Consider a set X and a set of binary functions H on the points of X. Then, a subset C of X is shattered by H if the restriction of H to the points of C yields all possible binary functions on the points of C. The VC-Dimension of H is the size of the largest shattered subset. Vapnik and Chervonenkis introduced the concept of VC-dimension in 1970, which characterizes hypothesis classes of binary functions and has applications in learning theory.

Previous research by Fitzpatrick, Wyman, Iosevich and McDonald investigated hypothesis classes which consisted of the characteristic functions of ‘‘spheres’’ of fixed nonzero radius in finite vector spaces.

In this talk, I outline work I did this past summer regarding hypothesis classes of the form the set of indicator functions on the intersection of two spheres in this finite field.