Research
Elliptic genera of Pfaffian-Grassmannian double mirrors
In progress.
Stringy E-functions of generalized Pfaffian double mirrors
In preparation.
Central charges in local mirror symmetry via hypergeometric duality
In this paper we study the central charges of Hori-Vafa mirror pairs, where the A-model is given by a family of affine hypersurfaces in algebraic torus and the B-model is given by toric Calabi-Yau orbifolds. We combine the tropical method of Abouzaid-Ganatra-Iritani-Sheridan and the hypergeometric duality of Borisov and myself to settle a conjecture of Hosono. This could also be seen as a generalization of the Gamma conjecture for the local mirror symmetry setting.
Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms
Under minor revision at Épijournal de Géométrie Algébrique. arXiv:2305.12241.
A companion paper to the paper “On hypergeometric duality conjecture”. We settled the analytic continuation conjecture of Borisov-Horja in full generality. We use the tool of Mellin-Branes integral to compute analytic continuations of hypergeometric series.
On hypergeometric duality conjecture
Joint with Lev Borisov, Advances in Mathematics, Volume 442 (2024), 109582. arXiv:2301.01374 journal
In this paper we settled the duality conjecture in Borisov-Horja in full generality. We construct an explicit non-degenerate pairing between the solution spaces of the bbGKZ D-modules and its holonomic dual. The novelty of this paper lies in the relationship between our formula for the pairing and the resolution of diagonal formula for toric varieties of Fulton-Sturmfels.
On duality of certain GKZ hypergeometric systems
Joint with Lev Borisov and Chengxi Wang, Asian Journal of Mathematics, Volume 25 (2021), No.1, 65-88. arXiv:1910.04039 journal
An undergraduate research project. We studied two conjectures of Borisov and Horja on the better-behaved GKZ systems, and proved them in the 2-dimensional case.