組織委員 森内 博正
| 日時 | 2013年2月1日（金）16：00～17：00 |
| 講演者（所属） | 門田 直之（京都大学） |
| タイトル | On stable commutator length of a Dehn twist |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Let $[G,G]$ be the commutator subgroup of a group $G$. For $x\in [G,G]$, we will denote by ${\rm cl}(x)$ the smallest number of commutators in G whose product is equal to $x$. We call ${\rm cl}(x)$ the commutator length of $x$. The stable commutator length of $x$, denoted by ${\rm scl}(x)$, is the limit $${\rm scl}(x)=\lim_{n\rightarrow \infty}\frac{{\rm cl}(x^n)}{n}.$$ In generally, computing (stable) commutator length is difficult. In this talk, we will present some background results of stable commutator length in mapping class groups. And we will give an upper bound of the stable commutator length of a Dehn twist. This is joint work with Danny Calegari and Masatoshi Sato. |
| 日時 | 2013年2月1日（金）15：00～16：00 |
| 講演者（所属） | 小畑 久美（OCAMI） |
| タイトル | On enumeration of edge colored graphs (joint work withYasuo Ohno (Kinki University)) |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | We previously gave a generalization of Ohno's theorem which gives a formula for enumeration of cyclic automorphism graphs. We analogously consider the enumeration of edge colored graphs under transposition. |
| 日時 | 2013年1月25日（金）16：00～17：00 |
| 講演者（所属） | 張 娟姫（奈良女子大学） |
| タイトル | Heegaard splittings of distance $n$ |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Hempel introduced the concept of distance of Heegaard splitting by using
curve complex, and showed that there exist Heegaard splittings of closed
orientable 3-manifolds with distance $>n$ for any integer $n$. In this
talk, we construct pairs of curves with distance exactly $n$ for any non-negative
integer $n$, and use them to show that there exist Heegaard splittings
of 3-manifolds with distance exactly $n$. (This is a joint work with Ayako Ido and Tsuyoshi Kobayashi.) |
| 日時 | 2012年12月14日（金）16：00～17：00 |
| 講演者（所属） | 清水 理佳（広島大学） |
| タイトル | The reducivity of spherical curves |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by three or less inverse-half-twisted splices, i.e., the reducivity, which represents how reduced a spherical curve is, is three or less. We also discuss some unavoidable sets of tangles for spherical curves. |
| 日時 | 2012年12月7日（金）16：00～17：00 |
| 講演者（所属） | Cheng Zhiyun（Beijing Normal University） |
| タイトル | A polynomial invariant of virtual knots and links |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Virtual knot theory was introduced by Professor Louis Kauffman in 1990s.
One simple invariant of virtual knots, the odd writhe was defined by Kauffman
himself in 2004. I will discuss the generalization of this invariant with
two viewpoints: one comes from V. O. Manturov's parity axioms, the other
approach was inspired by Professor Akio Kawauchi and Ayaka Shimizu's warping polynomial. If time permits, I will also give a similar generalization of the linking number of 2-component links. |
| 日時 | 2012年11月30日（金）16：10～17：10 |
| 講演者（所属） | Sang Youl Lee（Pusan National University） |
| タイトル | Studying knots and links via net diagrams |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | A net diagram is a knot or link diagram obtained from a quasitoric braid
diagram by replacing each positive (respectively, negative) crossing with
positive (respectively, negative) half-twists. Due to some recent works,
net diagrams for knots and links turned out to have various ramifications
and applications to study invariants for knots and links, including the
Casson invariant, genus, delta unknotting number, Alexander polynomial,
Jones polynomial and so on. In this talk, we will discuss some recent contributions
towards MFW inequality and the Jones conjecture on a minimal braid representation,
the Tripp conjecture on the canonical genus for Whitehead doubles of alternating
knots and the Hoste's conjecture on the Alexander polynomial of alternating
knots via net diagrams. This is partly a joint work with H. J. Jang and M. Seo. |
| 日時 | 2012年11月30日（金）15：30～16：00 |
| 講演者（所属） | Jieon Kim（Pusan National University） |
| タイトル | The Alexander biquandles for oriented surface links diagrams of types A and D |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | A biquandle is an algebraic structure consisting of a set with four binary operations satisfying axioms derived from the oriented Reidemeister moves, where generators of the algebra are identified with semi-arcs in an oriented link diagram. This relationship between the biquandle axioms and the Reidemeister moves makes biquandles a natural source of (virtual) knot and link invariants. The Alexander biquandle is an example of a biquandle that gives rise to the generalized Alexander polynomial for oriented virtual knots and links. In this talk, we will discuss a construction of the Alexander biquandle for oriented surface links via marked graph diagrams. We will show that the elementary ideals for a presentation matrix for the biquandle are invariants for the oriented surface link. To do this we first give a minimal generating set of Yoshikawa's moves and then investigate the behavior of presentation matrices under Yoshikawa's moves. We also compute the invariants for oriented surface links represented by marked graph diagrams with triangle-type and square-type ch-graphs. This is a joint work with Y. Joung and S. Y. Lee. |
