Riemannian Geometry Courses and Certifications

Bifurcation Phenomena in Geometric Variational Problems

Explore classical Bifurcation Theory and its modern applications in Riemannian Geometry, covering minimal and constant mean curvature surfaces and the Yamabe problem.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course

Institute for Advanced Study

Geometry of 2-Dimensional Riemannian Disks and Spheres - Regina Rotman

Explore 2D Riemannian geometry, focusing on disks and spheres. Learn about geodesics, sweep-outs, and curve shortening through examples and problem-solving.

• YouTube
• 1 hour
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

The Gromov-Hausdorff Distance Between Spheres

Explore the Gromov-Hausdorff distance between spheres, its applications in geometry and topology, and methods for calculating precise values between specific sphere pairs.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Curvature Bounds and the Length of the Shortest Closed Geodesic

Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.

• YouTube
• 47 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Symmetric Spaces by Pralay Chatterjee

Explore symmetric spaces in this advanced lecture on geometry, groups, and dynamics. Delve into modern research aspects and connect with cutting-edge theories in the field.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Crash Course in Riemannian Geometry by Harish Seshadri

Introductory lecture on Riemannian geometry, covering fundamental concepts and principles for graduate-level students in mathematics and theoretical physics.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces

Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.

• YouTube
• 24 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Discrete Homotopy Theory and Applications

Explore discrete homotopy theory's evolution, applications in topology, geometry, and group theory. Learn simplified approaches to fundamental groups and covering spaces, with insights into various mathematical domains.

• YouTube
• 49 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Geodesic Complexity of Riemannian Manifolds

Explore geodesic complexity in Riemannian manifolds, connecting robot motion planning to topology and geometry. Learn about cut loci, bounds, and applications in this advanced mathematical talk.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 1

Explore optimal transportation, Monge-Ampère equations, and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio from Scuola Normale Superiore di Pisa.

• YouTube
• 1 hour 48 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Differential Geometry - Lecture 19

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture by Claudio Arezzo.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Differential Geometry - Lecture 20

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry and physics.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Differential Geometry - Lecture 17

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Differential Geometry - Lecture 15

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture by Claudio Arezzo.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Online Course

ICTP Mathematics

Differential Geometry - Lecture 13

Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Online Course