Dispersive determination of low energy $\pi K$ interactions

We summarize the application of dispersion relations for the determination of low energy $\pi K$ interactions. In particular, we present our recent dispersive analyses for the complete study of both $\pi K\to \pi K$ and $\pi \pi \rightarrow K \bar K$ channels. First, we summarize our approach, we study both channels by using several families of dispersion relations and present the most relevant partial waves. Then we apply the dispersive formalism to the threshold region, where we extract many different low-energy parameters.