SF2742 Convex Polytypes 7.5 credits

Basic facts about polytopes and methods to study them such as projections, face lattice, Schlegel diagrams, scaling, Gale diagrams and something about oriented matroids. We will also discuss many beautiful and important designs of special polytopes: cyclic polytopes, the Birkhoff polytope, zonotopes, Minkovski sums, 0/1-polytopes, transport polytopes, the permutahedron, the associahedron, etc.

The course intends to give familiarity with basic theory and methods within the theory of convex polytopes. The aim is to give advanced knowledge which constitutes an appropriate a basis both for further studies in mathematics and for applications in related disciplines. Concretely, on completion of the course the student should

• Be familiar with the basic concepts and terms within the theory of convex polytopes.
• Be able to interpret the combinatorial properties of a polytope from its face lattice, Schlegel diagram or Gale diagram
• Be able to design examples of polytopes with certain desirable properties, such as diameter, vertex degree, face lattice structure, etc. and know something about when it is difficult to do this.
• Know and be able to use many explicit important polytopes and methods to design new ones.
• Increased ability to determine intuitively the properties of polytopes in higher dimensions and humility before the fact that intuition from 3 dimensions can easily lead incorrectly in higher dimensions.

SF1631 Discrete Mathematics and SF1604 linear algebra or the equivalent knowledge.

Ziegler, Günter M: "Lectures on Polytopes"; Springer Graduate Texts in Mathematics.

If the course is discontinued, students may request to be examined during the following two academic years.

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.