The aim of the REU, initiated by Miklós Abért, Péter Pál Pach and Dömötör Pálvölgyi in 2020, is to offer research opportunities to Hungarian math students during the summer. The participants are divided into smaller groups, and then they work together for one month on problems posed by senior researchers. This year, the Matroid Optimization Research Group also joined the initiative. As a result, two groups will work on the following matroidal problems: covering of cuts by pairs of edges, and covering graphs by rainbow spanning trees.