a kakeya set is a set of points in r^n which contains a unit line segment in every direction. the kakeya conjecture states that the dimension of any kakeya set is n. this conjecture remains wide open for all n \geq 3.

together with josh zahl, we study a special collection of the kakeya sets, namely the sticky kakeya sets, where the line segments in nearby directions stay close. we prove that sticky kakeya sets in r^3 have dimension 3.  in this talk, we will discuss background of the problem and its connection to analysis, combinatorics, and geometric measure theory.