Project III, 2018-2019
Combinatorics of polytopes
Anna Felikson and Pavel Tumarkin
Plytopes are higher-dimensional analogues of polygons and polyhedra. They have attracted scientists' attention starting from Plato's time, and remain an important object of study in different branches of contemporary mathematics. Some of the possible things to study in the project would be
Prerequisites: Algebra II.
Corequisite: Geometry III. Topology may also be useful.
Resources:There are many nice books and articles on combinatorics of polytopes. You may start with the following:
- Alexander Barvinok, Combinatorics of polytopes.
- V.M.Buchstaber, T.E.Panov, Toric Topology.
- Branko Grünbaum, Convex polytopes (library link).
- Günter Ziegler, Lectures on polytopes (library link).
- Günter Ziegler, Polytopes: Extremal Examples and Combinatorial Parameters. Slides.