# The 2nd Mini Workshop on Knot theory

## Knots and Spatial graphs

December 16–17, 2016

POSTECH Math. Bldg. #404, Pohang, Korea

sponsered by

## 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 88,000 KRW 80,000 KRW 80,000 KRW 70,000 KRW 90,000 KRW (1 Person)100,000 KRW (2 Persons) 88,000 KRW 80,000 KRW 80,000 KRW 80,000 KRW 100,000 KRW120,000 KRW (Deluxe) 13,200 KRW free 11,000 KRW free free 10 min. by walk 15 min. by car 15 min. by car 20 min. by car 20 min. by car +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