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In this paper, we prove a homological mirror symmetry equivalence for pairsof multiplicative hypertoric varieties, and we calculate monodromyautoequivalences of these categories by promoting our result to an equivalenceof perverse schobers. We prove our equivalence by matching holomorphicLagrangian skeleta, on the A-model side, with non-commutative resolutions onthe B-model side. The hyperk\"ahler geometry of these spaces provides eachcategory with a natural t-structure, which helps clarify SYZ duality in ahyperk\"ahler context. Our results are a prototype for mirror symmetrystatements relating pairs of K-theoretic Coulomb branches.

Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent C\^ot\'e and Justin Hilburn)