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Speaker ：Kumi Kobata (Osaka City University Advanced Mathematical Institute) Title ：A generalization of an enumeration on cyclic automorphism graphs for edge colored hypergraphs （Abstract） （PDF） Date ：February 3 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Chad Musick (Nagoya University) Title ：Recognizing Trivial Links in Polynomial Time （Abstract） （PDF） Date ：February 3 (Fri.) 15：00～16：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Kanako Oshiro (Japan Women's University) Title ：Minimal numbers of colors for surface-knots and quandle cocycle invariants （Abstract） （PDF） Date ：January 27 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Reiko Shinjo (Waseda University) Title ：On the collection of complementary faces associated to the diagrams of a link (partially joint work with Colin C. Adams and Kokoro Tanaka) （Abstract） （PDF） Date ：January 27 (Fri.) 15：00～16：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Roland van der Veen (University of California, Berkeley) Title ：The many faces of the colored Jones polynomial （Abstract） （PDF） Date ：December 16 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Inasa Nakamura (RIMS, Kyoto University) Title ：Unknotting numbers of torus-covering knots （Abstract） （PDF） Date ：December 16 (Fri.) 15：00～16：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Kazuto Takao (Osaka University) Title ：Heegaard splittings and singularities of product maps （Abstract） （PDF） Date ：December 9 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Naoyuki Monden (Osaka University) Title ：Sections of surface bundles and Lefschetz fibrations (joint work with R. Inanc Baykur and Mustafa Korkmaz) （Abstract） （PDF） Date ：November 25 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Masahide Iwakiri (Saga University) Title ：On $3$-component surface-links with braid index $4$ （Abstract） （PDF） Date ：November 18 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Takahiro Miura (Kobe University) Title ：On flat braidzel surfaces for links （Abstract） （PDF） Date ：November 11 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Yoshiro Yaguchi (Hiroshima University) Title ：Homological invariants of systems of simple braids （Abstract） （PDF） Date ：November 4 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Tetsuya Abe (RIMS, Kyoto University) Title ：Unoriented band-surgery on knots and links （Abstract） （PDF） Date ：October 28 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Tatsuya Tsukamoto (Osaka Institute of Technology) Title ：Simple ribbon fusions for links （Abstract） （PDF） Date ：October 21 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Yukari Funakoshi (Nara Women's University) Title ：On pseudo-fiber surfaces of level $n$ （Abstract） （PDF） Date ：October 7 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Takefumi Nosaka (RIMS, Kyoto University) Title ：Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere （Abstract） （PDF） Date ：July 15 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Sosuke Ashihara (Hiroshima University) Title ：Biquandle presentations of surface links from ch-diagrams （Abstract） （PDF） Date ：July 8 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Yoriko Kodani (Nara Women's University) Title ：A new bridge index for links with trivial knot components （Abstract） （PDF） Date ：July 8 (Fri.) 15：00～16：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Ryokichi Tanaka (Kyoto University) Title ：Penner-Andersen's Fatgraph Models of Proteins （Abstract） （PDF） Date ：July 1 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Taizo Kanenobu (Osaka City University) Title ：Band surgery on 2-component links （Abstract） （PDF） Date ：June 24 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Tsukasa Yashiro (Sultan Qaboos University) Title ：Cell-complexes for surface diagrams and Roseman moves （Abstract） （PDF） Date ：June 17 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Takanori Imabeppu (Hiroshima University) Title ：On normalized arrow polynomials of checkerboard colorable virtual links （Abstract） （PDF） Date ：June 10 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Takahito Kuriya (Osaka City University Advanced Mathematical Institute) Title ：Mosaic quantum knots and related topics （Abstract） （PDF） Date ：June 3 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Kenta Hayano (Osaka University) Title ：Classification of genus-1 simplified broken Lefschetz fibrations （Abstract） （PDF） Date ：May 20 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Yeonhee Jang (Hiroshima University) Title ：Bridge presentations of links and Heegaard splittings of 3-manifolds （Abstract） （PDF） Date ：May 13 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Ikuo Tayama (Osaka City University Advanced Mathematical Institute) Title ：Enumerating 3-manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10 （Abstract） （PDF） Date ：April 22 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Tetsuya Ito (The University of Tokyo) Title ：Links having non-left orderable 2-fold branched coverings （Abstract） （PDF） Date ：April 15 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top Speaker ：Ayaka Shimizu (Osaka City University Advanced Mathematical Institute) Title ：Region crossing change is an unknotting operation （Abstract） （PDF） Date ：April 8 (Fri.) 16：00～17：00 Place ：Dept. of Mathematics, Sci. Bldg., 3153 Top

Speaker：	Kumi Kobata (Osaka City University Advanced Mathematical Institute)
Title：	A generalization of an enumeration on cyclic automorphism graphs for edge colored hypergraphs

We plan to give a generalization of Ohno's theorem for hypergraphs which gives a formula for enumeration on cyclic automorphism graphs with given number of vertices. We consider the enumeration in case of edge colored hypergraphs. This is a joint work with Yasuo Ohno.

