplectic Geometry Seminar

Explore advanced symplectic geometry through expert lectures covering Floer theory, contact topology, Hamiltonian dynamics, and mirror symmetry from leading researchers.

• YouTube
• 5 days 18 hours 24 minutes
• Self-Paced
• Free Video

Tobias Osborne

Symplectic Geometry and Classical Mechanics

Explore the mathematical foundations connecting symplectic geometry with classical mechanics through comprehensive lectures covering geometric structures and physical applications.

• YouTube
• 1 day 4 hours 53 minutes
• Self-Paced
• Free Video

Simons Institute

On Gradient-Based Optimization - Accelerated, Distributed, Asynchronous and Stochastic

1 rating

Explore advanced gradient-based optimization techniques for machine learning, including accelerated, distributed, asynchronous, and stochastic methods, with insights from differential geometry and nonconvex optimization.

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

Institute for Advanced Study

Notions of Scalar Curvature - Mikhail Gromov

Explore scalar curvature concepts, spin bundles, and rich curves with renowned mathematician Mikhail Gromov in this advanced topology lecture from the Institute for Advanced Study.

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

World Science Festival

Einstein, The Big Bang, and the Expansion of the Universe

Explore Einstein's theory of relativity, the Big Bang, and cosmic expansion through visual explanations and essential mathematics, offering a fresh perspective on the universe's origins and evolution.

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

Mathologer

Archimedes' Claw and Carousel - Upgrading Ancient Discoveries

Explore Archimedes' mathematical discoveries upgraded after 2000 years, including the baggage carousel concept, inside-out animations, and the fascinating Archimedes' claw.

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

Mathemaniac

Exponentiating Vectors, Derivatives, and Vector Fields - Mathematical Concepts Explained

Explore the concept of exponentiation applied to vectors, derivatives, and vector fields, uncovering connections between seemingly different mathematical ideas and their practical applications.

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

Insights into Mathematics

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

Introduces a new rational definition of polytope curvature, using turn-angle to connect curvature with Euler number. Explores opposite cones and applies Harriot's theorem on spherical triangles.

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

Mathemaniac

How Physics Solves Plateau's Problem - Applications in Math and 3D Graphics

Explore how physics and mean curvature flow solve Plateau's problem, with applications in mathematics, soap films, and 3D graphics. Discover connections between minimal surfaces and active research areas.

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

Michael Penn

Differential Forms - Boundaries of M-Cells and M-Chains

Explore the concept of boundaries in differential forms, focusing on m-cells and m-chains. Learn to calculate examples and understand their mathematical significance in this concise tutorial.

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