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…
Chekanov torus and Gelfand--Zeitlin torus in
Yoosik Kim
The Chekanov torus was the first known \emph{exotic} torus, a monotone Lagrangian torus that is not Hamiltonian isotopic to the standard monotone Lagrangian torus. We explore the r…
Disk potential functions for quadrics
Yoosik Kim
We compute the disk potential of Gelfand--Zeitlin monotone torus fiber in a quadric hypersurface by exploiting toric degenerations, Lie theoretical mirror symmetry, and the structu…
DeepRegularizer: Rapid Resolution Enhancement of Tomographic Imaging using Deep Learning
DongHun Ryu, Dongmin Ryu, YoonSeok Baek +8
Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner.…
-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…
Small toric resolutions of toric varieties of string polytopes with small indices
Yunhyung Cho, Yoosik Kim, Eunjeong Lee +1
Let be a semisimple algebraic group over . For a reduced word of the longest element in the Weyl group of and a dominant integral weight , one can co…
A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems
Yunhyung Cho, Yoosik Kim, Yong-Geun Oh
Using the bulk-deformation of Floer cohomology by Schubert cycles and non-Archimedean analysis of Fukaya--Oh--Ohta--Ono's bulk-deformed potential function, we prove that every comp…
Lagrangian fibers of Gelfand-Cetlin systems
Yunhyung Cho, Yoosik Kim, Yong-Geun Oh
A Gelfand-Cetlin system is a completely integrable system defined on a partial flag manifold whose image is a rational convex polytope called a Gelfand-Cetlin polytope. Motivated b…
-equivariant disc potential and SYZ mirror construction
Yoosik Kim, Siu-Cheong Lau, Xiao Zheng
We develop a -equivariant Lagrangian Floer theory and obtain a curved algebra, and in particular a -equivariant disc potential. We construct a Morse model, which c…
On the combinatorics of string polytopes
Yunhyung Cho, Yoosik Kim, Eunjeong Lee +1
For a reduced word of the longest element in the Weyl group of , one can associate the string cone which parametrizes the dual…
Lagrangian fibers of Gelfand--Cetlin systems of -type
Yunhyung Cho, Yoosik Kim
In this paper, we study the Gelfand--Cetlin systems and polytopes of the co-adjoint -orbits. We describe the face structure of Gelfand--Cetlin polytopes and iterate…
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…
Monotone Lagrangians in flag varieties
Yunhyung Cho, Yoosik Kim
In this paper, we give a formula for the Maslov index of a gradient holomorphic disc, which is a relative version of the Chern number formula of a gradient holomorphic sphere for a…
Lagrangian fibers of Gelfand-Cetlin systems
Yunhyung Cho, Yoosik Kim, Yong-Geun Oh
Motivated by the study of Nishinou-Nohara-Ueda on the Floer thoery of Gelfand-Cetlin systems over complex partial flag manifolds, we provide a complete description of the topology…
Non-displaceable toric fibers on compact toric manifolds via tropicalizations
Yoosik Kim, Jaeho Lee
We give a combinatorial way to locate non-displaceable Lagrangian toric fibers on compact toric manifolds. By taking the intersection of certain tropicalizations coming from combin…