This seminar will look at remarkable polytopes — among them regular polytopes, cyclic/neighborly polytopes, hypersimplices, 2simple-2simplicial polytopes, cut polytopes, etc. We discuss the examples, their construction and their most interesting properties. Some of these examples were designed or used in order to solve problems, refute conjectures, or to support conjectures. Some of these have unexplored or unexplainable properties, and those of course we want to look at as well.
“It is not unusual that a single example or a very few shape an entire mathematical discipline. Examples are the Petersen graph, cyclic polytopes, the Fano plane, the prisoner dilemma, the real n-dimensional projective space and the group of two by two nonsingular matrices. And it seems that overall, we are short of examples. The methods for coming up with useful examples in mathematics (or counterexamples for commonly believed conjectures) are even less clear than the methods for proving mathematical statements.” — Gil Kalai (2000)
G. M. Ziegler: Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer, 1995, 7th updated printing 2007.
M. Henk, J. Richter-Gebert & G. M. Ziegler: Basic properties of convex polytopes,
Chap. 16 in "Handbook of Discrete and Computational Geometry" (J. E. Goodman & J. O'Rourke, eds.),
Chapman & Hall/CRC Press, 2nd ed. 2004, 355-382.
Topics will be discussed and specific references will be discussed/provided in the first meeting of the seminar.
Pre-Meeting: see KVV
A7/SR 140 Seminarraum (Hinterhaus)
12.03.2018 14:00 - 16:00
wöchentlich, ab 19.04.2018, 12:00 - 14:00 (13 Termine)