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We give a conjectural algebraic description of the Fukaya category of acomplexified hyperplane complement, using the algebras defined inarXiv:0905.1335 from the equivariant cohomology of toric varieties. We provethis conjecture for cyclic arrangements by showing that these algebras areisomorphic to algebras appearing in work of Ozsvath-Szabo arXiv:1603.06559 inbordered Heegaard Floer homology arXiv:0810.0687. The proof of our conjecturein the cyclic case extends work of Karp-Williams arXiv:1608.08288 on signvariation and the combinatorics of the m=1 amplituhedron. We then use thealgebras associated to cyclic arrangements to construct categorical actions ofgl(1|1).

From hypertoric geometry to bordered Floer homology via the m=1 amplituhedron