기초과학연구원 이산수학그룹
On June 29, 2021, Jeong Ok Choi (최정옥) from GIST and IBS Discrete Mathematics Group gave a talk at the Discrete Math Seminar on the non-singularity of some circulant matrices. The title of her talk was “Invertibility of circulant matrices of arbitrary size“.
In this talk, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations in terms of the entries in the first row with integer coefficients. Using these conditions we show the invertibility of some family of circulant matrices with particular forms of integers generated by a primitive element in $\mathbb{Z}_p$. Also, the invertibility of circulant 0, 1-matrices can be argued combinatorially by applying sufficient conditions. This is joint work with Youngmi Hur.
On October 27, 2020, Jeong Ok Choi (최정옥) from IBS Discrete Mathematics Group / GIST gave a talk on some game-theoretic problems on graphs, more specifically on the contagion game and the network creation game. The title of her talk was “Various game-theoretic models on graphs“.
We introduce some of well-known game-theoretic graph models and related problems.
A contagion game model explains how an innovation diffuses over a given network structure and focuses on finding conditions on which structure an innovation becomes epidemic. Regular infinite graphs are interesting examples to explore. We show that regular infinite trees make an innovation least advantageous to be epidemic considering the whole class of infinite regular graphs.
A network creation game model, on the other hand, tries to explain the dynamics on forming a network structure when each vertex plays independently and selfishly. An important question is how costly a formation can be made without any central coordination, and the concept of Price of Anarchy (PoA) is introduced. In the model originally suggested by Fabrikant et al., PoA measures how bad the forming cost can be at Nash equilibria compared to absolute minimum, and they conjectured that this inefficiency can happen only when some tree structures are formed (Tree Conjecture). We will introduce recent progress on this tree conjecture, remaining open problems, and possible variations.
This talk includes part of joint work with Unjong Yu.
The IBS Discrete Mathematics Group welcomes Prof. Jeong Ok Choi (최정옥) from GIST, Gwangju, Korea. She will visit the IBS Discrete Mathematics Group for 1 year until August 31, 2021 during her sabbatical leave from GIST. She received her Ph.D. from University of Illinois at Urbana-Champaign under the supervision of Prof. Douglas West. She was a visiting assistant professor at Furman University and Trinity College. In 2011, she moved to GIST (Gwangju Institute of Science and Technology) in Gwangju, Korea as an assistant professor and she is currently an associate professor.