Polyhedral and topological combinatorics

Combinatorics and Optimization (CO) 739: Topics in Combinatorics

Topic for winter 2015:

Polyhedral and topological combinatorics


Eric Katz

Class times:

1:30-2:20pm Monday, Wednesday, Friday.


UWaterloo Learn


Convex polytopes, duality, Schlegel diagrams, cyclic poly-topes, Gale transforms, Euler's relation, Dehn-Sommervill relation and it generalizations, extremal problems, polyhedral complexes, order complexes of posets, shellings, simplicial spheres, Sperner's Lemma and Brouwer fixed point theorem, Tucker's Lemma and the Borsuk-Ulam theorm, Lovasz's work on the Kneser conjecture, simplicial homology, Lefschetz fixed point theorem.


There will be no official textbook, but the following sources are recommended:

  1. Branko Grunbaum, Conver Polytopes
  2. Gunter M. Ziegler, Lectures on Polytopes
  3. Rekha R. Thomas, Lectures in Geometric Combinatorics
  4. Jiri Matousek, Using the Borsuk-Ulam Theorem
  5. Alan Hatcher, Algebraic Topology


Please do not use laptops or phones in class. You may take notes on a tablet.


There will be one midterm exam and a comprehensive final. 

The test dates are:

  1. Wednesday February 26: midterm in-class
  2. Final exam: to be announced


Homework will be due at the beginning of class on most Fridays. The lowest homework score will be dropped.


  • Homework: 40%
  • Midterm exam: 20%
  • Final exam: 40%

Individual test scores will not be re-centered. Raw scores will be used to compute course grades which will be re-centered to give a course grade. The instructor will not take personal factors into account when assigning course grades.