Algebraic Geometry and Discrete Periodic Operators

Spectral theory of  operators on a periodic medium is  a topic in
mathematical physics having deep interactions with analysis.  Its
discretization,  operators   on  periodic   graphs,  additionally
communicates  with discrete  mathematics and  algebraic geometry.
Many natural aspects of  discrete periodic operators are directly
understood  in  terms  of   algebraic  geometry  and  some  basic
questions are  answered using standard techniques  from algebraic
geometry.

My talk will explain some  algebraic aspects of discrete periodic
operators,  illustrating  how  the   interactions  flow  in  both
directions, to the benefit of both disciplines.