Geometry of Convex Polytopes
Abstract
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Next lectures
22.04.2026, 10:30 (G3 10 (Lecture hall))
29.04.2026, 10:30 (G3 10 (Lecture hall))
06.05.2026, 10:30 (G3 10 (Lecture hall))
13.05.2026, 10:30 (G3 10 (Lecture hall))
27.05.2026, 10:30 (G3 10 (Lecture hall))
03.06.2026, 10:30 (G3 10 (Lecture hall))
10.06.2026, 10:30 (G3 10 (Lecture hall))
17.06.2026, 10:30 (G3 10 (Lecture hall))
Much appeal of polytope theory stems from the fact that convex polytopes are simultaneously geometric and combinatorial objects. In this lecture will highlight the geometric side of this interaction by following two threads.
On the one hand we study the metric properties of individual polytopes, such as edge lengths, angles, and volumes, the relations between these quantities as well as the constraints imposed on them by the combinatorics. Tools employed range from convex and hyperbolic geometry to spectral graph theory.
On the other hand we study the geometric and topological properties of entire realization spaces, that is, the ways in which a fixed combinatorial type can be realized or a given realizations can be deformed. Realization spaces are real algebraic sets, and we address topics such as universality, parametrization and rigidity.
Keywords
convex polytopes, realization spaces, metric geometry, rigidity, reconstruction
Prerequisites
Basics of convex polytopes, face lattice
Remarks and notes
This course is conceived as a follow up on the block course "Convex Polytopes" by Bernd Sturmfels (https://www.mis.mpg.de/de/events/event/ringvorlesung-2)
