### Schedule

#### 2015-09-21

TimeSpeaker/ Title/ Abstract/ VODLocation
08:00 - 09:00 Registration & Opening(08:55)
1F, Main Conference Room (대회의실)
09:00 - 09:50 A chord diagram for a ribbon surface-link and faithful equivalence
Akio Kawauchi (Osaka City University),
In this talk, an essential part of the speaker’s recent paper, A chord diagram of a ribbon surface-link (preprint) is explained. A ribbon chord diagram, or simply a chord diagram, of a ribbon surface-link in the 4-space is introduced. Links, virtual links and welded virtual links can be described naturally by chord diagrams with the corresponding moves, respectively. Some moves on chord diagrams are introduces by overseeing these special moves. Then the faithful equivalence on ribbon surface-links is stated in terms of the moves on chord diagrams. This answers questions by Y. Nakanishi and Y. Marumoto affirmatively. The faithful TOP-equivalence on ribbon surface-links derives the same result. By combining a previous result on TOP-triviality of a surface-knot, a ribbon surface-knot is DIFF-trivial if and only if the fundamental group is an infinite cyclic group. This corrects T. Yanagawa’s erroneous proof published from Osaka J. Math. in 45 years ago.
1F, Main Conference Room (대회의실)
10:00 - 10:50 Graph-links: introduction, polynomial invariants and realization
Denis P. Ilyutko (M.V. Lomonosov Moscow State University),
In 2009 we introduced the notion of graph-link. A graph-link is, in some sense, a combinatoric generalization of a link: instead of chord diagrams and moves on them (virtual knots) we consider graphs and moves on them, obtained from moves on intersection graphs of chord diagrams. In this talk we give main definitions and constructions, also we present the first invariants of graph-links.
1F, Main Conference Room (대회의실)
11:10 - 12:00 Shadow coloring and ideal triangulation
Ayumu Inoue (Aichi University of Education),
A quandle is an algebraic system whose axioms closely relate to the Reidemeister moves. A shadow coloring of a knot diagram is a map from the arcs and the regions of the diagram to a quandle satisfying some conditions. The aim of this talk is to explain that a shadow coloring of a knot diagram gives a (topological) ideal triangulation of the knot complement. As an application of this framework, we see that we can compute the hyperbolic volume of a knot by a certain shadow coloring of its diagram. The contents of this talk are based on the work joint with Yuichi Kabaya.
1F, Main Conference Room (대회의실)
12:00 - 13:30 Lunch
Jeju National University International Center (Ara Campus, Bldg. 702)
13:30 - 14:10 On shadow biquandle cocycle invariants
Jieon Kim (Pusan National University),
L. H. Kauffman and D. E. Radford introduced a generalization of quandles, called biquandles. In 2003, J. S. Carter, M. Elhamdadi and M. Saito defined a (co)homology theory and cocycle invariants for biquandles. Shadow quandle colored diagram and shadow quandle cocycle invariants of oriented links and surface-links were introduced by J. S. Carter, S. Kamada and M. Saito. In this talk, we’d like to introduce shadow biquandle colored diagrams and shadow biquandle cocycle invariants of oriented links and surface- links. This is a joint work with Sang Youl Lee.
1F, Main Conference Room (대회의실)
14:20 - 15:00 Integer valued concordance invariants of general pretzel knots
Mijeong Yeon (Kyung Hee University),
We compute integer valued knot concordance invariants of a family of general pretzel knots if the invariants are equal to the negative values of signatures for alternating knots. Examples of such invariants are Rasmussen s–invariants and twice Ozsv ́ath–Szab ́o knot Floer homology τ–invariants. We use the crossing change inequalities of Livingston and the fact that pretzel knots are almost alternating. As a consequence, for the family of pretzel knots given in this paper, s–invariants are twice τ–invariants at the end. In contrast, we also find an infinite family of 4-strand pretzel knots whose Rasmussen invariants are not equal to the negative values of signature invariants. In order to prove this, we use the long exact sequence of Khovanov homologies arisen from a link skein relation.
1F, Main Conference Room (대회의실)
15:20 - 16:00 Polynomials and Reidemeister moves of virtual knot diagrams
Myeong-Ju Jeong (KSA of KAIST),
We associate two polynomials to each virtual knot diagram. We define even coloring and odd coloring of a virtual knot diagram and then an even degree and an odd degree of a crossing of a virtual knot diagram will be introduced. To show that two virtual knot diagrams represent the same knot, basically we find a sequence of Reidemeister moves and virtual Reidemeister moves which transform a diagram to the other. By using the two polynomials we may get a strategy to show that two given virtual knot diagrams are equivalent.
1F, Main Conference Room (대회의실)
16:10 - 17:00 A polynomial invariant for virtual surface-links in four space
Sang Youl Lee (Pusan National University),
A marked graph diagram is a link diagram possibly with 4-valent vertices equipped with extra information indicated by a marker. A virtual marked graph diagram is a marked graph diagram possibly with virtual crossings indicated by small circles as usual in virtual link diagrams. Recently, L. H. Kauffman formulated a theory of isotopy of virtual surface- links in four space by means of virtual marked graph diagrams modulo a generalization of Yoshikawa moves on marked graph diagrams. In this talk, I would like to take a glance at this theory of isotopy of virtual surface-links, and introduce a polynomial invariant for virtual surface-links in four space.
1F, Main Conference Room (대회의실)
17:00 - 17:40 On the n-th writhe of periodic virtual knots
Myoungsoo Seo (Kyungpook National University),
In 2014, Satoh and Taniguchi defined the n-th writhe of a virtual knot for each non-zero integer n and proved that the n-th writhe is a generalization of the index polynomial and the odd writhe polynomial. In this talk, we will review the n-th writhe of a virtual knot for each non-zero integer n and discuss some properties of the n-th writhe of periodic virtual knots.
1F, Main Conference Room (대회의실)
18:30 - 20:30 Welcome Dinner
TBA

