# Mini Workshop on Knot theory

**August 19–20, 2016**

POSTECH Math. Bldg. #404, Pohang, Korea

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

National Research Foundation of Korea,

Pohang Mathematics Institute

## Invited speakers

- Youngjin Bae (IBS-CGP)
- Jinseok Cho (PMI)
- Dongmin Gang (Kavli IPMU)
- Gyo Taek Jin (KAIST)
- Hyoungjun Kim (Korea University)
- Minhoon Kim (KIAS)
- Roland van der Veen (Leiden University)

## Venue

- POSTECH Math. Bldg. #404

## Organizers

- Byunghee An (IBS-CGP)
- Jinseok Cho (PMI)
- Hwajeong Lee (DGIST)

## Talk Schedule

August 19 (Fri) | August 20 (Sat) | |
---|---|---|

09:30 – 10:15 | Arrival | H. Kim |

10:15 – 10:45 | Coffee Break | |

10:45 – 11:30 | van der Veen | |

11:45 – 12:30 | Cho | |

12:30 – 14:00 | Lunch & Departure | |

14:00 – 14:45 | Jin | |

15:00 – 15:45 | Bae | |

15:45 – 16:15 | Coffee Break | |

16:15 – 17:00 | Gang | |

17:15 – 18:00 | M. Kim | |

18:00 – | Dinner |

## Title & Abstract

- Speaker
- Youngjin Bae (IBS-CGP)
- Title
- Introduction to Legendrian knot theory
- Abstract
- After a brief introduction to the concept of contact topology, we focus on Legendrin knots in R^3 with the standard contact structure. Classical invariants for Legendrin knots and their relation will be discussed. If time permits Chekanov's differential graded algebra will be introduced.

- Speaker
- Jinseok Cho (PMI)
- Title
- Volume conjecture of trivalent graph
- Abstract
- We introduce the colored Jones polynomials of knotted trivalent graphs and suggest generalized volume conjecture. The volume in this conjecture is of the hyperbolic manifold with parabolic meridians and we introduce a method to obtain the hyperbolic volume combinatorially. This work is joint with Roland van der Veen of Leiden University.

- Speaker
- Dongmin Gang (KAVLI-IPMU)
- Title
- 3-manifolds and 3 dimensional superconformal field theories
- Abstract
- In this talk, I will review so-called 3d-3d relation which relates some topological invariants of a 3-manifold to some physical quantities of a 3d superconformal field theory (SCFT) corresponding to the 3-manifold. After reviewing various aspects of the relation, I will give several examples of non-trivial mathematical predictions on 3-manifold invariants obtained from physical principal on 3d SCFTs.

- Speaker
- Gyo Taek Jin (KAIST)
- Title
- Examples and Counterexamples of the quadrisecant approximation conjecture
- Abstract
- We show smooth knots and polygonal knots, trivial and nontrivial, on which the quadrisecant approximation conjecture holds. We also show the counterexamples created by Bai-Wang-Wang, and discuss a possible modificaton of the conjecture.

- Speaker
- Hyoungjun Kim (Korea University)
- Title
- The restoring argument and some intrinsically knotted graphs.
- Abstract
- A graph is called intrinsically knotted if every embedding of the graph contains a non-trivially knotted cycle. Robertson and Seymour proved that there are only finitely many minor minimal intrinsically knotted graphs, but finding the complete set of them is still an open problem. Johnson, Kidwell and Michael showed that intrinsically knotted graphs have at least 21 edges. Lee, Kim, Lee, and Oh found the complete set of minor minimal intrinsically knotted graphs with 21 edges. It is also shown by Barsotti and Mattman, independently. Since $Y \nabla$ move preserve intrinsic knotting, every intrinsically knotted graph has at least one cousin that is triangle-free intrinsically knotted. This means that finding the set of triangle-free intrinsically knotted graphs is the first step for classifying the complete set of minor minimal intrinsically knotted graphs. The restoring argument is the constructing operation which helps us to determine the given graph is IK or not. By using operation, I will show that there are five triangle-free intrinsically knotted graphs with 22 edges and a single degree 5 vertex. This work is collaborated with Thomas Mattman and Seungsang Oh.

- Speaker
- Minhoon Kim (KIAS)
- Title
- An infinite-rank summand of knots with trivial Alexander polynomial
- Abstract
- We show that there exists an infinite-rank summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial. To this end we use the Upsilon invariant recently introduced by Ozsvath, Stipsicz and Szabo using knot Floer homology. We partially compute the upsilon of (n,1)-cable of the Whitehead double of the trefoil knot. For the computation, we determine a sufficient condition for two satellite knots to have identical upsilon for any pattern with nonzero winding number. This work is joint with Kyungbae Park.

- Speaker
- Roland van der Veen (Leiden University)
- Title
- Half way between Jones and Alexander
- Abstract
- We define a new knot invariant that is in some sense half way between the Jones polynomial and the Alexander polynomial. It is easy to compute like the Alexander polynomial yet retains some stronger 'quantum' properties of the Jones polynomial. Our framework for this discussion is the quantum double D of the two-dimensional non-commutative Lie algebra. First I will show how the Alexander polynomial arises from D and indicate how it naturally interpolates towards quantum sl_2 and hence the Jones polynomial. Time permitting we will also speculate on a four-dimensional interpretation. Joint work with Dror Bar-Natan

## Registration

Online registration is available here until August 12, 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