Math 697: Topics in combinatorics: polytopes

Instructor: Alejandro H. Morales
ahmorales at math dot umass dot edu

Class schedule: MWF 11:15 - 12:05 pm, LGRT 171

Office Hours: MW 1pm-2pm, T 9:30-10:30am, LGRT 1120

Course description: This course is an introduction to the theory of convex polytopes and their applications to algebraic combinatorics. The course will cover basic facts and properties of polytopes including faces of polytopes, valuation theory, Ehrhart theory, triangulations, zonotopes and tilings. We will also tentatively cover the following families of polytopes with interest in other fields: root polytopes, flow polytopes, polytopes from partially ordered sets, associahedra, and generalized permutahedra.

Main Reading Sources:

Other Reading Sources and links:


There will be five bi-weekly HW during the semester accounting for 80% of the grade. You should complete the homework on your own. Some reasonable collaboration in homework is allowed. Do not hand in a solution that you did not obtain on your own or by collaboration with another student in the class. If you do collaborate with one or more students on a problem, please indicate their names.

Final project:

The final project worth 20% of the grade where you have to read a selected paper on an additional topic and write a report of 12 page + references in LaTeX on the paper (due Thursday December 13 and give a 25 minute presentation during the final week of the semester. You can also include code related to the project.

Resources for your presentation

List of topics for final project:


Course notes:

Thanksgiving break