Combinatorics and Optimization (CO) 739: Topics in Combinatorics
Topic for winter 2015:
Polyhedral and topological combinatorics
Instructor:
Eric Katz
Class times:
1:30-2:20pm Monday, Wednesday, Friday.
Website:
Topics:
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.
Text:
There will be no official textbook, but the following sources are recommended:
- Branko Grunbaum, Conver Polytopes
- Gunter M. Ziegler, Lectures on Polytopes
- Rekha R. Thomas, Lectures in Geometric Combinatorics
- Jiri Matousek, Using the Borsuk-Ulam Theorem
- Alan Hatcher, Algebraic Topology
Technology:
Please do not use laptops or phones in class. You may take notes on a tablet.
Test:
There will be one midterm exam and a comprehensive final.
The test dates are:
- Wednesday February 26: midterm in-class
- Final exam: to be announced
Homework:
Homework will be due at the beginning of class on most Fridays. The lowest homework score will be dropped.
Grading:
- 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.