All things Riemannian: metrics, (sub)manifolds and gradients

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Related lectures (58)

Orthogonal Projection: Euclidean Space Log in to Mediaspace to watch this video

Explores orthogonal projection in Euclidean space, emphasizing uniqueness and calculation methods.

Regular Curves and Constant Speed Log in to Mediaspace to watch this video

Covers regular curves and constant speed, with examples of circles and helices.

Geometry: Opening Lecture 15.04.2021 (live)Log in to Mediaspace to watch this video

Covers the importance of digital tools and the study of different geometries.

Ellipses and Curves in Geometry Log in to Mediaspace to watch this video

Explores ellipses, curves, and their applications in astronomy and mathematics.

Riemannian Trust Regions framework Log in to Mediaspace to watch this video

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

TNB Frame: Frenet-Serret Formulas Log in to Mediaspace to watch this video

Covers the TNB frame and Frenet-Serret formulas for understanding curve behavior.

Singularities of Curves in Geometry Log in to Mediaspace to watch this video

Explores singularities in curves, including inflection points and points of reversal, and discusses the evolution of torsion along curves.

Introduction to Optimization Log in to Mediaspace to watch this video

Introduces linear algebra, calculus, and optimization basics in Euclidean spaces, emphasizing the power of optimization as a modeling tool.

Calculus Applications: Lengths and Surfaces of Revolution Log in to Mediaspace to watch this video

Discusses the applications of calculus in calculating lengths and surfaces of revolution, emphasizing integral calculus and geometric interpretations.

Geometric Analysis: Singularities in Architectural Design Log in to Mediaspace to watch this video

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Euclidean Isometries: Properties and Applications Log in to Mediaspace to watch this video

Explores the properties and applications of Euclidean isometries in R^2.

Orthogonal Linear Maps Log in to Mediaspace to watch this video

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Analytical Geometry: Circles and Tangents Log in to Mediaspace to watch this video

Explores circles, tangents, right lines, planes, and vector products in analytical geometry.

Ellipse and Circle: Geometric Analysis Log in to Mediaspace to watch this video

Covers the geometric analysis of ellipses and circles, including foci, center, and symmetry.

Untitled Log in to Mediaspace to watch this video

Surface Integrals: Implicit Surfaces Log in to Mediaspace to watch this video

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Conics in the Plane: Uniform Description of 3 Conics Log in to Mediaspace to watch this video

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

Symmetry in Modern Geometry Log in to Mediaspace to watch this video

Delves into modern geometry, covering transformations, isometries, and symmetries.

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