Abstract: In a joint work with Daniels, van Hoften and Kim, we have constructed "Igusa stacks" for certain Shimura varieties and applied these to study the cohomology of Shimura varieties. This turns out to be fruitful and leads to interesting results. In case of PEL type Shimura varieties, following a suggestion of Scholze, the Igusa stacks are shown to have minimal compactifications. In this talk, we investigate the possibility of studying the intersection cohomology of Shimura varieties using minimally compactified Igusa stacks. This is joint work, much in progress, with Ana Caraiani and Linus Hamann.