**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).

**Language:**EN