Abstract |
In this talk, we will discuss the significant role that the algebraic and
analytic properties of complex Bloch and Fermi varieties play in the study
of periodic operators. I will begin by highlighting recent discoveries
about these properties, especially their irreducibility. Then, I will show
how we can use these findings, together with techniques from complex
analysis and combinatorics, to study spectral and inverse spectral
problems arising from periodic operators.
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