Real algebraic geometry in spectral theory

A class of problems involving the spectrum of operators on a
discrete periodic graph were recenty realized as algebraic-geometric
in nature, opening up the possibility of using ideas and methods
from algebraic geometry to address these problems.

In my talk, I will describe one of these problems, and how ideas
from algebraic geometry were used to study it.  I am offering this 
talk at this conference because these questions are naturally
posed as problems in real algebraic geometry and are instances
of nonstandard real structures on toric varieties---a topic that
I first learned of from Slava Kharlamov.

This is joint work with Peter Kuchment, Ngoc Do, and Matthew Faust.