Yunhyung Cho

activity

20102026

most citedOn the f-vectors of Gelfand-Cetlin polytopes

26 citations · 70 across the 33 of their papers we have counts for

collaborators

33 papers

math.AG2026

Mutation of Fano Simplices and Markov type equations

Yunhyung Cho

It is well known that there is a bijective correspondence between the set of positive integer solutions to the Markov equation and the set of Fano triangles mutation equivalent to…

math.AG2026

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…

math.SG2024

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…

math.AG2023

Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures

Yunhyung Cho, Naoki Fujita, Akihiro Higashitani +1

A flag variety is a smooth projective homogeneous variety. In this paper, we study Newton-Okounkov polytopes of the flag variety $F l (C^{4})$ arising from its cluster structu…

math.AG2023

$c_{1}$ -cohomological rigidity for smooth toric Fano varieties of Picard number two

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

The $c_{1}$ -cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a $c_{1}$ -preserving isomorphism between their integra…

math.CO2023

On combinatorics of string polytopes in types $B$ and $C$

Yunhyung Cho, Naoki Fujita, Eunjeong Lee

A string polytope is a rational convex polytope whose lattice points parametrize a highest weight crystal basis, which is obtained from a string cone by explicit affine inequalitie…

math.AG2021

On the enumeration of Fano Bott manifolds

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

Fano Bott manifolds bijectively correspond to signed rooted forests with some equivalence relation. Using this bijective correspondence, we enumerate the isomorphism classes of Fan…

math.CO2020★ 3 cited

Enumeration of Gelfand-Cetlin type reduced words

Yunhyung Cho, Jang Soo Kim, Eunjeong Lee

The combinatorics of reduced words and commutation classes plays an important role in geometric representation theory. A string polytope is a lattice polytope associated to each re…

math.SG2020★ 1 cited

Unique toric structure on a Fano Bott manifold

Yunhyung Cho, Eunjeong Lee, Mikiya Masuda +1

We prove that if there exists a $c_{1}$ -preserving graded ring isomorphism between integral cohomology rings of two Fano Bott manifolds, then they are isomorphic as toric varieties.…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that $(M, ω_{M})$ is $S^{1}$ -equivariant symplec…

math.AG2019★ 1 cited

Small toric resolutions of toric varieties of string polytopes with small indices

Yunhyung Cho, Yoosik Kim, Eunjeong Lee +1

Let $G$ be a semisimple algebraic group over $C$ . For a reduced word $i$ of the longest element in the Weyl group of $G$ and a dominant integral weight $λ$ , one can co…

math.SG2019★ 3 cited

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…

math.SG2019

Remark on the Betti numbers for Hamiltonian circle actions

Yunhyung Cho

In this paper, we establish a certain inequality in terms of Betti numbers of a closed Hamiltonian $S^{1}$ -manifold with isolated fixed points.

math.SG2019

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…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III

Yunhyung Cho

In this paper, we complete the classification of six-dimensional closed monotone symplectic manifolds admitting semifree Hamiltonian $S^{1}$ -actions. We also show that every such man…

math.SG2019

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions II

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that if the maximal and the minimal fixed c…

math.CO2019★ 3 cited

On the combinatorics of string polytopes

Yunhyung Cho, Yoosik Kim, Eunjeong Lee +1

For a reduced word $i$ of the longest element in the Weyl group of $SL_{n + 1} (C)$ , one can associate the string cone $C_{i}$ which parametrizes the dual…

math.SG2018

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I

Yunhyung Cho

Let $(M, ω_{M})$ be a six dimensional closed monotone symplectic manifold admitting an effective semifree Hamiltonian $S^{1}$ -action. We show that if the minimal (or maximal) fixed comp…

math.SG2018★ 1 cited

Lagrangian fibers of Gelfand--Cetlin systems of $SO (n)$ -type

Yunhyung Cho, Yoosik Kim

In this paper, we study the Gelfand--Cetlin systems and polytopes of the co-adjoint $SO (n)$ -orbits. We describe the face structure of Gelfand--Cetlin polytopes and iterate…

math.SG2018★ 5 cited

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…

math.SG2017★ 12 cited

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…

math.CO2016★ 26 cited

On the f-vectors of Gelfand-Cetlin polytopes

Byung Hee An, Yunhyung Cho, Jang Soo Kim

A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent descript…

math.SG2016

On the Chern numbers for pseudo-free circle actions

Byung Hee An, Yunhyung Cho

Let $(M, ψ)$ be a $(2 n + 1)$ -dimensional oriented closed manifold equipped with a pseudo-free $S^{1}$ -action $ψ : S^{1} \times M \to M$ . We first define a \textit{local data} $\mat…

math.SG2014

Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps

Yunhyung Cho

The unimodality conjecture posed by Tolman in the conference `Moment maps in Various Geometry" in 2005 states that if (M,w) is a 2n-dimensional smooth compact symplectic manifold e…

Mutation of Fano Simplices and Markov type equations

Newton--Okounkov bodies of partial flag varieties via cluster algebras

Cluster algebras and monotone Lagrangian tori

Newton-Okounkov polytopes of type A flag varieties of small ranks arising from cluster structures

c1​-cohomological rigidity for smooth toric Fano varieties of Picard number two

On combinatorics of string polytopes in types B and C

On the enumeration of Fano Bott manifolds

Enumeration of Gelfand-Cetlin type reduced words

Unique toric structure on a Fano Bott manifold

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions

Small toric resolutions of toric varieties of string polytopes with small indices

A critical point analysis of Landau--Ginzburg potentials with bulk in Gelfand--Cetlin systems

Remark on the Betti numbers for Hamiltonian circle actions

Lagrangian fibers of Gelfand-Cetlin systems

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions III

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions II

On the combinatorics of string polytopes

Classification of six dimensional monotone symplectic manifolds admitting semifree circle actions I

Lagrangian fibers of Gelfand--Cetlin systems of SO(n)-type

Monotone Lagrangians in flag varieties

Lagrangian fibers of Gelfand-Cetlin systems

On the f-vectors of Gelfand-Cetlin polytopes

On the Chern numbers for pseudo-free circle actions

Unimodality of the Betti numbers for Hamiltonian circle actions with index-increasing moment maps

Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures

$c_{1}$ -cohomological rigidity for smooth toric Fano varieties of Picard number two

On combinatorics of string polytopes in types $B$ and $C$

Lagrangian fibers of Gelfand--Cetlin systems of $SO (n)$ -type