Seminario Teoría de grupos 

11:00 Aula Naranja ICMAT

3/10/2022

Speaker: Henrique Mendes da Silva e Souza (ICMAT/UAM)

Title: The Atiyah conjecture

Abstract: The Atiyah conjecture states that the L²-Betti numbers of a countable group are always rational numbers, and a stronger version bounds the denominator of such numbers in terms of the torsion in the group. This conjecture has strong relations to other problems in group theory, such as the Lück approximation conjecture, Kaplansky's zero divisor conjecture, the strengthened Hanna Neumann conjecture and the problem of localization in group rings. In this talk we will explore how these questions and their pro-p variants are related, survey positive results among certain classes of groups and explain how these connections led to a recent solution of the strong Atiyah conjecture for pro-p free-by-cyclic groups (in joint work with Andrei Jaikin).