240163 L^2-invariants (V) (SoSe 2019)
Contents, comment
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The aim of this course is to introduce the theory of L^2 homology and apply it to the study of groups. We will see how L^2 invariants interact with amenability, and how the knowledge of the possible values L^2 Betti numbers can take can be helpful in many (often surprising) situations.
More specifically, we will introduce all the necessary notions from functional analysis (von Neumann algebras, etc.) which will enable us to define the theory of L^2 invariants, and then we will proceed towards an investigation of the Atiyah conjecture.
Requirements for participation, required level
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Basics of group theory and algebraic topology (e.g. familiarity with the first two chapters of `Algebraic Topology' by Hatcher).
Bibliography
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`L^2-Invariants: Theory and Applications to Geometry and K-Theory' by W. Lück
The university library has one copy of the book; the preface and introduction can be read here:
https://www.him.uni-bonn.de/lueck/data/shortbook.pdf
External comments page
Teaching staff
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period |
|---|
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-P1a Profilierung 1 Teil A | Profilierungsvorlesung (mit Übung) - Typ 2 | Student information | |
| 24-M-P1b Profilierung 1 Teil B | Profilierungsvorlesung (mit Übung) - Typ 2 | Student information | |
| 24-M-P2 Profilierung 2 | Profilierungsvorlesung (mit Übungen) - Typ 2 | Study requirement
|
Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Bielefeld Graduate School in Theoretical Sciences / Promotion | |||||||
| Mathematik / Promotion | Subject-specific qualification | 2 | aktive Teilnahme |
- Registered number: 10
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- Last update basic details/teaching staff:
- Wednesday, January 29, 2020
- Last update times:
- Wednesday, May 29, 2019
- Last update rooms:
- Wednesday, May 29, 2019
- Type(s) / SWS (hours per week per semester)
- V / 2
- Language
- This lecture is taught in english
- Department
- Faculty of Mathematics
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