Antonio Macchia
Arnimallee 2, Raum 107
macchia[at]zedat.fu-berlin.de
Thursdays from 10 to 12
Arnimallee 7, Seminar Raum 140
First lecture: October 17
Shellability is a fundamental property of the boundary complexes of polytopes and of some simplicial complexes that allows to construct these combinatorial objects by tidily gluing together their maximal faces. We will illustrate some important consequences of shellability for polytopes and clarify the role of shellability in the hierarchy of pure simplicial complexes.
List of possible topics for the seminar. You can also suggest a different topic.
Every student will choose a topic related to shellability and give a 90 minutes presentation. Within two weeks from the presentation the student should also hand in a report on the same topic, written in LaTeX using this template (right click on the link and save the file).
For any question, feel free to contact me at the above e-mail address.
- October 17: Overview on shellability, part 1 (Antonio)
- October 24: Overview on shellability, part 2 (Antonio)
- October 31: Extendable shellability (Joseph)
- November 14: h-vectors and Dehn-Sommerville equations (Martha)
- November 21: Polytopes are shellable: Bruggesser and Mani’s Theorem, Euler-Poincaré formula (Heba)
- November 28: Non-shellable triangulation of balls and spheres (Duong)
- December 5: The partitionability conjecture (Sampada)
- December 12: Non-pure shellability (Steph)
- January 9: The hierarchy of pure simplicial complexes (Ellinor)
- January 16: Face lattices of convex polytopes are CL-shellable (Erin)
- February 6: Some applications of polytopes and simplicial complexes (Antonio)
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- G. Ziegler, Lectures on Polytopes, (Chapter 8), Graduate Texts in Mathematics 152, Springer-Verlag, New York, 1995.
- A. Björner, M. L. Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983), 323–341 (Sections 2,3,4).
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