# Groups & Dynamics Seminar. Maria Gerasimova (BIU) : “Isoperimetry, Littlewood functions, and unitarisability of group”

## Location:

any uniformly bounded representation π : Γ → B(H) of Γ on H there exists a bounded operator

S : H → H such that S^{−1}π(g)S is a unitary representation for any g ∈ Γ. It is well known that

amenable groups are unitarisable. It has been open ever since whether amenability characterises unitarisability of groups.

Dixmier: Are all unitarisable groups amenable?

One of the approaches to study unitarisability is related to the space of the Littlewood functions