Riemannian Manifolds Courses and Certifications

Simons Institute

Constrained Optimization on Riemannian Manifolds

Explore advanced mathematical techniques for solving optimization problems on curved spaces, with applications in machine learning and data analysis.

• YouTube
• 37 minutes
• On-Demand
• Free Video

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 Video

Institut des Hautes Etudes Scientifiques (IHES)

Waists Measured via Urysohn Width in Riemannian Manifolds

Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Fields Institute

Riemannian Manifolds, Isometries, and Geodesics - Lecture 3

Explore Riemannian manifolds, isometries, and geodesics, with a focus on the upper half-plane and hyperbolic metric in this advanced geometry lecture.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

The Formulation of the Navier-Stokes Equations on Riemannian Manifolds

Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.

• YouTube
• 1 hour
• On-Demand
• Free Video

Stony Brook Mathematics

Mapping Riemannian Manifolds in Metric Spaces

Explore Riemannian manifold mappings, their applications in geometry, and the construction of canonical shapes. Gain insights into special mappings, stability problems, and geometric inequalities.

• YouTube
• 56 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Mathematical Preliminaries II - Riemannian Manifolds

Explore Riemannian manifolds, metric tensors, coordinate transformations, and tensor operations essential for advanced differential geometry and physics applications.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

Graph Structure of the Nodal Set on Riemannian Manifolds

Explore the geometric analysis of eigenfunction zero sets on Riemannian manifolds, examining connections between graph theory, nodal sets, and critical point estimation in spectral geometry.

• YouTube
• 40 minutes
• On-Demand
• Free Video

HyperComplex Seminar

The Grad Div Operator in Symmetric Tensors on Riemannian Manifolds

Explore the grad div operator in symmetric tensors on Riemannian manifolds, focusing on gradient and divergence definitions and their composition in differential geometry.

• YouTube
• 16 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Mikhail Katz - Collapsing Surfaces

Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Exploiting Geometric Structure in Matrix-Valued Optimization

Exploring optimization on matrix manifolds, introducing Riemannian Frank-Wolfe methods for constrained problems, and discussing applications in machine learning and mathematics.

• YouTube
• 58 minutes
• On-Demand
• Free Video

International Mathematical Union

Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces

Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes

Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Fields Institute

Harmonic Maps and Rigidity

Explore harmonic maps, rigidity theorems, and their applications in geometry. Delve into existence theory, Mostow's strong rigidity, and approaches to rigidity using harmonic maps and the Bochner method.

• YouTube
• 51 minutes
• On-Demand
• Free Video

BIMSA

Hyperbolic Manifolds in Dimension Higher Than 3

Explore hyperbolic manifolds in dimensions 4 and higher, examining their properties, challenges in description, and current understanding in topology.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video