Using 2-Ovoids to Generate Tight Sets In W(Q)

A generalized quadrangle is a type of geometry that contains within it no triangles. In particular, we will be considering these structures in the finite case. In this thesis, we focus on a particular generalized quadrangle W(q). We use ovoids in PG(3,q) to construct a tight set in W(q) for q odd consisting of exactly half of the points of W(q). We then use this tight set to find previously unknown tight sets within W(q) for q = 5,7. Through this process, we use tools from geometry, algebra, graph theory, and we also make ample use of computer software to create and observe these tight sets. This field of study marries together a veritable plethora of mathematical fields that are not often brought together.