ALGB Seminar: Matteo Vanacci (University of Düsseldorf)
Title: PFG, PRF and probabilistic finiteness properties of profinite groups
Abstract: A profinite group G equipped with its Haar measure is a probability space and one can talk about "random elements" in G. A profinite group G is said to be positively finitely generated (PFG) if there is an integer k such that k Haar-random elements generate G with positive probability. PFG has been well studied in the past. In this talk I will introduce a variation of PFG, called "positive finite relatedness" (PFR) for profinite groups. Finally I will survey some recent work-in-progress defining higher probabilistic homological finiteness properties (PFP_n), building on PFG and PFR. This is joint work with Ged Corob Cook and Steffen Kionke.