| 日時 | 2012年11月30日（金）15：00～15：30 |
| 講演者（所属） | Yewon Joung（Pusan National University） |
| タイトル | Obstructions for Yoshikawa's moves on marked graph diagrams for surface links |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | A surface link is a closed, possibly orientable or nonorientable, surface
F smoothly embedded in the oriented 4-space R^4 or S^4. If F is a connected
surface, then it is called a surface knot. If F is oriented, then we call
it an oriented surface link. A surface link can be represented by a marked
graph diagram, that is, a knotted regular 4-valence rigid vertex graph
diagram in which each 4-valence vertex has a marker. Two marked graph diagrams
represent the same surface link if and only if they are transformed into
each other by a finite sequence of Yoshikawa's moves. In this talk, we
will discuss some obstructions for Yoshikawa's moves derived from a polynomial
defined by a state model analogous to the Kauffman's state model for the
Jones polynomial of classical knots and links, and calculated by using
a skein relation based on marked graph diagrams. We also discuss some applications
of these obstructions. This is a joint work with J. Kim and S. Y. Lee. |
| 日時 | 2012年11月9日（金）16：00～17：00 |
| 講演者（所属） | 早野 健太（大阪大学） |
| タイトル | Vanishing cycles and homotopies of wrinkled fibrations |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Wrinkled fibrations are fibration structures on four-manifolds, which have been studied recently for the purpose of understanding some invariants of four-manifolds. In this talk, we will explain how vanishing cycles of wrinkled fibrations are changed by several homotopies. As an application, we also give new examples of surface diagrams of four-manifolds, which are combinatorial descriptions of four-manifolds introduced by Williams. Part of the results in this talk is joint-work with Stefan Behrens (The Max Plank Institute for Mathematics). |
| 日時 | 2012年11月2日（金）16：00～17：00 |
| 講演者（所属） | 岡崎 建太（京都大学数理解析研究所(RIMS)） |
| タイトル | On the state-sum invariants of 3-manifolds constructed from the E_6 and E_8 linear skeins |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | The state-sum invariants of 3-manifolds, introduced by Turaev and Viro and generalized by Ocneanu, are formulated as a state-sum on triangulations of 3-manifolds derived from certain 6j-symbols. In this talk, we give elementary and self-contained constructions of the state-sum invariants of 3-manifolds derived from 6j-symbols of the E_6 and E_8 subfactors. We give such constructions by introducing E_6 and E_8 linear skeins, motivated by the E_6 and E_8 planar algebras. |
| 日時 | 2012年11月2日（金）15：00～16：00 |
| 講演者（所属） | 森 淳秀（OCAMI） |
| タイトル | Essential dichotomy in contact topology |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | A contact structure is a completely non-integrable hyperplane field usually
defined by a global Pfaff equation. However, in saying so, I suspect that
1) three dimensional contact topology is just a three dimensional topology for an imaginary person who does not know a mirror, and 2) higher dimensional contact topology is just an analogue of three dimensional contact topology. Indeed a contact structure fixes the orientation of the manifold even locally, while it has no moduli even globally. (A person who knows a mirror must wonder about the fact that two closed braids present the same contact knot iff they are related by only right-handed stabilizations/destabilizations.) Though a 3-manifold admits infinitely many contact structures, most of them (i.e., overtwisted ones) are spoiled and uniquely determined by homotopy data of plane fields. Contrastingly, the topology of the other decent structures (i.e., tight ones) adds a few extra data to the topology of the 3-manifold itself. I will talk about this dichotomy (overtwisted vs. tight) and its tentative generalizations. |
| 日時 | 2012年10月26日（金）16：00～17：00 |
| 講演者（所属） | 岡崎 真也（OCAMI） |
| タイトル | Bridge genus and braid genus of lens space |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | The bridge genus and the braid genus are invariants of an oriented closed connected $3$-manifold which are introduced by Kawauchi. In this talk, we calculate the bridge genus and braid genus for some lens spaces $L(p,q)$, and we give an upper bound of $L(p,q)$ such that $p$ is an even number. |
| 日時 | 2012年10月19日（金）16：00～17：00 |
| 講演者（所属） | 石井 敦（筑波大学） |
| タイトル | On some properties of handlebody-knots |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | A handlebody-knot is a handlebody embedded in the 3-sphere, and a handlebody-link is a disjoint union of handlebodies embedded in the 3-sphere. Two handlebody-links are equivalent if one can be transformed into the other by an isotopy of the 3-sphere. I will explain the basics of handlebody-knots, which include fundamental moves on diagrams. Then I will talk about some properties of handlebody-knots. This talk consists of short topics. |
