Differential Geometry Courses and Certifications

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

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

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

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

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

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

Michael Penn

The Geometry of the Third Derivative - Understanding Curves and Their Rate of Change

Explore the geometric interpretation and significance of third derivatives in calculus through clear visual explanations and mathematical insights.

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

Math with Professor V

Calculus 3 Quick Tips - Double Integrals, Surface Integrals, and Lagrange Multipliers

Master essential Calculus 3 techniques including double integrals, surface integrals, Lagrange multipliers, polar coordinates, and order of integration through focused problem-solving sessions.

• YouTube
• 2 hours 58 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Introduction to Gauge Theory

Dive into gauge theory fundamentals through comprehensive mathematical lectures covering connections, curvature, and applications in modern geometry and physics.

• YouTube
• 4 hours 46 minutes
• Self-Paced
• Free Video

Mathemaniac

Every Power-Law Force Has a Conformal Dual

Explore conformal transformations between power-law forces and discover how any force can be mapped to another (except inverse cube law) through mathematical duality.

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

Institute for Advanced Study

Mathematical Physics Seminar - Log-Sobolev Inequality, Maass Spectra, Grassmann Integrals, and Advanced Topics

Explore advanced mathematical physics topics including Ising models, Maass spectra, Grassmann integrals, flat surfaces, Gibbs measures, and conformal field theory.

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

Institute for Advanced Study

Symplectic Dynamics and Geometry Seminar

Explore advanced topics in symplectic geometry through expert lectures on Jordan loops, sub-Riemannian geometry, contact topology, and Floer cohomology from leading researchers.

• YouTube
• 11 hours 17 minutes
• Self-Paced
• Free Video