matthias beck

some of matt's pictures

Discrete Geometry III:

Enumerative Geometric Combinatorics

FU Berlin Winter 2019/20

Lecture & Exercises Tue/Thu 12-14, Seminarraum @ Villa
Instructor Prof. Matthias Beck
Office Villa
Office hours Wed 11-12, 14-15 & by appointment

Course description. This is the last in a series of three courses on discrete geometry. This advanced course will cover a selection of topics from enumerative geometric combinatorics:

  • Lattice-point structure of rational polyhedra
  • Rational generating functions
  • Hyperplane arrangements
  • Applications to combinatorial number theory, poset theory, and partition analysis

Prerequisites. Linear algebra, basic combinatorics, polyhedral geometry (convex polytopes, faces, polarity, etc.) as covered in Discrete Geometry I-II.


Exercises & final project. I will post (below) weekly homework problems, due on Thursdays before class. To obtain the Aktive Teilnahme stamp, you will need to reach at least a 50% total score on the homework. The final project is a written report on a research topic related to the material covered in our course; I will mention numerous possible topics during class and collect them here. A first draft of your report is due on 1 March; the final draft is due on 1 April (no joke).

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.