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Speaker：	Chad Musick (Nagoya University)
Title：	Recognizing Trivial Links in Polynomial Time

Trivial links are unique up to number of link components, but they can be hard to recognize from arbitrary diagrams. We define a measure, the crumple, on link diagrams and then demonstrate that for trivial links there is a sequence of moves by which the crumple may be strictly monotonically reduced. By our definition, the minimum possible crumple over all link diagrams is achieved only by embedding components disjointly in parallel planes, and so a link will be able to obtain this crumple if and only if it is trivial. The crumple is quadratic in the number of crossings, and we show that finding each reducing move takes only polynomial time and linear space. Therefore, we may decide whether a link is trivial in time polynomial on the number of crossings of a diagram of the link.
arXiv: 1110.2871v1 [math.GT]

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Speaker：	Kanako Oshiro (Japan Women's University)
Title：	Minimal numbers of colors for surface-knots and quandle cocycle invariants

We study the minimal number of colors used for non-trivial Fox colorings of surface-knots. A lower bound for the minimal number is given by using quandle cocycle invariants. In particular, we show that the minimal number of the $2$-twist spinning of the $5_2$ knot for Fox 7-colorings is six. This is a joint work with Shin Satoh (Kobe University).

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Speaker：	Reiko Shinjo (Waseda University)
Title：	On the collection of complementary faces associated to the diagrams of a link (partially joint work with Colin C. Adams and Kokoro Tanaka)

Given a diagram of a link, one can ignore which strand is the overstrand at each crossing and think of it as a planar $4$-valent graph embedded on the $2$-sphere. This graph divides the sphere into $n$-gons, which we call faces. In this talk, we investigate the possibilities for the collection of complementary $n$-gon faces associated to the diagrams of a link.

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Speaker：	Roland van der Veen (University of California, Berkeley)
Title：	The many faces of the colored Jones polynomial

In this talk we will discuss an elementary definition of the colored Jones polynomial for knots and show how it relates to many other aspects of knot theory. In particular we will give a survey of conjectures on the colored Jones polynomial including the volume conjecture and the AJ conjecture and report on recent progress.

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Speaker：	Inasa Nakamura (RIMS, Kyoto University)
Title：	Unknotting numbers of torus-covering knots

A torus-covering knot is an oriented surface knot which is in the form of a covering over the standard torus. The unknotting number of an oriented surface knot $F$ is the minimal number of disjoint 1-handles necessary to deform $F$ to an unknotted surface knot by 1-handle surgery. In this talk we study unknotting numbers of torus-covering knots. In particular, we give examples of torus-covering knots with the unknotting number exactly $n$.

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Speaker：	Kazuto Takao (Osaka University)
Title：	Heegaard splittings and singularities of product maps

We give an upper bound for the Reidemeister-Singer distance between two Heegaard splittings in terms of the genera plus a somewhat unexpected number. It is unfortunately ambiguous but suggests that a certain development in singularity theory may lead to the best possible bound for the Reidemeister-Singer distance.

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Speaker：	Naoyuki Monden (Osaka University)
Title：	Sections of surface bundles and Lefschetz fibrations (joint work with R. Inanc Baykur and Mustafa Korkmaz)

We will discuss the possible self-intersection numbers for sections of surface bundles & Lefschetz fibrations over surfaces, and the (un)boundedness of the number of critical points of a Lefschetz fibration with maximally self-intersecting sections, for fixed fiber and base genera. We will also calculate the stable commutator length of certain elements in the mapping class groups of surfaces with boundary.

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Speaker：	Masahide Iwakiri (Saga University)
Title：	On $3$-component surface-links with braid index $4$

Any surface-links with braid index at most $3$ are ribbon, and any $m$-component surface-links with braid index $m$ are trivial $2$-links. There are examples of non-ribbon $1$- or $2$-component $2$-links with braid index $4$. In this talk, we show that any $3$-component surface-links with braid index $4$ are ribbon.

