Algebraic Geometry in Spectral Theory
algebraic geometry
| Audience: | Researchers in the topic |
| Conference dates: | 24-Feb-2023 to 26-Feb-2023 |
| Curator: | Shadira Presbot* |
| *contact for this listing |
Discrete periodic Schrodinger operators describe the behavior of individual electrons in "ideal" crystals in the tight-binding model of solid state physics. Spectra of such operators have the usual band-gap structure, and the corresponding dispersion relations are algebraic varieties. In the 1990's Gieseker, Knorrer, and Trubowitz used toroidal compactifications to solve questions such as irreducibility of Bloch and Fermi varieties and the density of states, for a class of mono-atomic models. Their work showed that while spectral theory is focused on the real part of the Bloch variety, the study of complex singularities and compactifications is crucial for describing formation of bands and gaps.
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