Riemannian Trust Regions framework

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Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Geodesic Convexity: Basic Facts and Definitions

Explores geodesic convexity, focusing on properties of convex functions on manifolds.

Hands on with Manopt: Optimization on Manifolds

Introduces Manopt, a toolbox for optimization on smooth manifolds with a Riemannian structure, covering cost functions, different types of manifolds, and optimization principles.

Riemannian metrics and gradients: Examples and Riemannian submanifolds

Explores Riemannian metrics on manifolds and the concept of Riemannian submanifolds in Euclidean spaces.

Computing the Newton Step: Matrix-Based Approaches

Explores matrix-based approaches for computing the Newton step on a Riemannian manifold.

Riemannian Gradient Descent: Convergence Theorem and Line Search Method

Covers the convergence theorem of Riemannian Gradient Descent and the line search method.

Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Riemannian metrics and gradients: Why and definition of Riemannian manifolds

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Taylor expansions: second order

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.