Abstract: Given a polarized hyperplane arrangement, Braden-Licata-Proudfoot-Webster defined two convolution algebras: A &  B. We show that both of them can be realized as Fukaya categories of hypertoric varieties. This proves a conjecture of Braden-Licata-Phan-Proudfoot-Webster in 2009 and gives a geometric interpretation of the Koszul duality between A & B. The proof relies on the construction of non-commutative vector fields on Fukaya categories (Abouzaid-Smith), the surgery quasi-isomorphism for singular Legendrians (Asplund-Ekholm), and the cobar interpretation of the Chekanov-Eliashberg DGA (Ekholm-Lekili). Time permitted, I’ll also talk about the homological mirror symmetry for hypertoric varieties and the relation to knot Floer homology. This is based on joint works in progress with Sukjoo Lee, Siyang Liu and Cheuk Yu Mak.