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Lecture WS 23/24 Advanced Topics in Numerical Analysis

Geometric Calculus in Shape Spaces and its Discretization

Prof. Martin Rumpf

Over the last two decades a rich mathematical theory of shape spaces has been developed. The lecture course will unfold this theory in a self contained fashion and study fundamental tasks such as the definition of suitable distances or the interpolation between objects in these spaces. It will then discuss how to define geometry on these spaces and how to discretize the geometric calculus in an efficient and effective way. The course will introduce a variety of different shape spaces, namely spaces of images, spaces of curves or surfaces, and spaces of diffeomorphisms with application in image processing or in computer graphics.

The course does not require specific knowledge in geometry but participants should have some background in analysis.