Research
Here are the summaries of my papers.
GKZ hypergeometric systems and toric mirror symmetry
Ph.D. Thesis.
My Ph.D. Thesis written under the guidance of Lev Borisov at Rutgers University. It is mainly based on my papers arXiv:2305.12241 and arXiv:2404.16258.
Elliptic genera of Pfaffian-Grassmannian double mirrors
In progress.
The Pfaffian-Grassmannian double mirror is the first example of derived-equivalent Calabi-Yau varieties but not birationally equivalent. They appear as different geometric phases of certain nonabelian gauged linear sigma models (nonabelian GLSM). It is believed that their mirror-symmetry-theoretic invariants (such as stringy Hodge numbers, elliptic genus, Gromov-Witten theory etc) should be equivalent. In this project we aim to prove that their elliptic genera coincide.
Stringy Hodge numbers of generalized Pfaffian double mirrors
arXiv:2409.17449. Submitted.
We study the stringy Hodge numbers of Pfaffian double mirrors, generalizing previous results of Borisov and Libgober. In the even-dimensional cases, we introduce a modified version of stringy E-functions and obtain interesting relations between the modified stringy E-functions on the two sides. We use them to make numerical predictions on the Lefschetz decompositions of the categorical crepant resolutions of Pfaffian varieties.
Central charges in local mirror symmetry via hypergeometric duality
arXiv:2404.16258. Submitted.
In this paper we study central charges of Hori-Vafa mirror pairs, where the A-model is given by a family of affine hypersurfaces in an 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 Hosono’s conjecture. This could also be viewed as a generalization of the Gamma conjecture within the context of local mirror symmetry.
Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms
Épijournal de Géométrie Algébrique, to appear. 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.