15 citations · 45 across the 20 of their papers we have counts for
20 papers
Lifting holomorphic disks from flag varieties to basic affine spaces
Yoosik Kim
Let be a complex reductive algebraic group, the complexification of a compact Lie group . Consider a holomorphic principal -bundle whose total space contains a -invari…
Newton--Okounkov bodies of partial flag varieties via cluster algebras
Yunhyung Cho, Myungho Kim, Yoosik Kim +1
We construct Newton--Okounkov polytopes of Schubert varieties in partial flag varieties of arbitrary type using the cluster structure on a unipotent cell. When the governing cluste…
Holomorphic disks and GIT quotients
Yoosik Kim
Let be a connected compact Lie group and let be its complexification. In this paper, we establish a correspondence between the moduli spaces of holomorphic disks b…
Cluster algebras and monotone Lagrangian tori
Yunhyung Cho, Myungho Kim, Yoosik Kim +1
Motivated by the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO25], we consider a family of Newton--Okounkov polytopes of a com…
On non-displaceable Lagrangian submanifolds in two-step flag varieties
Yoosik Kim
We prove that the two-step flag variety carries a non-displaceable and non-monotone Lagrangian Gelfand--Zeitlin fiber diffeomorphic to $S^3 \times T^{2n-…
Disk potential functions for polygon spaces
Yoosik Kim, Siu-Cheong Lau, Xiao Zheng
We derive a Floer theoretical SYZ mirror for an equilateral and generic polygon space. The disk potential function of the monotone torus fiber of the caterpillar bending system is…