# Mini Workshop on Knot theory

August 19–20, 2016

POSTECH Math. Bldg. #404, Pohang, Korea

sponsered by

## 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 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