Several recent papers by authors including Matilla, Orponen, Liu, Shmerikin, and Wang give upper bounds on the Hausdorff dimension of the set of points for which the radial projection of a Borel set in a real vector space is much smaller than expected. In recent work, joint with Thang Pham and Vu Thi Huong Thu, we prove analogs of several of these theorems for point sets in vector spaces over finite fields. In several cases, we are able to prove stronger bounds than the most natural analogs to the known theorems in the continuous case. I will discuss these results, and if time permits I'll mention a connection to the Erdos and Falconer problems on distinct distances.
