Kim, Minki

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

Before, I was working

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

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

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

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

• Publications

• Scopus

• Google Scholar

• MR Author ID: 1183004

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 and investigating combinatorial properties 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:

"Extensions of the Colorful Helly Theorem for d-collapsible and d-Leray complexes"

Forum of Mathematics, Sigma, 12:e44 1-14, 2024.

(arXiv:2305.12360)

• Minki Kim and Alan Lew:

      Leray numbers of tolerance complexes

      Combinatorica, 43:985-1006, 2023. 

      (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).

• Jinha Kim and Minki Kim: 

      Domination numbers and noncover complexes of hypergraphs

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

(arXiv:2101.01850)

• Andreas Holmsen, Minki Kim, and Seunghun Lee:

      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.

Gwangju, Republic of Korea

Jinha Kim in the Department of Mathematics at Chonnam National University also works on combinatorial and topological aspects of simplicial complexes and (hyper)graphs. Please feel free to contact us if you want to visit Gwangju for research collaboration.

Teachings

• 22Spring: Single-variable Calculus

• 22Fall: Single-variable Calculus, Multivariable Calculus

• 23Spring: Single-variable Calculus, Linear Algebra

• 23Fall: Multivariable Calculus, Introduction to Topology, Elementary and Analytic Number Theory and Applications

• 24Spring: Single-variable Calculus, Geometric and Topological Combinatorics

Grants

• GIST Research Project grant (Starting grant)
  - Feb 2022 ~ Dec 2023: 30,000,000 KRW (about 23,000 USD) for 2 years. 

• Basic Science Research Program, National Research Foundation of Korea (NRF)
  - June 2022 ~ Feb 2025: 176,000,000 KRW (about 135,000 USD) for 2.75 years.