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Speaker：	Takahiro Miura (Kobe University)
Title：	On flat braidzel surfaces for links

Rudolph introduced a notion of braidzel surfaces as a generalization of pretzel surfaces in his study on quasipositivity for pretzel surfaces, and Nakamura showed that any oriented link has a braidzel surface as a Seifert surface for the link. In this talk, we introduce the notion of flat braidzel surfaces as a special kind of braidzel surfaces, and show that any oriented link has a flat braidzel surface. Moreover, we also introduce the genus and the crossing number of bands with respect to flat braidzel surfaces, and study their properties.

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Speaker：	Yoshiro Yaguchi (Hiroshima University)
Title：	Homological invariants of systems of simple braids

Hurwitz equivalence on systems of simple braids is studied, which can be used in the study of surface braids and surface links. In this talk, we define a matrix for a system of simple braids by using the first homology classes of a punctured disk. As applications, we give some invariants of surface braids by using the matrices obtained from the systems of their braid monodromies.

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Speaker：	Tetsuya Abe (RIMS, Kyoto University)
Title：	Unoriented band-surgery on knots and links

A band-surgery is a local move on knots and links. It is well known that a band-surgery is an unknotting operation. In this talk, we survey some results on band-surgeries, and study how the orientability of a band-surgery relates to its unknotting sequences when we unknot a given knot by band-surgeries.
This is a joint work with Taizo Kanenobu.

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Speaker：	Tatsuya Tsukamoto (Osaka Institute of Technology)
Title：	Simple ribbon fusions for links

We define and study special kinds of fusions, called simple ribbon fusions, for a link and a trivial link. A simple ribbon move, which we have previously worked on, is a simple ribbon fusion. Main theorem gives a sufficient condition for a knot obtained from the trivial knot by a simple fusion to be non-trivial. As a corollary, we show that the Kinoshita-Terasaka knot is non-trivial. This is a joint work with K.Kishimoto and T.Shibuya.

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Speaker：	Yukari Funakoshi (Nara Women's University)
Title：	On pseudo-fiber surfaces of level $n$

The concept of pre-fiber surface in the 3-sphere $S^3$ was introduced by Kobayashi in [Ko]. In the paper, it is shown that any pre-fiber surface is transformed into a fiber surface by twisting is along arcs with certain properties. In this talk, we introduce pseudo-fiber surfaces of level $n$ for each non-negative integer $n$. (We note that a surface is a fiber surface if and only if it is a pseudo-fiber surface of level 0, and it is a pre-fiber surface if and only if it is a pseudo-fiber surface of level 1.) We show some fundamental properties of pseudo-fiber surfaces. Then we show that if an arc proper embedded in a pseudo-fiber surface of level $n$ satisfies certain properties, then the twist along the arc transforms it into a pseudo-fiber surface of level $n-1$. This gives a natural generalization of a result of Kobayashi's. Finally we propose an application of pseudo-fiber surface for giving an estimation of unknotting numbers of fibered knots.

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Speaker：	Takefumi Nosaka (RIMS, Kyoto University)
Title：	Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere

We introduce quandle cocycle invariants of 4-dimensional Lefschetz fibrations over the 2-sphere, using quandle cocycles of Dehn quandles with non-abelian coefficients. In this talk, we first review a topological interpretation of quandle 2-cocycle invariants for links in $S3$ shown by M. Eisermann. We next present a 2-cocycle so that the associated invariant is equivalent to the signature of 4-dimensional manifolds.

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Speaker：	Sosuke Ashihara (Hiroshima University)
Title：	Biquandle presentations of surface links from ch-diagrams

A biquandle is a set with four binary operations which satisfy some axioms corresponding to Reidemeister moves. A surface link is a closed oriented surface embedded in four-space. It is known that a biquandle gives an invariant for a surface link and any surface link is presented by a link diagram with some markers which is called a ch-diagram. The speaker gives a method that we directly calculate the biquandle of a surface link from a ch-diagram presenting the surface.

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Speaker：	Yoriko Kodani (Nara Women's University)
Title：	A new bridge index for links with trivial knot components

In 1954, H. Schubert introduced the concept of bridge indices for knots. For satellite knots, he gave an estimation of bridge indices by using index of the pattern and the bridge index of the companion of the satellite knot under consideration. In 2003, J.Schultens gave a modern proof of the result by using foliation.

In this talk, we consider bridge indices of links. We introduce a new bridge index for non-split 2-component links such that one component of each link is a trivial knot. Roughly speaking, the bridge index is the minimum of the bridge numbers of a link under the constraint that one component of the link is in a minimal bridge position. We give an estimation of the bridge index for satellite links by using the technique of Schultens'. We show, by using the estimation, the new bridge index is essentially different from the standard one.

