Actually Doing It! : A Computational Introduction to Polyhedral Geometry

These are some materials and resources I use in the mini-course ``Computational Polyhedral Geometry'' presented at the Rocky Mountain Mathematics Consortium Summer School (RMMC 2011) and previously at the MAA Northern section Summer school.

The minicourse deals with various computational problems associated with convex polyhedra in general dimension. Typical problems include the feasibility problem (is the convex polytope empty?), the representation conversion problem (between halfspace and vertex representations), the polytope volume computation, the construction of hyperplane arrangements and zonotopes, the computation of integrals and counting of lattice points. We aim to show some of the most important algorithms to solve such problems. All these essential algorithms have applications in a wide variety of topics including discrete optimization, game theory, algebraic and enumerative combinatorics, probability and statistics, cryptography and others.

Lecture Notes and Slides