Title: Unitals in the Regular Nearfield Planes

Abstract: A unital of order q is a 2-(q^3+1, q+1, 1) design. As such, it is a point-block incidence structure with q^3 + 1 points such that any

block contains precisely q + 1 points, and any two points are contained in exactly one block. Unitals find applications in linear codes and have connections to blocking sets, polarities, and the Hasse-Weil bound. They have been studied extensively in the last 50 years, especially those embedded in the classical planes. Although much is unknown about fully classifying unitals in the classical planes, even more is unknown about unitals in the closely related nearfield planes. This talk gives a classification result of unitals in the regular nearfield planes that is similar to known classification results in the classical planes.