An explicit tower of abelian covers of the genus-2 curve y^2=x^6-1 has Dirac operator spectral gap uniformly bounded below by a positive constant.
High Dimensional Expanders
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abstract
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the references therein). In the last decade, a theory of "high dimensional expanders" has begun to emerge. The goal of the current paper is to describe some paths of this new area of study.
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A Spectral Gap for Spinors on Hyperbolic Surfaces
An explicit tower of abelian covers of the genus-2 curve y^2=x^6-1 has Dirac operator spectral gap uniformly bounded below by a positive constant.