Publications and preprints

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• Minimal resolutions of toric substacks by line bundles, arXiv preprint (2026), submitted version.

  We develop a strategy for constructing minimal resolutions from explicit non-minimal cellular resolutions via the homological perturbation lemma. As an application, we construct minimal resolutions by line bundles for pushforwards of structure sheaves of toric substacks of smooth toric stacks. The submitted version differs slightly from the arXiv version, mainly fixing typos and making minor changes to the abstract and introduction.
• Hanlon-Hicks-Lazarev resolution revisited (with Lev Borisov), arXiv preprint (2025), submitted.

  This project grew out of an attempt to understand the work of Hanlon-Hicks-Lazarev on resolutions of structure sheaves of toric subvarieties. The proof we obtained is much simpler and, in a sense, more conceptual.
• Stringy Hodge numbers of Pfaffian double mirrors and Homological Projective Duality, arXiv preprint (2024), submitted.

  In this paper, we study the so-called generalized Pfaffian double mirrors, which are predicted to share the same mirror family and therefore are expected to have equivalent derived categories (or, more precisely, certain categorical resolutions) and equal Hodge numbers, interpreted in terms of Batyrev's stringy Hodge numbers. The odd-dimensional cases are well-behaved, and both statements have been established (see Rennemo-Segal and Borisov-Libgober); however, the even-dimensional cases are more subtle. More precisely, to obtain the desired equality of Hodge numbers, one has to modify the discrepancies of a log resolution of Pfaffian varieties. It would be interesting to understand this modification conceptually and ideally replace it with a less ad hoc construction.
• Central charges in local mirror symmetry via hypergeometric duality, Advances in Mathematics (2024)

  This project grew out of an (unsuccessful) attempt to construct a global integral structure for bbGKZ systems. We prove that a certain A-brane integral structure, defined by the homology group of the complement of an affine hypersurface in an algebraic torus, is equivalent to the B-brane integral structure defined by the Grothendieck group of the corresponding toric CY.
• Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms, Épijournal de Géométrie Algébrique (2023)

  This is a generalization and simplification of Borisov-Horja's work on analytic continuation of GKZ systems. We prove that the Fourier-Mukai transforms between derived categories of toric CYs induced by toric wall-crossings are compatible with the analytic continuation of bbGKZ systems.
• On hypergeometric duality conjecture (with Lev Borisov), Advances in Mathematics (2023)

  We construct an explicit non-degenerate pairing between the solution spaces of bbGKZ systems in arbitrary dimensions, which can be seen as a globalization of the Euler pairing on derived categories of toric CYs.
• On duality of certain GKZ hypergeometric systems (with Lev Borisov and Chengxi Wang), Asian Journal of Mathematics (2019)

  This was an undergraduate research project. We settled the hypergeometric duality conjecture in dimension two by a direct computation.

In preparation

• On the classification of topological toric surfaces and almost complex structures (with Amin Gholampour, Tristan Hübsch) (2026), in preparation.