Possible topics

Here is a list of possible topics and for most of them we have added a possible reading.
Possible dates: May 10 (full), May 17 (full) and May 24 plus possibly one more time.

-The cd-index - survey by Marge Bayer, https://bayer.ku.edu/pub/preprints/cd-survey.pdf Links to an external site.
-inside-out polytope Links to an external site. - paper by Matt Beck and Thomas Zaslavsky
-Gröbner basis for toric varieties - Book by Sturmfels, chapter 2 and 8 Links to an external site.
-Oriented matroids and polytopes - DRS 4.1 and examples from 4.2 or other parts
-Fiber polytopes - Ziegler Chapter 9.1 and DRS Chapter 9.1 
-Universal polytope and optimization, DRS Chapter 8.5
-Random polytopes - Start from the preprint by Schneider: https://arxiv.org/abs/2202.06774 Links to an external site.
-Triangulations of Flow Polytopes, Ample Framings, and Gentle Algebras   Links to an external site.https://arxiv.org/abs/2203.01896
-Lower bound centrally symmetric polytopes - by Klee, Nevo, Novik, Zeng Links to an external site.
-The Polyhedral Geometry of Pivot Rules and Monotone Paths Links to an external site., by Black, De Loera, Lütjeharms, Sanyal

-Reconstructibility of Polytopes - survey by Bayer Links to an external site.,
-On the Reconstruction of Polytopes - Doolittle, Nevo, Pineda-Villavicencio, Ugon, Yost Links to an external site.

-Zonotopes and their Ehrhart theory - Ziegler Chapter 7.3, Beck-Robins Computing the continuous discretely Chapter 9

-Neighborly cubical polytopes - article by Joswig - Ziegler Links to an external site.

-Polytopes from posets - article by Stanley

-McMullen's polytope algebra Links to an external site.

-Splines - Possible starting point: Billera - Homology of Smooth Splines Links to an external site.

-A chapter or two from Robins - Fourier Analysis on Polytopes Links to an external site.

-Fatness of 4 dim polytopes
-Faces of directed polytope
-Newton polytopes