Differential Geometry Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Workshop on Quantum Geometry

Explore advanced quantum geometry through expert lectures on Gromov-Witten theory, Donaldson-Thomas invariants, integrable systems, and spectral curve quantization from leading researchers.

• YouTube
• 14 hours 45 minutes
• Self-Paced
• Free Video

Institut Henri Poincaré

Mathematical General Relativity - 2015 Trimester

Explore advanced mathematical frameworks of general relativity, black hole theory, and self-gravitating matter through expert lectures from Princeton and leading researchers.

• YouTube
• 1 day 14 hours 14 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Master Class in Geometry, Topology and Physics

Explore advanced mathematical physics through algebraic geometry, symplectic geometry, quantum topology, field theory, and Poisson geometry in this intensive master class series.

• YouTube
• 1 week 20 hours 28 minutes
• Self-Paced
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Between Geometry and Relativity - Summer School

Explore advanced mathematical physics connecting differential geometry with Einstein's general relativity through expert lectures on initial data construction, energy theorems, and spacetime dynamics.

• YouTube
• 14 hours 42 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups (2025)

Explore cutting-edge developments in hyperbolic geometry and group theory through expert lectures and hands-on minicourses from leading mathematicians worldwide.

• YouTube
• 1 day 6 hours 39 minutes
• Self-Paced
• Free Video

Utrecht Geometry Centre

Geometry, Mechanics, and Control - Young Researchers Workshop

Explore advanced topics in differential geometry, optimal control theory, and mathematical physics through expert lectures on Pontryagin principles, contact manifolds, and Hamiltonian systems.

• YouTube
• 9 hours 47 minutes
• Self-Paced
• Free Video

Tobias Osborne

General Relativity

Master Einstein's theory through manifolds, tensors, curvature, field equations, and solutions including Schwarzschild metrics, gravitational waves, and cosmological models.

• YouTube
• 21 hours 40 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

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

Insights into Mathematics

Infinity in Greek Mathematics - Math History - NJ Wildberger

Explore ancient Greek mathematics, focusing on Eudoxus and Archimedes' groundbreaking work in calculus, geometry, and mechanics. Discover their ingenious formulas and principles that laid the foundation for modern mathematics.

• YouTube
• 54 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

Joint Mathematics Meetings

The Concept of Holonomy - Its History and Recent Developments

Explore the concept of holonomy, its historical evolution, and recent advancements in mathematics with Duke University's Robert L. Bryant in this insightful lecture.

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