**MATH 890**

Polytopes and Varieties:

Enumerative Geometric Combinatorics

**
**
Fall 2015

### Possible Topics for Student Lectures

- Birkhoff's theorem (Theorem 2.9 in the text)
- Minkowski-Weyl theorem (Theorem 3.1)
- Dehn-Sommerville relations (Theorem 3.20)
- Brianchon-Gram relation (Section 3.6)
- Unimodular triangulations (Section 5.5)
- Zonotopes
- Brion's theorem
- Solid angles (Section 5.6)
- Order and chain polytopes
- Integer partitions
- Shi arrangements
- Inside-out polytopes