I will present joint work with Michael Cowling (UNSW, Sydney) and Bianca Di Blasio (Milano-Bicocca) about irreducible and uniformly bounded representations of $\mathrm{SL}(2,\mathbb{R})$. We are interested in finding uniformly bounded representations with minimal norm in their similarity class and computing their norm. Moreover, we shall explore the link between admissibility and a famous question in functional analysis: the invariant subspace problem.

The video of this talk is available on the IISc Math Department channel.