Erdos conjectured that a set of n points in the Euclidean plane has at least c n/sqrt(log(n))) distinct distances for some universal constant c>0. Guth and Katz nearly resolved this question, but many related problems remain wide open. I will discuss recent results on a variant of this problem for points in a plane over a finite field. This is joint work with Giorgis Petridis.

---------------------------------- Next week: Fall break. Week after: Alex Scott