# Seminar

#### Group Theory Seminar

Analogues of L2-Betti numbers in positive characteristic and homology growth

Speaker:  Sam Fisher (University of Oxford)
Date:  Tuesday, 24 January 2023 - 11:30
Place:  Aula Naranja, ICMAT

Abstract:

For a group G satisfying the Atiyah conjecture, L2-Betti homology can be described as group homology with coefficients in the "Linnell-skew field" D(G), in which the group ring ℚG embeds. One approach to defining positive characteristic analogues of L2-Betti numbers is to find an analogous skew-field D_FₚG which contains the group ring FₚG and take homology with these coefficients. In this talk, we will present some results about these positive characteristic invariants, in particular we will see how they relate to positive characteristic homology growth.