Algebraic Geometry and Discrete Periodic Operators
Exploring the intersection of algebraic geometry and spectral theory, this talk delves into using algebraic methods to analyze the spectra of discrete periodic operators on Z^d-periodic graphs.
Frank Sottile (Texas A&M)
Beyond Graph Laplacians
When viewed from the representation theory of Z^d, the spectrum of an operator on a Z^d-periodic graph becomes a real-algebraic hypersurface in (S^1)^d x R. This opens the door to methods from algebraic geometry for use in spectral theory. While this perspective is not new, there is renewed interest in it, to the benefit of both spectral theory and algebraic geometry. My talk will discuss some recent work in this direction.
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