Hilbert C*-modules (Operator Algebra)
This reading group will be an introduction to Hilbert C*-modules. These objects are like a Hilbert space except that the inner product is not scalar-valued, but takes its value in a C*-algebra. The theory of Hilbert C*-modules have applications to other topics in operator algebras such as Morita equivalence, KK-theory and compact quantum groups.
The aim is to follow the book Hilbert C*-Modules: A Toolkit for Operator Algebraists by E. Christopher Lance, with the goal to cover approximately one chapter per week. In the last weeks of the reading group, we will add other topics of interest.
When: Tuesdays 13:00-15:00
Where: Gilbert Scott Building 251, University of Glasgow
Organiser: Rodrigo Samuel Roemig
Schedule:
| Week | Date | Room | Speaker | Chapter/Title | Notes |
|---|---|---|---|---|---|
| 1 | 06/10 | 311B | Noam Zeise | Chapter 1 – Modules and mappings | Download |
| 2 | 13/10 | GS251 | Toby Mann | Chapters 2 & 3 – Multipliers, morphisms, projections and unitaries | Download |
| 3 | 20/10 | GS251 | Husam Ismaeel | Chapter 4 – Tensor products | Download |
| 4 | 27/10 | GS251 | Xulong Lu | Chapter 5 – The KSGNS construction | Download |
| 5 | 03/11 | GS251 | Rodrigo Roemig | Chapter 6 – Stabilisation and absorption | – |
| 6 | TBC | TBC | TBC (change due to student conference) | Chapter 7 – Full modules, Morita equivalence | – |
| 7 | 17/11 | GS251 |
TBC |
Chapter 8 – Slice maps and bialgebras | – |
| 8 | 24/11 | GS251 |
TBC |
Chapter 9 – Unbounded operators | – |
| 9 | 01/12 | GS251 | TBC | Chapter 10 – The bounded transform, bounded multipliers | – |
| 10 | 08/12 | GS251 | Rory Morrison (TBC) | Vector bundles and Serre-Swan’s theorem | – |