Geometry of Finite-dimensional Normed Spaces

What it is about

You deal with the geometry of finite-dimensional normed spaces and convex bodies. You learn fundamental theorems of convex and discrete geometry as well as tools (e.g. Helly, Carathéodory, Radon, John ellipsoid, Banach–Mazur distance) and apply these to concrete problems in finite normed spaces.

What you will be able to do

• Know fundamental properties of finite-dimensional normed spaces and convex bodies
• Apply important theorems of convex geometry (Helly, Carathéodory, Radon)
• Understand concepts such as smoothness and strict convexity of convex bodies
• Carry out projections and estimates of projection constants in classical cases
• Apply Banach–Mazur distance and John ellipsoid theorem
• Tackle distance and metric problems in normed spaces

What the module consists of

• Vorlesungdelivers the fundamental theoretical tools and examples
• Übungsgruppe/Exercise classescentral problem-solving portion; assignments are released in advance and worked on together in the exercise

Teaching method

• Problemorientierte Übungenenable development of problem-solving skills and teamwork
• Begleitvorlesungenprovide the necessary theoretical tools and illustrative examples