This seminar will look at remarkable polytopes — among them regular polytopes, cyclic/neighborly polytopes, hypersimplices, 2-simple 2-simplicial 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)
The seminar will take place mostly in English.
Dates, Speakers and Topics:
19. April First meeting
10. May: Danijela Zanko - "The 14th Archimedian solid"
> Grünbaum "An enduring error", Cromwell: "Polyhedra"
24. May: Pablo Martin - "Walkup's polytope W_9"
> Walkup; Santos-Kim JDMV 2010
31. May: Emanuele Ventura - "The 24-cell: reflexive and deformed"
> Kreuzer-Skarke classification; Andreas Paffenholz, PhD thesis
7. June: Justine Mullon - "The Hansen polytope of the 4-path"
> Kalai, Sanyal-Werner-Ziegler
14. June: Nikolay Stefanov - "A Wythoff 9-polytope without 3-simplex or 3-cube face"
> Pfeifle; Rasi master thesis
21. June: Hilko Paschke - "The 5-dimensional hypersimplex \Delta(3,6)"
> Kalai; Sanyal-Werner-Ziegler
12. July: Jose Antonio Akieme Rodriguez - "The smallest 2-simple 2-simplicial 4-polytope"
> Axel Werner, PhD thesis
19. July: Gil Kalai at 7ECM http://www.7ecm.de/program/plenary_talks.html