Seminario de Geometría, Álgebra y Topología

John Cobb, Auburn University

Abstract: I’ll describe how a version of spectral graph theory serves as a “tight-binding” model describing electron dynamics in crystalline solids, such as those found in nano-materials and topological insulators. This model turns out to be entirely algebraic and allows one to prove facts about the approximate electronic properties of materials using algebraic geometry and, more generally, interact with a larger world of spectral theory and periodic operators. I’ll spend some time developing this dictionary with lots of pictures, and then I’ll describe upcoming joint work with Matthew Faust and Andreas Kretschmer using some ideas from deformation theory to completely determine when a periodic discrete potential can be isospectral to the trivial potential.

https://sites.google.com/im.unam.mx/seminariogato/2025