Recent developments on intersection searching in 3-spaces

Recently, polynomial partitioning became a central tool in solving fundamental algorithmic problems in computational geometry, including eliminating depth cycles, point location, and semi-algebraic range searching.
In this talk I will present several recent developments in the study of intersection searching - a family of range searching problems. In particular, I will describe data structures that efficiently support "arc-shooting" queries amid flat objects in 3-space, where polynomial partitioning serves as a main tool. I will also discuss the relation between intersection searching and nearest-neighbor search, and present solutions to 

proximity problems in 3-space.