Intersection properties of convex (n,d)-bodies

A convex (n,d)-body is a union of convex sets from n disjoint copies of R^d. In this talk, we will motivate the definition of convex (n, d)-bodies by introducing a problem about piercing rectangles in the plane. We will then prove some basic results about convex (n, d)-bodies published by Kaiser and Rabinovich in 1999.