Title of the course: Introduction to polytopes
Instructor: Dr. Eleni Tzanaki
Institution: University of Crete
Dates: 21-27 August 2017
Prerequisites: Basic knowledge of combinatorics and linear algebra. I will also adjust the level of the course to that of the students. (If we do not have enough time to cover some of the topics, I will just skip them.)
Level: Graduate, advanced undergraduate
Abstract: Introduction to polytopes (definition, V- and H- representation). Basic examples (simplex, cube, crosspolytopes etc.) and then more interesting ones (i.e., permutahedron, cyclic polytope, 0/1 polytopes) simple and simplicial polytopes, dual of a polytope face lattice, f-vector, h-vector, Euler's formula. Shellings of polytopes (what does the h-vector count in terms of shellings?) Integer and rational polytopes, Ehrhart polynomials and Ehrhart reciprocity theorem (Applications and examples in sage).