Thursday 12 December 2024 at 11 am, as part of the Al@Bicocca seminar cycle, Giada Serafini (University of Düsseldorf) will talk about
Title: Profinite properties of ℓ2-invariants
Abstract: Although higher ℓ2-Betti numbers bn(2), n ≥ 2 are in general not profinite invariants, some interesting information on the ℓ2-cohomology of S-arithmetic groups still seems to be preserved under profinite commensurability. This leads us to prove a stability result for another ℓ2-invariant strictly related to the ℓ2-Betti numbers: the sign of the Euler characteristic, which indeed can be seen as the alternating sum of such bn(2). In this talk we will introduce the basics and motivations for being interested in Profinite rigidity and then we will discuss the key steps needed to prove our result for S-arithmetic groups in terms of local-global principles in the setting of Galois cohomology.
All of this is joint work with Holger Kammeyer.
Information to attend
The seminar will be held in Room 3014 (3rd Floor) - U5 Building, University of Milan-Bicocca and will also be available online at the following Webex link