Akash Sengupta, Department of Pure Mathematics, University of Waterloo
"Furstenberg sets over finite fields"
A Kakeya set is a subset S of R^n that contains a unit line segment in every direction. The Kakeya conjecture in harmonic analysis states that a Kakeya set S in R^n has Hausdorff dimension n. The Kakeya conjecture is still open, however an analogous statement over finite fields is known due to a beautiful algebraic-geometric proof by Dvir. In this talk, we will consider a generalization of the Kakeya sets over finite fields, which are called Furstenberg sets. Furstenberg sets are subsets of F_q^n which have large intersection with linear spaces in every direction, where F_q is a finite field. We will discuss an algebraic geometric proof of lower bounds on the size of Furstenberg sets, due to Ellenberg-Erman.
MC 5417