Monday 15 December 2025 form 3 pm to 5:30 pm, as part of the Al@Bicocca seminar cycle, Bianca Marchionna (Université Catholique de Louvain) and Ilaria Castellano (Politecnico di Torino) will give the following talks
Speaker: Bianca Marchionna
Title: Topological right-angled Artin groups
Abstract: Right-angled Artin groups (RAAGs) form a family of finitely generated groups that play an important role in geometric and computational group theory. Their study is often related to the one of their universal Salvetti complex, a CAT(0)- cube complex on which they act geometrically. In this talk, we introduce a generalisation of RAAGs to topological groups. Remarkably, those groups have a cellular action on a thicker version of the universal Salvetti complex of a RAAG with controlled cell stabilisers. Due to the high connectivity of this complex, we can deduce homological/homotopical finiteness properties for topological RAAGs. Work in progress with I. Castellano, B. Nucinkis, and Y. Santos Rego.
Speaker: Ilaria Castellano
Title: Geometric invariants of TDLC completions
Abstract: Let Γ be a Hausdorff topological group and Λ an open commensurated subgroup of Γ. A TDLC completion (short for totally disconnected locally compact completion) of (Γ, Λ) is a pair (G, ϕ) where: G is a TDLC group, ϕ: Γ → G is a continuous homomorphism with dense image and Λ = ϕ−1(L) for some compact open subgroup L ⊆ G. One important example is given by Schlichting completions, which have become a significant concept in topological group theory, as they establish a connection between abstract groups and TDLC groups. Recently, Bonn and Sauer investigated how the compactness properties behave under Schlichting completion. They showed that, from this point of view, the Schlichting completion of a pair (Γ, Λ) acts precisely as if it were the quotient of Γ by Λ [BS24]. Motivated by this result, Jos´e Pedro Quintanilha and I set out to explore whether a similar phenomenon holds for the Σ-sets [BHQ24a,BHQ24b]. In this talk, I will present our results along with some applications.
Between the two talks, there will be a short coffee break.
Information to attend
The seminar will be held in Room U7-12 (U7 Building | Ground Floor | Via Bicocca degli Arcimboldi 8, Milano) and will also be available online by this link.
For more information, visit the website