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MATH-F408

Convex polytopes

academic year
2023-2024

Course teacher(s)

Samuel FIORINI (Coordinator)

ECTS credits

5

Language(s) of instruction

english

Course content

Basics of polytopes (lattice of faces, facets, etc.). Properties of the graph of a polytope. Steinitz Theorem on three-dimensional polytopes. Hirsch Conjecture, counter-example of Santos. McMullen Upper Bound Theorem on the number of facets. Gale Transforms and polytopes with few vertices. 0/1 polytopes. Group of a polytope, regular polytopes.

Objectives (and/or specific learning outcomes)

After completing the teaching unit, the student will have a general knowledge of the theory of polytopes. Moreover, he will be able to solve problems on polytopes and to expose in a clear way his/her solutions.

Teaching methods and learning activities

Lectures, exercises and personal work.

References, bibliography, and recommended reading

B. Grünbaum, Convex Polytopes (2nd ed.), Springer-Verlag, 2003;

G.M. Ziegler, Lectures on Polytopes (6th print.), Springer-Verlag, 2006

Course notes

  • Université virtuelle

Other information

Contacts

Samuel FIORINI : Samuel.Fiorini@ulb.be

Campus

Plaine

Evaluation

Method(s) of evaluation

  • written examination

written examination

Written exam; oral exam if necessary.

Mark calculation method (including weighting of intermediary marks)

The mark of the written examen, except if the student decides to take the oral exam--in which case the oral exam counts for a third of the final mark.

Language(s) of evaluation

  • french
  • english

Programmes