Lunedì 24 Novembre 2025 alle ore 15:00, nel quadro del ciclo di seminari Al@Bicocca, Tommaso Toti (Università degli Studi di Milano-Bicocca e UPV/EHU) terrà il seguente intervento
Titolo: 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.
Informazioni per partecipare
Il seminario si terrà in Aula U6-21 (Edificio U6, 1° Piano) Università degli Studi di Milano-Bicocca e sarà possibile partecipare anche online da questo link
Per maggiori informazioni, visita il sito