1/22 & 1/24 most of Ch 2 and some of Ch 3 from From polytopes to enumeration and most of Ch 2 from Lectures in Geometric Combinatorics (we are going to cover more from these chapters in class next week)
1/29 more of Ch 2 of From polytopes to enumeration
1/31 part of Sections 2.1 and 2.2 from Ziegler's book (on reserve in the library). Also see Sections 3.2 and 3.3 in From polytopes to enumeration
2/5 & 2/7 vertex figure and its properties (Prop. 2.4), Thm 2.7 (proof), Def 2.10 (polars), most of Thm 2.11 (proof) from Ziegler's book (on reserve in the library)
2/12 & 2/14 Cyclic polytopes: pages 11-16 in Ziegler's book (on reserve in the library)
2/19 Complexes, subdivisions, and (regular) triangulations Section 5.1 Ziegler's book (on reserve in the library)
2/21 Catalan numbers: the number of triangulations of an n-gon
2/26 Bijection between triangulations of an n-gon and plane binary trees; triangulations of d-crosspolytopes
2/28 Triangulations of d-crosspolytopes continued.
3/5 Counting lattice points in polytopes; Sections 2.1, 2.2, 2.3 in this ebook (hard copy also on reserve in the library)
3/7 Partition functions, Section 1.5 in this ebook and cones Section 3.1 in this ebook (hard copy also on reserve in the library)
3/12 Cones and generating functions for their integer points. Sections 3.1 & 3.2 in this ebook (hard copy also on reserve in the library)
3/14 Exam
3/19 & 3/21 Spring break
3/26 & 3/28 Ehrhart polynomials and series of integer polytopes. Sections 3.3, 3.4 & 3.5 in this ebook (hard copy also on reserve in the library) as well as Pick's theorem (2.6) and magic squares (Birkhoff polytope) (Ch 6).
4/2 & 4/4 Euler relation, h-vectors, f-vectors Chapter 5 in this ebook (hard copy also on reserve in the library) as well as volumes of Minkowski sums, mixed volumes.
4/9 & 4/11 Zonotopes and hyperplane arrangements. See Ch 8 in From polytopes to enumeration Ch 1 in An introduction to hyperplane arrangements and Ch 7 in Ziegler's book (on reserve in the library).
4/16-4/25 Hyperplane arrangements, intersection poset, characteristic polynomial. Ch 1 in An introduction to hyperplane arrangements.
4/30-5/2 Properties of the intersection poset and graphical arrangements. Ch 2 in An introduction to hyperplane arrangements.