Periodic Graph Operators for Algebraic Geometers

Understanding the spectrum of the  Schröodinger operator in a periodic
medium is a fundamental problem  in mathematical physics. The discrete
version  concerns  operators  on  periodic graphs.  In  this  discrete
version, the  primary objects are  real algebraic varieties,  and thus
algebraic geometry becomes relevant for the study of discrete periodic
operators. The purpose of this talk will be to explain some of this to
algebraic  geometers, and  describe  some results  obtained from  this
perspective, as  well as some computational  and combinatorial aspects
of this study.