| Date | Chapter | Description |
|
| Sep 1 | | Simplicial complexes: CW-structure, examples |
| Sep 3 | | Simplicial complex examples, Stanley-Reisner rings |
|
| Sep 6 | | Labor Day! (no class) |
| Sep 8 | | The Nerve Lemma and Helly Theorem |
| Sep 10 | | Alexander Duality; proof of Topological Helly Theorem |
|
| Sep 13 | | Poset topology and Möbius inversion |
| Sep 15 | | Hall's Theorem: Möbius = reduced Euler |
| Sep 17 | | Lattices; Hall's application of Möbius inversion |
|
| Sep 20 | | Poset duality, complements |
| Sep 22 | | Crapo and Homotopy Complementation Theorems |
| Sep 24 | | Homotopy Complementation proof |
|
| Sep 27 | | Homotopy Complementation applications |
| Sep 29 | | Partition lattices, distributive and modular lattices |
| Oct 1 | | Modular and left-modular elements |
|
| Oct 4 | | Homotopy of lattices with modular chains via complementation |
| Oct 6 | | EL-labelings |
| Oct 8 | | Left-modular elements and labelings |
|
| Oct 11 | | Supersolvable lattices |
| Oct 13 | | Semimodular lattices |
| Oct 15 | | Fall Break! (no class) |
|
| Oct 18 | | Semimodular lattice examples, geometric lattices |
| Oct 20 | | Matroids <-> geometric lattices |
| Oct 22 | | EL-labelings of semimodular lattices |
|
| Oct 25 | | Shellings, rearrangement lemmas |
| Oct 27 | | Collapsing, homotopy type of shellable complexes |
| Oct 29 | | EL-labelings give shellings |
|
| Nov 1 | | Cohen-Macaulay complexes and local homology |
| Nov 3 | | The dunce cap; various definitions of skeleton |
| Nov 5 | | sequentially Cohen-Macaulay complexes |
|
| Nov 8 | | connectivity parameter: depth |
| Nov 10 | | depth is a topological invariant; Krull dimension |
| Nov 12 | | (ring theoretic) depth |
|
| Nov 15 | | Local cohomology of a ring: Koszul and modified Cech complexes |
| Nov 17 | | Cohomology <-> Local cohomology of Stanley-Reisner |
| Nov 19 | | Hilbert series and h-vectors |
|
| Nov 22 | | h-vectors, M-vectors, and the Upper Bound Theorem |
| Nov 24 | | Thanksgiving! (no class) |
| Nov 26 | | Thanksgiving! (no class) |
|
| Nov 29 | | h-vectors of shellable and partitionable complexes |
| Dec 1 | | CL-labelings; vertex-decomposability |
| Dec 3 | | Discrete Morse theory: connection with continuous Morse theory |
|
| Dec 6 | | Discrete Morse theory: Morse functions give collapsing |
| Dec 8 | | Discrete Morse theory: examples, Morse matchings |
| Dec 10 | | Discrete Morse theory: shellings, brief idea of poset Morse theory |