I am a graduate student in the harmonic analysis research group in UBC's mathematics department.
The Kakeya problem in geometric measure theory concerns the size of Kakeya sets- sets in space that contain a unit line segment in every direction. Finite, combinatorial analogues of the Kakeya problem have been formulated in order to better understand the Kakeya problem. Recently, lots of progress has been made on the combinatorial versions of these problems using a technique known as the polynomial method. I am currently reading up on the polynomial method to learn more about it.