J. Ginsburg has asked what is the relation between the pseudocompactness of the $\omega$-th power of a topological space $X$ and the pseudocompactness of its Vietoris Hyperspace, $\exp(X)$. M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form $\Psi(A)$ where A is an almost disjoint family. Regarding these spaces, if $\exp(X)$ is pseudocompact, then $X^\omega$ is also pseudocompact, and $X^\omega$ is pseudocompact iff $A$ is a MAD family. They showed that if the cardinal characteristic $\mathfrak{p}$ is $\mathfrak{c}$, then for every MAD family $A$, $\exp(\Psi(A))$ is pseudocompact, and if the cardinal characteristic $\mathfrak{h}$ is less than $\mathfrak{c}$, there exists a MAD family $A$ such that $\exp(\Psi(A))$ is not pseudocompact. They asked if there exists a MAD family $A$ (in ZFC) such that $\exp(\Psi(A))$ is pseudocompact.

In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.