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Creators/Authors contains: "Licata, Anthony M"

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  1. ; ; (, Selecta Mathematica)
    Abstract We relate the Fukaya category of the symmetric power of a genus zero surface to deformed category$$\mathcal {O}$$ O of a cyclic hypertoric variety by establishing an isomorphism between algebras defined by Ozsváth–Szabó in Heegaard–Floer theory and Braden–Licata–Proudfoot–Webster in hypertoric geometry. The proof extends work of Karp–Williams on sign variation and the combinatorics of the$$m=1$$ m = 1 amplituhedron. We then use the algebras associated to cyclic arrangements to construct categorical actions of$$\mathfrak {gl}(1|1)$$ gl ( 1 | 1 ) , and generalize our isomorphism to give a conjectural algebraic description of the Fukaya category of a complexified hyperplane complement. 
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  2. ; ; (, Advances in Mathematics)
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  3. ; ; ; (, Journal of the Institute of Mathematics of Jussieu)
    The trace (or zeroth Hochschild homology) of Khovanov’s Heisenberg category is identified with a quotient of the algebra $$W_{1+\infty }$$. This induces an action of $$W_{1+\infty }$$ on the center of the categorified Fock space representation, which can be identified with the action of $$W_{1+\infty }$$ on symmetric functions. 
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