組織委員 森内 博正
| 日時 | 2012年2月3日（金）16：00～17：00 |
| 講演者（所属） | 小畑 久美（OCAMI） |
| タイトル | A generalization of an enumeration on cyclic automorphism graphs for edge colored hypergraphs |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2012年2月3日（金）15：00～16：00 |
| 講演者（所属） | Chad Musick（名古屋大学） |
| タイトル | Recognizing Trivial Links in Polynomial Time |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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] |
| 日時 | 2012年1月27日（金）16：00～17：00 |
| 講演者（所属） | 大城 佳奈子（日本女子大学） |
| タイトル | Minimal numbers of colors for surface-knots and quandle cocycle invariants |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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). |
| 日時 | 2012年1月27日（金）15：00～16：00 |
| 講演者（所属） | 新庄 玲子（早稲田大学） |
| タイトル | On the collection of complementary faces associated to the diagrams of
a link (partially joint work with Colin C. Adams and Kokoro Tanaka) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年12月16日（金）16：00～17：00 |
| 講演者（所属） | Roland van der Veen（University of California, Berkeley） |
| タイトル | The many faces of the colored Jones polynomial |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年12月16日（金）15：00～16：00 |
| 講演者（所属） | 中村 伊南沙（京都大学数理解析研究所） |
| タイトル | Unknotting numbers of torus-covering knots |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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 $n$. |
| 日時 | 2011年12月9日（金）16：00～17：00 |
| 講演者（所属） | 高尾 和人（大阪大学） |
| タイトル | Heegaard splittings and singularities of product maps |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年11月25日（金）16：00～17：00 |
| 講演者（所属） | 門田 直之（大阪大学） |
| タイトル | Surface bracket polynomials of twisted links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年11月18日（金）16：00～17：00 |
| 講演者（所属） | 岩切 雅英（佐賀大学） |
| タイトル | On $3$-component surface-links with braid index $4$ |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年11月11日（金）16：00～17：00 |
| 講演者（所属） | 三浦 嵩広（神戸大学） |
| タイトル | On flat braidzel surfaces for links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年11月4日（金）16：00～17：00 |
| 講演者（所属） | 矢口 義朗（広島大学） |
| タイトル | Homological invariants of systems of simple braids |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年10月28日（金）16：00～17：00 |
| 講演者（所属） | 安部 哲哉（京都大学数理解析研究所(RIMS)） |
| タイトル | Unoriented band-surgery on knots and links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年10月21日（金）16：00～17：00 |
| 講演者（所属） | 塚本 達也（大阪工業大学） |
| タイトル | Simple ribbon fusions for links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年10月7日（金）16：00～17：00 |
| 講演者（所属） | 船越 紫（奈良女子大学） |
| タイトル | On pseudo-fiber surfaces of level $n$ |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年7月15日（金）16：00～17：00 |
| 講演者（所属） | 野坂 武史（京都大学数理解析研究所(RIMS)） |
| タイトル | Quandle cocycle invariants of Lefschetz fibrations over the 2-sphere |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年7月8日（金）16：00～17：00 |
| 講演者（所属） | 芦原 聡介（広島大学） |
| タイトル | Biquandle presentations of surface links from ch-diagrams |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年7月8日（金）15：00～16：00 |
| 講演者（所属） | 小谷 賀子（奈良女子大学） |
| タイトル | A new bridge index for links with trivial knot components |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年7月1日（金）16：00～17：00 |
| 講演者（所属） | 田中 亮吉（京都大学） |
| タイトル | Penner-Andersen's Fatgraph Models of Proteins |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年6月24日（金）16：00～17：00 |
| 講演者（所属） | 金信 泰造（大阪市立大学） |
| タイトル | Band surgery on 2-component links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年6月17日（金）16：00～17：00 |
| 講演者（所属） | 屋代 司（Sultan Qaboos University） |
| タイトル | Cell-complexes for surface diagrams and Roseman moves |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年6月10日（金）16：00～17：00 |
| 講演者（所属） | 今別府 孝規（広島大学） |
| タイトル | On normalized arrow polynomials of checkerboard colorable virtual links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年6月3日（金）16：00～17：00 |
| 講演者（所属） | 栗屋 隆仁（OCAMI） |
| タイトル | Mosaic quantum knots and related topics |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年5月20日（金）16：00～17：00 |
| 講演者（所属） | 早野 健太（大阪大学） |
| タイトル | Classification of genus-1 simplified broken Lefschetz |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年5月13日（金）16：00～17：00 |
| 講演者（所属） | 張 娟姫（広島大学） |
| タイトル | Bridge presentations of links and Heegaard splittings of 3-manifolds |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年4月22日（金）16：00～17：00 |
| 講演者（所属） | 田山 育男（OCAMI） |
| タイトル | Enumerating 3-manifolds with the first homology groups isomorphic to (Z/nZ)+(Z/nZ) with lengths up to 10 |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年4月15日（金）16：00～17：00 |
| 講演者（所属） | 伊藤 哲也（東京大学） |
| タイトル | Links having non-left orderable 2-fold branched coverings |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
| 日時 | 2011年4月8日（金）16：00～17：00 |
| 講演者（所属） | 清水 理佳（OCAMI） |
| タイトル | Region crossing change is an unknotting operation |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | 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. |
