November 6, 2012: Joshua Zahl (UCLA) On the Wolff circular maximal function I will discuss a new proof of the boundedness of the Wolff circular maximal function. This maximal function helps us understand BRK sets---compact subsets of the plane that contain a circle of every radius, and it is also a stepping stone towards understanding the Kakeya problem in three dimensions. This new proof uses some modern ideas from combinatorial geometry, namely the "discrete polynomial partitioning" method developed by Guth and Katz to solve the Erdos distinct distances problem in the plane.