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Speaker：	Ryokichi Tanaka (Kyoto University)
Title：	Penner-Andersen's Fatgraph Models of Proteins

In 2009, R.C.Penner and J.E.Andersen proposed to classify conformations of proteins by using topological invariants. They introduced the Fatgraph for modeling proteins and constructed an algorithm to calculate those invariants. Their methods are suitable for computation and existing database implies that their invariants could be useful for structural classification of proteins. I would like to introduce their methods and also propose some questions.

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Speaker：	Taizo Kanenobu (Osaka City University)
Title：	Band surgery on 2-component links

An oriented 2-component link is called band-trivializable, if it can be unknotted by a single band surgery. We consider whether a given 2-component link is band-trivializable or not. Then we can completely determine the band-trivializability for the prime links with up to 9 crossings. We use the signature, the Jones and Q polynomials, and the Arf invariant. Since a band-trivializable link has 4-ball genus zero, we also give a table for the 4-ball genus of the prime links with up to 9 crossings. Furthermore, we give an additional answer to the problem of whether a $(2n+1)$-crossing 2-bridge knot is related to a $(2,2n)$ torus link or not by a band surgery for $n=3$, $4$, which was brought from the study of a DNA site-specific recombination.

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Speaker：	Tsukasa Yashiro (Sultan Qaboos University)
Title：	Cell-complexes for surface diagrams and Roseman moves

A surface-knot is a connected oriented closed surface embedded in 4-space. If we project a surface-knot in 3-space, then we obtain a surface diagram that may have double points or triple points or branch points. The preimage of the set of multiple points is the union of two families of connected components called the upper and lower double decker set. The lower decker set induces a cell-complex for the surface diagram. There is a set of local deformations of the cell-complex induced from Roseman moves. In this talk we discuss about a relation between these local moves and cell-complexes.

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Speaker：	Takanori Imabeppu (Hiroshima University)
Title：	On normalized arrow polynomials of checkerboard colorable virtual links

It is known that every classical knot diagram is checkerboard colorable, but every virtual knot diagram is not checkerboard colorable. Normalized arrow polynomials introduced by Kauffman are a generalization of Jones polynomials. We show that some virtual links are not checkerboard colorable by using a certain property of normalized arrow polynomials.

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Speaker：	Takahito Kuriya (Osaka City University Advanced Mathematical Institute)
Title：	Mosaic quantum knots and related topics

In a recent work of Samuel J. Lomonaco Jr and Louis H. Kauffman, they consider the concept of mosaic quantum knots in the context of quantum graphs. We review mosaic knot theory and introduce related topics and our recent results.

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Speaker：	Kenta Hayano (Osaka University)
Title：	Classification of genus-1 simplified broken Lefschetz fibrations

Broken Lefschetz fibrations were introduced as a generalization of Lefschetz fibrations to near-symplectic setting. In this talk, we first construct a family of genus-1 simplified broken Lefschetz fibrations. We then show that all genus-1 simplified broken Lefschetz fibrations with small number of Lefschetz singularities are contained in the family we construct.

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Speaker：	Yeonhee Jang (Hiroshima University)
Title：	Bridge presentations of links and Heegaard splittings of 3-manifolds

It is known that bridge presentations of links in the 3-sphere are deeply related with Heegaard splittings of 3-manifolds. The speaker has used this relation and studied Heegaard splittings of certain 3-manifolds to obtain several results on bridge presentations of links. In this talk, we give a brief survey on the results and show you how to use the relation.

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Speaker：	Ikuo Tayama (Osaka City University Advanced Mathematical Institute)
Title：	Enumerating 3-manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10

This is a joint work with A. Kawauchi. A well-order was introduced on the set of links by A. Kawauchi. This well-order also naturally induces a well-order on the set of prime link exteriors and eventually induces a well-order on the set of closed connected orientable $3$-manifolds. With respect to this order, we enumerated the prime links and the prime link exteriors with lengths up to 10. In this talk, we show a list of the enumeration of $3-$manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10 by using the enumeration of the prime link exteriors.

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Speaker：	Tetsuya Ito (The University of Tokyo)
Title：	Links having non-left orderable 2-fold branched coverings

The (left) orderability of 3-manifold groups is closely related to the existence of certain foliations or laminations. Recently, it is observed that the left-orderbility is also related to Heegaard Floer homologies. Thus it is interesting to construct examples of 3-manifolds having non-left orderable fundamental group. In this talk I will give a family of links whose 2-fold branched covering has non-left orderable fundamental group.

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Speaker：	Ayaka Shimizu (Osaka City University Advanced Mathematical Institute)
Title：	Region crossing change is an unknotting operation

K. Kishimoto proposed a new local transformation on a knot or link diagram called a region crossing change. In this talk, we show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot.

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