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  1. ; ; (, International Mathematics Research Notices)
    Abstract We introduce a categorical analogue of Saito’s notion of primitive forms. For the category $$\textsf{MF}(\frac{1}{n+1}x^{n+1})$$ of matrix factorizations of $$\frac{1}{n+1}x^{n+1}$$, we prove that there exists a unique, up to non-zero constant, categorical primitive form. The corresponding genus zero categorical Gromov–Witten invariants of $$\textsf{MF}(\frac{1}{n+1}x^{n+1})$$ are shown to match with the invariants defined through unfolding of singularities of $$\frac{1}{n+1}x^{n+1}$$. 
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  2. ; (, Compositio Mathematica)
    null (Ed.)
    We compute the $g=1$ , $n=1$ B-model Gromov–Witten invariant of an elliptic curve $$E$$ directly from the derived category $$\mathsf{D}_{\mathsf{coh}}^{b}(E)$$ . More precisely, we carry out the computation of the categorical Gromov–Witten invariant defined by Costello using as target a cyclic $$\mathscr{A}_{\infty }$$ model of $$\mathsf{D}_{\mathsf{coh}}^{b}(E)$$ described by Polishchuk. This is the first non-trivial computation of a positive-genus categorical Gromov–Witten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov–Witten invariants of a symplectic 2-torus computed by Dijkgraaf. 
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