#### 2015-09-22

TimeSpeaker/ Title/ Abstract/ VODLocation
08:00 - 09:00 Registration
1F, Seminar Room 3 (세미나실 3)
09:00 - 09:50 Differential geometry of foliations
Seoung Dal Jung (Jeju National University),
In this talk, I will give the basic concepts in the theory of foliations including many examples. Moreover, I review the transversal geometry on foliations and compare to the Riemannian manifolds. Finally, I will present my recent works about the transversal ge- ometry.
1F, Seminar Room 3 (세미나실 3)
10:00 - 10:50 Picture valued invariants of graph-links and classification (the joint work with V.O.Manturov)
Denis P. Ilyutko (M.V. Lomonosov Moscow State University),
V.O.Manturov constructed an invariant of free links by using construction of Kuper- berg’s sl(3)-invariants. This invariant is valued in linear combinations of “pictures” and allows one to nearly classify free links. In our talk we are generalizing this construction for graph-links. It means that by using only adjacent matrices of graphs we can construct invariants valued in linear combinations of “pictures”. Moreover, we obtain some minimal results and results concerning classification of free graph-links.
1F, Seminar Room 3 (세미나실 3)
11:10 - 12:00 Virtual knot diagrams and double covers of twisted knot diagrams
Naoko Kamada (Nagoya City University),
Twisted link diagrams are virtual link diagrams possibly with some bars on their arcs. With a twisted link diagram, we associate a virtual link diagram which we call a double cover. We show an application. Then we introduce a method of converting a virtual link diagram to a normal virtual link diagram.
1F, Seminar Room 3 (세미나실 3)
12:00 - 13:30 Lunch
Jeju National University International Center (Ara Campus, Bldg. 702)
13:30 - 14:10 On Gauss diagrams of 2-component symmetric links
Insook Lee (Kyungpook National University ),
A symmetric link is a link with a diagram on which a finite group can act. In this talk, we study the Gauss diagrams for 2-component symmetric links. Also we will find the relationship between a link admitting Z4-action and a link admitting Z2 ⊕ Z2-action for some restriction. It is joint work with Yongju Bae.
1F, Seminar Room 3 (세미나실 3)
14:20 - 15:00 Stick presentation of embedded graphs
Sungjong No (Ewha Womans University),
The arc index is a very useful invariant for knot. By using the arc presentation of graphs, we get an upper bound of arc index and stick number of an embedded graph. The arc index α(G) is less than or equal to c(G) + e(G) for the crossing number c(G) and the number of edges e(G) of the embedded graph G. And the stick number s(G) ≤3 c(G) + 2e(G) − v(G) . 22
1F, Seminar Room 3 (세미나실 3)
15:20 - 16:00 Intrinsic knotting of bipartite graphs with at most 22 edges
Hyoungjun Kim (Korea University),
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K7 and the 13 graphs obtained from K7 by ∇Y moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set includes exactly one bipartite graph, the Heawood graph. In this talk we classify the intrinsically knotted bipartite graphs with at most 22 edges.
1F, Seminar Room 3 (세미나실 3)
16:10 - 16:35 Algebraic structure on the set of finite quandles I
Byeorhi Kim (Kyungpook National University),
Let $Q$ be a finite set and let $*_{1}, *_{2}, \cdots, *_{m}$ be finite quandle operations on $Q$. One can define the operation $*_{i}*_{j} : Q\times Q \rightarrow Q$ by $x$ $*_{i}*_{j}$ $y=(x*_{i}y)*_{j}y$ for every $x, y \in Q$. In this talk, we will study whether $*_{i}*_{j}$ is a quandle operation on $Q$ or not by illustrating examples.
1F, Seminar Room 3 (세미나실 3)
16:35 - 17:00 Algebraic structure on the set of finite quandles II
Seonmi Choi (Kyungpook National University),
Let $Q$ be a finite set and let $\{*_{1}, *_{2}, \cdots, *_{m}\}$ be the set of all quandle operations of $Q$. The product $*_{i}*_{j}$ of two quandle operations $*_{i}$ and $*_{j}$ can be defined by $x$ $*_{i}*_{j}$ $y=(x*_{i}y)*_{j}y$ for every $x, y \in Q$. In this talk, we will study an algebraic structure on the set $\{*_{1}, *_{2}, \cdots, *_{m}\}$ of quandle operations.
1F, Seminar Room 3 (세미나실 3)
17:00 - 17:40 Geometric model for quandle homology
Yongju Bae (Kyungpook National University),
The homology group of a quandle is a very important tool to get quandle cocycle invariants. The calculation of quandle homology or quandle co-homology is very difficult in general. In this talk, we will correspond a geometric object to a quandle whose homology coincide the quandle homology group of the quandle.
1F, Seminar Room 3 (세미나실 3)

