Families of graphs whose Bloch varieties are perfect Morse functions

A Bloch variety of a Z^d periodic graph with m orbits of vertices has at least 2^d m critical points. (These are at the corner points.)

I will describe two families of Z^d periodic graphs whose Bloch varieties have only these critical points.  Such graphs satisfy Kuchment's Spectral Edges nondegeneracy conjecture.

This is joint work with Matthew Faust.