This is a website for the reading group on L2-invariants that we are doing in the Winter semester 2023/24 in Ljubljana.
The main reference is Kammeyer's book.
Each participant chooses a topic and prepares a 45 minute lecture for the group. You do not need to cover the whole material in great detail and it is completely OK to only explain the main ideas (after all, you only have 1 hour).
If you decide to participate, send an email to urban.jezernik@fmf.uni-lj.si so that I mark the topic has been chosen.
A list of topics together with references is available here (prepared by Andoni Zozaya).
von Neumann algebra (Marco Barbieri)
von Neumann dimension (Jon Mikoš)
CW-complexes and l2-chain complexes (Jaka Smrekar)
l2-Betti numbers of spaces: definition, examples and basic computations (Žiga Gladek)
Applications to algebra and topology. Atiyah's conjecture (Marko Čmrlec)
Extended von Neumann dimension and l2-Betti numbers of general G-spaces (Andoni Zozaya)
l2-Betti numbers of groups (Primož Moravec)
Spectral measures: definition and weak convergence (Andraž Maier)
Luck's approximation theorem (Urban Jezernik)
Rank gradient and cost
Atiyah's conjecture: outlook and applications
Torsion invariants, part 1
Torsion invariants, part 2
We meet on Fridays at 13-14 in classroom 3.06.
06/10/2023 Andoni Zozaya: Introduction to l2-invariants [video]
13/10/2023 Marco Barbieri: von Neumann algebra [video]
20/10/2023 Jon Mikoš: von Neumann dimension [video]
27/10/2023 Jaka Smrekar: CW-complexes and l2-chain complexes [video]
03/11/2023 Žiga Gladek: l2-Betti numbers of spaces: definition, examples and basic computations [audio]
10/11/2023 Marko Čmrlec: Applications to algebra and topology. Atiyah's conjecture [video]
17/11/2023 Andoni Zozaya: Extended von Neumann dimension and l2-Betti numbers of general G-spaces [audio]
01/12/2023 Primož Moravec: l2-Betti numbers of groups [video]
15/12/2023 Andraž Maier: Spectral measures: definition and weak convergence [video]
22/12/2023 Urban Jezernik: Luck's approximation theorem [video]