| 日時 | 2012年10月19日（金）15：00～16：00 |
| 講演者（所属） | Javier Arsuaga（San Francisco State University） |
| タイトル | Using knot theory to model the formation of minicircle networks on trypanosomatida |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Trypanosomatida parasites, such as trypanosoma and lishmania, are the cause of deadly diseases in many third world countries. A distinctive feature of these organisms is the three dimensional organization of their mitochondrial DNA into maxi and minicircles. In some of these organisms minicircles are confined into a small disk shaped volume and are topologically linked, forming a gigantic linked network. The origins of such a network as well as of its topological properties are mostly unknown. In this paper we quantify the effects of the confinement on the topology of such a minicircle network. We introduce a simple mathematical model in which a collection of randomly oriented minicircles are spread over a rectangular grid. We present analytical and computational results showing that a positive critical percolation density exists, that the probability of formation of a highly linked network increases exponentially fast when minicircles are confined, and that the mean minicircle valence (the number of minicircles that a particular minicircle is linked to) increases linearly with density. When these results are interpreted in the context of the mitochondrial DNA of the trypanosome they suggest that confinement plays a key role on the formation of the linked network. This hypothesis is supported by the agreement of our simulations with experimental results that show that the valence grows linearly with density. Our model predicts the existence of a percolation density and that the distribution of minicircle valences is more heterogeneous than initially thought. |
| 日時 | 2012年10月5日（金）16：00～17：00 |
| 講演者（所属） | 門上 晃久（East China Normal University） |
| タイトル | Switching scheme and switching complex |
| 場所 | 共通研究棟4階401室（数学 第3セミナー室） |
| アブストラクト | Motivated by a notion, region crossing change, which is defined by A. Shimizu, we define generalized notions, switching scheme and switching complex. |
| 日時 | 2012年7月20日（金）16：00～17：00 |
| 講演者（所属） | Michael Yoshizawa（University of California, Santa Barbara） |
| タイトル | Generating Examples of High Distance Heegaard Splittings |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Given a closed orientable 3-manifold M, a surface S in M is a Heegaard surface if it separates the manifold into two handlebodies of equal genus. This decomposition is called a Heegaard splitting of M. The Hempel distance of this splitting is the length of the shortest path in the curve complex of S between the disk complexes of the two handlebodies. In 2004, Evans developed an iterative process to construct a manifold that admits a Heegaard splitting with arbitrarily high distance. We first provide an introduction to Heegaard splittings and Hempel distance and then improve on Evans' results. |
| 日時 | 2012年7月13日（金）16：00～17：00 |
| 講演者（所属） | Greg McShane（Universite Joseph Fourier） |
| タイトル | Orthospectra and identities |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | The orthospectra of a hyperbolic manifold with geodesic boundary consists of the lengths of all geodesics perpendicular to the boundary. We discuss the properties of the orthospectra, asymptotics, multiplicity and identities due to Basmajian, Bridgeman and Calegari. We will give a proof that the identities of Bridgeman and Calegari are the same. |
| 日時 | 2012年7月13日（金）15：00～16：00 |
| 講演者（所属） | 矢口 義朗（群馬工業高等専門学校） |
| タイトル | On the extended 1-st Johnson homomorphism of the braid group |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | The braid group $B_m$ of degree $m$ is regarded as a mapping class group $M(D_m)$ of the $m$-puncterd disk $D_m$. There exists a natural surjective homomorphism from $B_m$ to the symmetric group $S_m$ of degree $m$, which is regarded as a homomorphism from $M(D_m)$ to the automorphism group of the 1-st homology group $H_1(D_m)$. By using an analogy of the Johnson's theory for mapping class groups of compact oriented surfaces, we construct a homomorphism from $B_m$ to a group extension of $S_m$. We call it the extended 1-st Jhonson homomorphism of $B_m$. We also study a way to caluculate the extended 1-st Johnson homomorphism by using braid diagrams. This is a joint work with Yusuke Kuno. |
| 日時 | 2012年7月6日（金）16：00～17：00 |
| 講演者（所属） | 鈴木 咲衣（京都大学数理解析研究所(RIMS)） |
