Intersecting Spanning Trees

In 2017 Gil Kalai asked the speaker about the largest family of $t$-intersecting spanning trees of the complete graph on n vertices. We will discuss these questions: What motivates this problem? Which common techniques for EKR-problems fail? How can we actually solve the problem? Based on joint work with Peter Frankl, Glenn Hurlbert, Andrey Kupavskii, Nathan Lindzey, Karen Meagher, and Venkata Raghu Tej Pantangi.