Title: Mutual Stationarity at the least singular cardinal

Abstract: Let X be any set. We say a collection of subsets of X is stationary if it contains at least one set closed under any given algebra on X. This is, perhaps, the closest we get to a universal system of measure. In this talk we will discuss what sets on the least singular cardinal can be stationary using the notion of mutual stationarity introduced by Foreman and Magidor. We will see that a rich set of sequences can consistently be mutually stationarity if we have the right set of total, non-principal 0-1 measures of a fixed uncountable additivity. This is joint work with Omer Ben-Neria.