Polyhedra in the Wild, Spring 2016

Here is the original flyer advertising the class, including textbook information.

We meet 12:30PM - 01:50PM Tuesdays and Thursdays in 143 Henry Administration Bldg.

The Syllabus.

Lecture Schedule (Check Regularly for Updates!)

Go here for the lecture schedule, including related links and (partial) source material for each lecture. Roughly, the course will be divided as follows:

Introductory Material: 1/19-1/28/16

Number Theory Connections: 2/2/16- 2/15/16

Operations Research Connections 2/16/16-3/10/16

Mathematical Biology and Algebraic Statistics Connections 3/8/16-4/14/16 (Note: overlap with OR connection)

Student Presentations 4/19/16-5/3/16. Go here for expectations, schedule, linked papers, titles, and abstracts.

Homework

Go here for homework.

Homework is always suggested and never required, but looking at suggested problems will likely improve what you get out of following lectures. Handouts given in class are usually found here when they are not on the Lecture Schedule. Beginning at the end of February we switched to paper discussions from homework.

Textbook and Other Useful Books

The main text was chosen because it is a very simple, rapid introduction to the field so that we all quickly develop a a common lexicon to move on to applications of polyhedra in other fields of math. I would base a graduate class about the pure mathematics of polyhedral geometry on (1) or (2), and a graduate class about Linear Programming on (3). However, this class is about applying these topics in other fields of math, so we want to move on quickly from the background. The supplementary text information is only provided to you as a resource if you want to learn more.

Main Text: Lectures in Geometric Combinatorics by Rehka Thomas. In the AMS Bookstore Student Mathematical Library: 2006; 143 pp; softcover Volume: 33 ISBN-10: 0-8218-4140-8, ISBN-13: 978-0-8218-4140-2 (Also of course supposed to be in the UIUC bookstore)

Supplementary Texts

(1) Lectures on Polytopes by G.M. Ziegler, Graduate Texts in Mathematics, vol. 152, Springer-Verlag, New York, 1995

(2) Convex Polytopes by B. Grünbaum, Springer Graduate Texts in Mathematics, New York, 2nd, Ed., 2003.

(3) Introduction to Linear Optimization by Bertsimas, D. and Tsitsiklis, J. N. Athena Scientific, Nashua, NH, 1997.

Papers and Supplements

Go here for the promised, ever-growing list of supplementary reading and papers you could present as your projects.

Student Presentations

March 17: Deadline 1. for deciding (and clearing with me) the general subject of your presentation and 2. setting up a meeting with me during the week of March 29 about your presentation. Go here for expectations, schedule, linked papers, titles, and abstracts.

Other Useful Resources

Stefan Forcey is building a "Hedra Zoo" of polyhedra called the similar to the OEIS

Komei Fukuda's Homepage (Especially the FAQ, still dated 2004 but still very handy!)

The polymake software is an excellent basic tool for most (all?) things polyhedral. The SageMath software system can also handle a lot of polyhedral computations. Use Sage first if you like Python instead of Perl, but polymake can do things Sage cannot. Another free software of possible interest to you is LattE which can, for example, do exact volume computations and integrate polynomial functions over polyhedra!