15 citations · 93 across the 26 of their papers we have counts for
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Mirror functor for deformed preprojective algebras
Hansol Hong, Siu-Cheong Lau, Ju Tan
We study localized homological mirror symmetry associated to an immersed Lagrangian brane , possibly equipped with a higher rank flat bundle, of a symplectic manifold $…
Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Sam Bardwell-Evans, Man-Wai Mandy Cheung, Hansol Hong +1
We construct special Lagrangian fibrations for log Calabi-Yau surfaces, and scattering diagrams from Lagrangian Floer theory of the fibres. Then we prove that the scattering diagra…
Maurer-Cartan deformation of Lagrangians
Hansol Hong
The Maurer-Cartan algebra of a Lagrangian is the algebra that encodes the deformation of the Floer complex as an -algebra. We identify the Maurer-Cartan a…
Big Quantum cohomology of orbifold spheres
Lino Amorim, Cheol-Hyun Cho, Hansol Hong +1
We construct a Kodaira-Spencer map from the big quantum cohomology of a sphere with three orbifold points to the Jacobian ring of the mirror Landau-Ginzburg potential function. Thi…
-equivariant disc potentials for toric Calabi-Yau manifolds
Hansol Hong, Yoosik Kim, Siu-Cheong Lau +1
We study the equivariant disc potentials for immersed SYZ fibers in toric Calabi-Yau manifolds. The immersed Lagrangians play a crucial role in the partial compactification of the…
Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period
Hansol Hong, Yu-Shen Lin, Jingyu Zhao
We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for…
Gluing Localized Mirror Functors
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry an…
Immersed two-spheres and SYZ with Application to Grassmannians
Hansol Hong, Yoosik Kim, Siu-Cheong Lau
We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sp…
Mirror of Atiyah flop in symplectic geometry and stability conditions
Yu-Wei Fan, Hansol Hong, Siu-Cheong Lau +1
We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct…
Counting of Holomorphic Orbi-spheres in and Determinant Equation
Hansol Hong, Hyung-Seok Shin
We count the number of holomorphic orbi-spheres in the -quotient of an elliptic curve. We first prove that there is an explicit correspondence between the holomorphic…
On quantum cohomology ring of elliptic orbifolds
Hansol Hong, Hyung-Seok Shin
We compute quantum cohomology ring of elliptic orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-cur…
Localized mirror functor constructed from a Lagrangian torus
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A-infinity funct…
Lagrangian Floer potential of orbifold spheres
Cheol-Hyun Cho, Hansol Hong, Sang-hyun Kim +1
For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and…
Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
Cheol-Hyun Cho, Hansol Hong, Siu-Cheong Lau
This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fuk…
Finite group actions on Lagrangian Floer theory
Cheol-Hyun Cho, Hansol Hong
We construct finite group actions on Lagrangian Floer theory when symplectic manifolds have finite group actions and Lagrangian submanifolds have induced group actions. We first de…