Monday 24 November 2025 at 3 pm, as part of the Al@Bicocca seminar cycle, Tommaso Toti (Università degli Studi di Milano-Bicocca and UPV/EHU) will give the following talk
Title: Probabilistic Identities in Profinite Groups
Abstract: In this talk, we study some probabilistic aspects of the theory of identities in profinite groups. Given a word w(x1,…, xd) in d letters, we say that w is a probabilistic identity on a profinite group G if the set of d-tuples of elements of G that satisfy w has positive Haar measure. First, we focus on torsion words, that is, words for the form xk with k ∈ N. Through the study of conjugacy classes of torsion elements, we introduce a new class of profinite groups satisfying the Lévai-Pyber conjecture. As an application, given a prime number p, we characterize compact p-adic analytic groups admitting torsion probabilistic identities. Then, we move our attention to general words. We show that compact p-adic analytic groups satisfy a probabilistic version of the Tits alternative and we discuss a criterion to establish whether a pro-p group does not satisfy any probabilistic identity in terms of its Zp-representations. This is based on a joint with Steffen Kionke, Nowras Otmen, Matteo Vannacci and Thomas Weigel.
Information to attend
The seminar will be held in Room U6-21 (U6 Building, 1st Floor) University of Milano-Bicocca and will also be available online by this link
For more information, visit the website