During this talk we will introduce the problem of symmetry (and inverse-closedness) for Banach *-algebras related to groups. Then we will turn our attention to the case of $L^1(G)$, for $G$ being an extension of a normal compact subgroup $K$. In a general setting, we will provide sufficient conditions on $G/K$ for $L^1(G)$ to be symmetric. For splitting extensions we show that the symmetry of $L^1(G)$ is equivalent to the symmetry of $L^1(G/K)$.

Bio: Felipe Flores is a Chilean PhD student at the University of Virginia, under the supervision of Ben Hayes. His research focuses on group and groupoid algebras, both at the von Neumann algebra level and the Banach *-algebra level.