Source author record

Min Kyu Kim

Explore this author’s publications, collaborators and research topics. This catalog record has not been claimed by its author.

ResearcherUnclaimed source record

math.GR math.RT math.KT math.SG math.AT Artificial Intelligence cs.CY math-ph math.MP math.QA

Catalog footprint

Research overview

10works

10topics

4close collaborators

Actions

Is this your work?

Open graph Browse papers

preprint2026arXiv

Guidelines for Designing AI Technologies to Support Adult Learning

AI-powered educational technologies have demonstrated measurable benefits for learners, but their design and evaluation have largely centered on K-12 contexts. As a result, many AI-supported learning systems remain poorly aligned with the needs, constraints, and goals of adult learners. To better understand how AI systems function in adult education, this paper examines the deployment of several AI learning technologies developed within a multidisciplinary, national research institute in the United States focused on adult learning and online education. Drawing on longitudinal deployment data, we conducted a reflexive thematic analysis to identify recurring challenges and design considerations across systems. These insights were synthesized into a set of 19 design guidelines intended to inform future AI-supported adult learning technologies. We demonstrate the utility of these guidelines through a heuristic evaluation of the deployed systems. Lastly, we present a guideline exploration tool that aids in the ideation of technologies by connecting the guidelines to stakeholder statements surfaced in the analysis process.

preprint2016arXiv

Embedded surfaces for symplectic circle actions

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces. More precisely, we will show that (1) if $(M,ω)$ admits a Hamiltonian $S^1$ -action, then there exists an $S^1$ -invariant symplectic $2$ -sphere $S$ in $(M,ω)$ such that $\langle c_1(M), [S] \rangle > 0$ , and (2) if the action is non-Hamiltonian, then there exists an $S^1$ -invariant symplectic $2$ -torus $T$ in $(M,ω)$ such that $\langle c_1(M), [T] \rangle = 0$ . As applications, we will give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott \cite{AB}, Lupton-Oprea \cite{LO}, and Ono \cite{O2} : suppose that $(M,ω)$ is a smooth closed symplectic manifold satisfying $c_1(TM)=λ\cdot [ω]$ for some $λ\in \R$ and let $G$ be a compact connected Lie group acting effectively on $M$ preserving $ω$ . Then (1) if $λ< 0$ , then $G$ must be trivial, (2) if $λ=0$ , then the $G$ -action is non-Hamiltonian, and (3) if $λ> 0$ , then the $G$ -action is Hamiltonian.

preprint2015arXiv

Equivariant pointwise clutching maps

In the paper, we introduce the terminology equivariant pointwise clutching map. By using this, we give details on how to glue an equivariant vector bundle over a finite set so as to obtain a new Lie group representation such that the quotient map from the bundle to the representation is equivariant. Then, we investigate the topology of the set of all equivariant pointwise clutching maps with respect to an equivariant vector bundle over a finite set. Results of the paper play a key role in classifying equivariant vector bundles over two-surfaces in other papers.

preprint2013arXiv

Crystal $\Bla$ in $B(\infty)$ for $G_2$ type Lie Algebra

A previous work gave a combinatorial description of the crystal $B(\infty)$ , in terms of certain simple Young tableaux referred to as the marginally large tableaux, for finite dimensional simple Lie algebras. Using this result, we present an explicit description of the crystal $B(λ)$ , in terms of the marginally large tableaux, for the $G_2$ Lie algebra type. We also provide a new description of $B(\la)$, in terms of Nakajima monomials, that is in natural correspondence with our tableau description.

preprint2013arXiv

Hamiltonian circle action with self-indexing moment map

Let $(M,ω)$ be a $2n$ -dimensional smooth compact symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points and let $μ: M \rightarrow \R$ be a corresponding moment map. Let $Λ_{2k}$ be the set of all fixed points of index $2k$ . In this paper, we will show that if $μ$ is constant on $Λ_{2k}$ for each $k$ , then $(M,ω)$ satisfies the hard Lefschetz property. In particular, if $(M,ω)$ admits a self-indexing moment map, i.e. $μ(p) = 2k$ for every $p \in Λ_{2k}$ and $k=0,1,\cdots,n,$ then $(M,ω)$ satisfies the hard Lefschetz property.

preprint2013arXiv

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Let $(M,ω)$ be an eight-dimensional closed symplectic manifold equipped with a Hamiltonian circle action with only isolated fixed points. In this article, we will show that the Betti numbers of $M$ are unimodal, i.e. $b_0(M) \leq b_2(M) \leq b_4(M)$ .

preprint2011arXiv

Classification of equivariant vector bundles over real projective plane

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

preprint2011arXiv

Classification of equivariant vector bundles over two-sphere

We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles except a few cases. To do it, we calculate equivariant homotopy of the set of equivariant clutching maps. Holomorphic version of this will be treated in other paper. Classification on two-torus, real projective plane, Klein bottle will appear soon.

preprint2011arXiv

Log-concavity of complexity one Hamiltonian torus actions

Let $(M,ω)$ be a closed $2n$ -dimensional symplectic manifold equipped with a Hamiltonian $T^{n-1}$ -action. Then Atiyah-Guillemin-Sternberg convexity theorem implies that the image of the moment map is an $(n-1)$ -dimensional convex polytope. In this paper, we show that the density function of the Duistermaat-Heckman measure is log-concave on the image of the moment map.

preprint2010arXiv

Classification of equivariant vector bundles over two-torus

We exhaustively classify topological equivariant complex vector bundles over two-torus under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) six points are sufficient to classify equivariant vector bundles except a few cases. To do it, we calculate homotopy of the set of equivariant clutching maps. And, classification on real projective plane, Klein bottle will appear soon

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Min Kyu Kim

Research overview

Is this your work?

10 publications

Guidelines for Designing AI Technologies to Support Adult Learning

Embedded surfaces for symplectic circle actions

Equivariant pointwise clutching maps

Crystal $\Bla$ in $B(\infty)$ for $G_2$ type Lie Algebra

Hamiltonian circle action with self-indexing moment map

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Classification of equivariant vector bundles over real projective plane

Classification of equivariant vector bundles over two-sphere

Log-concavity of complexity one Hamiltonian torus actions

Classification of equivariant vector bundles over two-torus

See the researcher in context

Building this map preview

Min Kyu Kim

Research overview

Is this your work?

10 publications

Guidelines for Designing AI Technologies to Support Adult Learning

Embedded surfaces for symplectic circle actions

Equivariant pointwise clutching maps

Crystal $\Bla$ in B(∞)B(\infty)B(∞) for G2G_2G2​ type Lie Algebra

Hamiltonian circle action with self-indexing moment map

Unimodality of the Betti numbers for Hamiltonian circle action with isolated fixed points

Classification of equivariant vector bundles over real projective plane

Classification of equivariant vector bundles over two-sphere

Log-concavity of complexity one Hamiltonian torus actions

Classification of equivariant vector bundles over two-torus

See the researcher in context

Building this map preview

Crystal $\Bla$ in $B(\infty)$ for $G_2$ type Lie Algebra