Explore the intricacies of discrete honeycombs, rational edges, and edge states in this 46-minute lecture by Michael Weinstein from Columbia University's Applied Physics and Applied Mathematics department. Delve into the derivation of tight binding models from continuum Schroedinger Hamiltonians in both non-magnetic and strongly magnetic systems. Examine recent work on the tight binding model of graphene with sharp termination along rational edges, classifying them into "zigzag" and "armchair" types. Discover the conditions for zero energy/flat band edge states and their explicit formulas. Investigate evidence for dispersive edge state curves of nonzero energy. Learn about the collaborative research with C.L. Fefferman and S. Fliss, covering topics such as typebinding reduction, magnetic problems, honeycomb lattices, rational edge geometry, edge Hamiltonians, and edge state spectra.