# The 2^{nd} Mini Workshop on Knot theory

## Knots and Spatial graphs

**December 16–17, 2016**

POSTECH Math. Bldg. #404, Pohang, Korea

sponsered by### Institute for Basic Science, Center for Geometry and Physics,

National Research Foundation of Korea

## Invited speakers

- Byunghee An (IBS-CGP)
- Youngsik Huh (Hanyang University)
- Sungjong No (Ewha Womans University)
- Danielle O'Donnol (Indiana University)
- Seungsang Oh (Korea University)
- Hyowon Park (Seoul National University)
- Dai Tamaki (Shinshu University)

## Venue

- POSTECH Math. Bldg. #404

## Organizers

- Byunghee An (IBS-CGP)
- Hwajeong Lee (DGIST)

## Talk Schedule

December 16 (Fri) | December 17 (Sat) | |
---|---|---|

09:30 – 10:15 | Arrival | Seungsang Oh |

10:15 – 10:45 | Coffee Break | |

10:45 – 11:30 | O'Donnol | |

11:45 – 12:30 | Byunghee An | |

12:30 – 14:00 | Lunch & Departure | |

14:00 – 14:45 | Youngsik Huh | |

15:00 – 15:45 | Sungjong No | |

15:45 – 16:15 | Coffee Break | |

16:15 – 17:00 | Dai Tamaki | |

17:15 – 18:00 | Hyowon Park | |

18:00 – | Dinner |

## Title & Abstract

- Speaker
- Byunghee An (IBS-CGP)
- Title
- DGA invariants for Legendrian spatial graphs
- Abstract
- The Chekanov-Eliashberg DGA is an invariant of Legendrian knots consisting of a differential graded algebra(DGA) whose differential is determined by counting rigid, punctured holomorphic disks in the plane with exactly one positive puncture and with boundary on the Lagrangian projection of a knot $L$. We extend this invariant to Legendrian spatial graphs. This is a joint work with Youngjin Bae.

- Speaker
- Youngsik Huh (Hanyang University)
- Title
- Minimal stick number of tangles
- Abstract
- A tangle is a set of disjoint arcs properly embedded in the standard 3-ball, and a stick tangle is a tangle such that every arc consists of finitely many line segments, called sticks. In this talk we give an elementary fact on the minimal number of sticks necessary for nontrivial tangles. This is a joint work with Jeonghoon Lee at CBU and Kouki Taniyama at Waseda Univ.

- Speaker
- Sungjong No (Ewha Womans University)
- Title
- Arc index and stick number of spatial graphs
- Abstract
- Bae and Park found an upper bound on the arc index of prime links in terms of the minimal crossing number. We extend the definition of the arc presentation to spatial graphs and find an upper bound on the arc index $\alpha (G)$ of any spatial graph $G$ such as $$\alpha (G) \leq c(G) + e + b,$$ where $c(G)$ is the minimal crossing number of $G$, $e$ is the number of edges, and $b$ is the number of bouquet cut-components. This upper bound is lowest possible. Furthermore, we find an upper bound of stick number $s(G)$ by using the upper bound of the arc index as follow: $$s(G) \leq \frac{3}{2}c(G)+2e+\frac{3b}{2}-\frac{v}{2}$$ where $v$ is the number of vertices of G.

- Speaker
- Danielle O'Donnol (Indiana University)
- Title
- Simplicity in Legendrian graphs and Legendrian theta-graphs
- Abstract
- We will work in three-space with the standard contact structure. An embedded graph is Legendrian if it is everywhere tangent to the contact structure. I will give an overview of a few different invariants. Then I will talk about our recent work on Legendrian simplicity for topologically planar Legendrian graphs and our classification of planar Legendrian theta-graphs. This is joint with Peter Lambert-Cole (Indiana).

- Speaker
- Seungsang Oh (Korea University)
- Title
- Enumeration of rigid lattice links
- Abstract
- The author recently introduced the state matrix recursion algorithm to enumerate various two-dimensional lattice models. In this talk, stepping up a dimension, we extend this algorithm to the enumeration of rigid lattice links which are links in the three-dimensional cubic lattice. We also consider the enumeration of fully-packed rigid lattice links. Lastly, their asymptotic behaviors are also discussed.

- Speaker
- Hyowon Park (Seoul National University)
- Title
- Presentations and homologies of graph braid groups
- Abstract
- A graph braid group is the fundamental group of the configuration space on a connected graph as 1-dimensional finite CW-complex. In this talk, I will survey results about presentations and homologies of graph braid groups since 1998, in which graph braid groups were introduced by Ghrist as motivated by robotics.

- Speaker
- Dai Tamaki (Shinshu University)
- Title
- A combinatorial model for graph braid groups
- Abstract
- Given a graph G, regarded as a 1-dimensional cell complex, the fundamental group of the unordered configuration space $Conf_n(G)/\Sigma_n$ of $n$ distinct points in $G$ is called the graph braid group of $n$ strands in $G$. After the pioneering work by Rob Ghrist [Ghr01], the structure of graph braid groups has been investigated by many people. A standard technique is to use Abrams' combinatorial model for $Conf_n(G)$ described in his thesis [Abr00] and then use discrete Morse theory to reduce the number of cells. Here we propose an alternative model based on the notion of cellular stratified spaces and its face categories, developed in [Tam]. Sample computations will be given based on the works [FMT15; Uno16] of former students of mine.

## Registration

Online registration is available here until December 13, 2016.

## How to get to POSTECH

Visit here for information about how to get to Pohang.

For the location of the conference site, click here for POSTECH Campus Map.

## Accommodation

*To visit the website of the hotel, please click the name of the hotel.*

POSCO Int'l Center | Apple Tree Hotel | Philos Hotel | Benikea Hotel Pohang | Eco Hotel | |
---|---|---|---|---|---|

Double Room | 88,000 KRW | 80,000 KRW | 80,000 KRW | 70,000 KRW | 90,000 KRW (1 Person) 100,000 KRW (2 Persons) |

Twin Room | 88,000 KRW | 80,000 KRW | 80,000 KRW | 80,000 KRW | 100,000 KRW 120,000 KRW (Deluxe) |

Breakfast (1 person) |
13,200 KRW | free | 11,000 KRW | free | free |

Distance from Venue | 10 min. by walk | 15 min. by car | 15 min. by car | 20 min. by car | 20 min. by car |

Contact | +82-54-279-8500 | +82-54-241-1234 | +82-54-250-2000 | +82-54-282-2700 | +82-54-282-8787 |

* The above rate is as of July, 2016 (VAT included)

** The rate may vary

## Visa

Please visit here and if you need to apply for the visa to attend the conference, please contact eunyoung.jang@ibs.re.kr. We would request a copy of your passport and up-to-date CV for review.

## Contact

eunyoung.jang@ibs.re.kr