Jan 13-17, and 20-25, 2019

Main Organizers:

• Ilkyoo Choi (Hankuk University of Foreign Studies)
• Suil O (SUNY-Korea)

Additional Organizers for winter of 2019:

• Ringi Kim (KAIST)
• Boram Park (Ajou University)

• KB Ingenium

Accomodation

• KB Ingenium

• Jan 13 (Sunday)
• 13:00 -- 14:00 registration & check in
• 14:00 -- 18:00 research session

Jan 14 (Monday)

• 10:00 -- 12:00 introduction and problem session (mandatory)
• 12:00 -- 14:00 lunch + coffee break
• 14:00 -- 18:00 afternoon research session
• 18:00 -- banquet

Jan 15 (Tuesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 16 (Wednesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 1 (Semin Oh): On Unique Maximal Fixed Point Automorphisms of Graphs

We call a non-identity automorphism $\sigma$ of a graph $\Gamma$ a unique maximal fixed point automorphism (UFA) if every automorphism of $\Gamma$ fixing all fixed points of $\sigma$ is equal to $\sigma$ or the identity, i.e., there is no non-identity automorphism of $\Gamma$ which fixes all fixed points of $\sigma$. Since every UFA is an involution, every involution-free graph is a UFA-free graph. In 2017, minimal involution-free graphs are completely classified with 18 graphs. In this talk, we show the classification of minimal UFA-free graphs. This is joint work with Yun Jeong Kim.

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 17 (Thursday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 20 (Sunday)

• 13:00 -- 14:00 registration & check in
• 14:00 -- 18:00 research session

Jan 21 (Monday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 2 (Boran Kim): Lower bound on the minimum weights of algebraic geometry codes

We investigate two-point algebraic geometry codes (AG codes) on algebraic curves over a finite field. We define the order-like bound on the minimum weights of two-point AG codes on arbitrary algebraic curves. We prove that this order-like bound is better than the Goppa bound. We explicitly determine the order-like bounds for one-point AG codes and two-point AG codes on norm-trace curves over finite fields. This is a joint work with Yoonjin Lee (Ewha Womans University).

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 22 (Tuesday)

• 10:00 -- 18:00 research activity
• 18:00 -- banquet

Jan 23 (Wednesday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 24 (Thursday)

• 10:00 -- 12:00 morning research session
• 12:00 -- 14:00 lunch
• 14:00 -- 14:30 lecture 3 (Jinha Kim): A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path

We say a graph $G$ has a Hamiltonian path if it has a path containing all vertices of $G$. For a graph $G$, let $\sigma_2(G)$ denote the minimum degree sum of two nonadjacent vertices of $G$; restrictions on $\sigma_2(G)$ are known as Ore-type conditions. It was shown by Mon\'ege that if a connected graph $G$ on $n$ vertices satisfies $\sigma_2(G) \geq {3 \over 2}n$, then $G$ has a Hamiltonian path or an induced subgraph isomorphic to $K_{1,4}$. In this talk, I will present the following analogue of the result by Mom\`ege. Given an integer $t\geq 5$, if a connected graph $G$ on $n$ vertices satisfies $\sigma_2(G)>{t-3 \over t-2}n$, then $G$ has either a Hamiltonian path or an induced subgraph isomorphic to $K_{1, t}$. This is joint work with Ilkyoo Choi.

• 14:30 -- 18:00 afternoon research session
• 18:00 -- dinner

Jan 25 (Friday)

• 10:00 -- 12:00 activity report (mandatory)
• 12:00 -- 14:00 lunch