Periodic points of Prym eigenforms

We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.