Here is a list of topics for my set of lectures for the special topics course in Wuppertal this (Summer 2023) semester. The list will be updated after each lecture, so that irregular participants can decide whether they would like to join on short notice. I will also upload handwritten notes after each lecture.
Each topic is intended to cover roughly 40 minutes of the 90 minute time-slot, which will include a 10 minute break.
The usual lecture times are Monday (G.13.18) and Wednesday (G.15.25) between 12:15 and 13:45. In addition, there will also be a lecture on the Fridays 23.06 and 30.06, in G.15.25 between 14:15 and 15:45.
| Topic | Day |
|---|---|
| Overview and motivation | 14.06.23 |
| Module of differentials | 14.06.23 |
| The cotangent complex | 19.06.23 |
| Properties of the cotangent complex | 19.06.23 |
| Review cotangent complex; cotangent complex of a regular quotient | 21.06.23 |
| Hochschild homology | 21.06.23 |
| Hochschild homology of truncated polynomial rings | 23.06.23 |
| Homotopy ring of a simplicial commutative ring | 23.06.23 |
| Spectral sequences | 26.06.23 |
| Hochschild homology of polynomial rings | 26.06.23 |
| The André--Quillen spectral sequence | 28.06.23 |
| ---=--- | 28.06.23 |
| Smooth ring maps and proof of HKR | 30.06.23 |
| Further properties of Hochschild homology | 30.06.23 |
| The B-operator on Hochschild homology | 10.07.23 |
| The Loday construction | 10.07.23 |
| Quillen's cotangent complex formalism | 12.07.23 |
| ---=--- | 12.07.23 |