Kim, Minki


Division of Liberal Arts and Sciences

Gwangju Institute of Science and Technology (GIST)

email: minkikim [at] gist [dot] ac [dot] kr

Currently, I am an assistant professor in the Division of Liberal Arts and Sciences at GIST, Gwangju, South Korea.

Before, I was working

  • as a Senior Researcher in the Discrete Mathematics Group at the IBS, Daejeon, South Korea from 2020 September to 2022 January, and

  • as a Postdoctoral Research Fellow in the Faculty of Mathematics at the Technion, Haifa, Israel from 2018 September to 2020 August, hosted by Ron Aharoni.

I obtained my PhD degree on August 26, 2018 from the Department of Mathematical Sciences at KAIST, Daejeon, South Korea, where my advisor was Andreas Holmsen.

My research interests lie on discrete geometry, topological combinatorics and graph theory.

Positions

  • GIST, Gwangju, Republic of Korea
    - 2022.02 to present: Assistant Professor

  • IBS, Daejeon, Republic of Korea
    - 2020.09 to 2022.01: Senior Researcher

  • Technion - Israel Institute of Technology, Haifa, Israel
    - 2018.09 to 2020.08: Post-doctoral Research Fellow

Education

  • KAIST, Daejeon, Republic of Korea
    - 2018.08 Ph.D. Mathematical Sciences - Advisor: Andreas Holmsen
    - 2014.02 M.S. Mathematical Sciences - Advisor: Andreas Holmsen
    - 2012.02 B.S. Mathematical Sciences

Research

Given an abstract simplicial complex, its Leray number is defined as the minimal integer k such that all induced subcomplexes has trivial homology groups in dimension k or greater. The Leray number of a simplicial complex is equivalent to the Castelnuovo-Mumford regularity of the square-free monomial ideal that corresponds to the complex.

These days, I am interested in finding bounds on Leray numbers of various simplicial complexes arising from combinatorial situation (such as independence complexes, nerve complexes, ...). Here are selected publications in this derection:


  • Minki Kim and Alan Lew:

Leray numbers of tolerance complexes

(arXiv:2109.03030).


  • Minki Kim and Alan Lew:

Complexes of graphs with bounded independence number

Israel Journal of Mathematics, 249:83-120, 2022

(arXiv:1912.12605).


Domination numbers and noncover complexes of hypergraphs

Journal of Combinatorial Theory Series A, 180:105408, 2021.

(arXiv:2101.01850)


Choice functions in the intersection of matroids

Electronic Journal of Combinatorics, 26: Paper 4.26, 2019.

(arXiv:1905.00043)


Nerves, minors, and piercing numbers

Transactions of the American Mathematical Society, 371(12):8755-8779, 2019.

(arXiv:1706.05181)


A full list of my publication can be found in Publications page.

Teachings

  • 22Spring: Single-variable Calculus

  • 22Fall: Single-variable Calculus, Multivariable Calculus

Grants

  • Basic Science Research Program, National Research Foundation of Korea (NRF)
    - June 2022 ~ Feb 2024: 176,000,000 KRW (about 135,000 USD) for 2.75 years.