#### 2015-09-23

TimeSpeaker/ Title/ Abstract/ VODLocation
08:00 - 09:00 Registration
1F, Seminar Room 3 (세미나실 3)
09:00 - 09:50 On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links
Kanako Oshiro (Sophia University),
We show a calculation result of the twisted Alexander ideals for spatial graphs, handlebody- knots, and surface-links. Especially for spatial graphs, we calculate the invariants of Suzuki’s theta-curves and show that the invariants are nontrivial for Suzuki’s theta-curves whose Alexander ideals are trivial. This is a joint work with Atsushi Ishii (University of Tsukuba) and Ryo Nikkuni (Tokyo Woman’s Christian University).
1F, Seminar Room 3 (세미나실 3)
10:00 - 10:50 Braid representations and knot invariants
Zhiqing Yang (Dalian University of Technology),
Braids, braid representations and knot invariants are closely related. However, there are not many braid representations. The author invents a new systematic way to construct families of braid representations and their corresponding knot invariants. Furthermore, ev- idence shows that there are knot invariants with nonlinear skein relations. References [1] Boju Jiang, On Conway’s potential function for colored links, Acta Mathematica Sinica, English Series. [2] Jun Murakami, A state model for the multi-variable Alexander polynomial, Pacific J. Math., Vol. 157 no. 1, 109-135 , 1993. [3] V. F. R. Jones, Hecke Algebra Representations of Braid Groups and Link Polyno- mials, Annals of Mathematics, Second Series, Vol. 126 no. 2, 335-388 , 1987.
1F, Seminar Room 3 (세미나실 3)
10:50 - 11:10 Tea Break
11:10 - 12:00 On Alexander and Markov theorems for spatial graphs and surface-links
Seiichi Kamada (Osaka City University),
Alexander and Markov theorems state that every knot and link in 3-space is presented by a braid, and such a braid presentation is uniqu up to equivalence generated by braid equivalence, conjugations and stabilizations. We discuss about its generalization to spatial graphs in 3-space and to surface-links in 4-space. This former part is a joint work with Victoria Lebed.
1F, Seminar Room 3 (세미나실 3)
12:00 - 13:00 Lunch
13:00 - 17:00 Excursion