Kim, Minki


Department of Mathematical Sciences

Gwangju Institute of Science and Technology (GIST)

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

Currently, I am an associate professor in the Department of Mathematical Sciences at GIST, Gwangju, Republic of Korea.

I have been at GIST since 2022. Before, I was working

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.

Positions

Education

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, motivated by Helly type theorems, I am interested in finding bounds on Leray numbers and investigating combinatorial properties of various simplicial complexes (such as independence complexes, nerve complexes, ...) arising from combinatorial situation. Here are selected publications in this direction:


"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)


      Leray numbers of tolerance complexes

      Combinatorica, 43:985-1006, 2023. 

      (arXiv:2109.03030).


      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)


      Nerves, minors, and piercing numbers

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

      (arXiv:1706.05181)


A full list of my publications 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. 

Teaching

Grants