| タイトル | Bing doubling and the colored Jones polynomials |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | The colored Jones polynomial is a quantum invariant associated with the quantized enveloping algebra of the Lie algebra sl2. We are interested in the relationship between topological properties of links and algebraic properties of the colored Jones polynomial. Bing doubling is an operation which gives a satellite of a knot. Habiro defined a certain series of the colored Jones polynomials to construct the unified WRT invariant of 3-manifolds. In this talk, we derive Habiro's colored Jones polynomials of the Bing double of a knot K from these of K. We aim to apply the result to study the unified WRT invariant. |
| 日時 | 2012年7月6日（金）15：00～16：00 |
| 講演者（所属） | 屋代 司（Sultan Qaboos University） |
| タイトル | On surface-knots with cross-exchangeable cycles |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | A surface-knot is a closed oriented surface embedded in 4-space. A surface diagram of a surface-knot is the projected image in 3-space under the orthogonal projection with crossing information. It is not known whether or not any surface diagram can be obtained from a trivial surface diagram by applying crossing changes along double curves. For some surface diagrams, there exist special double curves along which crossing information can be changed so that the surface diagram is deformed into a trivial surface diagram. In this talk, we present a construction to obtain a family of surface-knots with exchangeable cycles. This research consists of collaboration projects with A. Mohamad and also with A. AlKharusi. |
| 日時 | 2012年6月29日（金）15：00～16：00 |
| 講演者（所属） | 三浦 嵩広（神戸大学） |
| タイトル | On the flat braidzel length of links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | It is known that any link has a flat braidzel surface as a Seifert surface. We introduce the flat braidzel length of a link defined as the minimal length of all braids which represent flat braidzel surfaces for the link. In this talk, we study relationships between the flat braidzel length and the Alexander-Conway polynomial and give a lower bound for the flat braidzel length. If time allows, we will show that, for any integer n greater than or equal to three, there exists a knot whose flat braidzel length is n. |
| 日時 | 2012年6月22日（金）16：00～17：00 |
| 講演者（所属） | 鎌田 直子（名古屋市立大学） |
| 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 | Bourgoin defined the notion of a twisted link. Twisted links are equivalent to abstract links on non-orientable surfaces. Dye and Kauffman defined the surface bracket polynomials of virtual links. In this talk I introduced those of twisted links. We discuss a relationship between the multivariable invariant and the surface bracket polynomials of twisted links. |
| 日時 | 2012年6月15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 | The knot 12a990 is ribbon |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Herald, Kirk and Livingston showed that the knot 12a990 is slice. Indeed,
they showed that the connected sum of 12a990 with T(2,3) and T(2,-3) is
ribbon, where T(2,3) and T(2,-3) are right- and left-handed trefoils. We
observe that 12a990 is ribbon and generalize this fact. The rest of the
time, we study homotopically slice knots obtained from unknotting number
one ribbon knots by applying annulus twists. This is a joint work with In Dae Jong and Motoo Tange. |
| 日時 | 2012年6月8日（金）16：00～17：00 |
| 講演者（所属） | 田山 育男（OCAMI） |
| タイトル | Tabulation of 3-manifolds of 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 groups 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, the prime link groups and 3-manifolds with lengths up to 10. In this talk, we show a list of the enumeration of $3$-manifolds and discuss a relationship between link exteriors and link groups. |
| 日時 | 2012年6月1日（金）16：00～17：00 |
| 講演者（所属） | 能城 敏博（OCAMI） |
| タイトル | On extendibility of a map induced by Bers isomorphism |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | Let $T(S)$ be the Teichmuller space of a closed Riemann surface $S$ of
genus $g(>1)$. Denote by $U$ the universal covering of $S$, that is,
the upper half-plane and denote by $\dot{S}$ the surface obtained by removing
a point from $S$. By Bers isomorphism theorem, we have a map from $T(S)
\times U$ to $T(\dot{S})$. It is known that the Teichmuller space $T(\dot{S})$
is embedded in $(3g-2)$-dimensional complex vector space. Thus the boundary
$\partial T(\dot{S})$ of $T(\dot{S})$ is naturally defined. Let $A$ be a subset of $\partial U$ consisting of all points filling $S$. In this talk, we show that the map of $T(S) \times U$ to $T(\dot{S})$ has a continuous extension of $T(S)\times (U \cup A)$ into $T(\dot{S}) \cup \partial T(\dot{S})$. This is a joint work with Hideki Miyachi (Osaka University). |
| 日時 | 2012年5月25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) / 日本学術振興会特別研究員PD） |
| タイトル | Mochizuki's quandle 3-cocycles and Inoue-Kabaya chain map |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | In 2003, T. Mochizuki has determined the third quandle cohomologies of all Alexander quandles $X$ over finite fields; further he listed polynomials-presentations of their basis, as solutions of differential equations. I show that all the Mochizuki's 3-cocycles are derived from certain group 3-cohomologies via Inoue-Kabaya chain map. For example, if $X$ is the dihedral quandle, the Mochizuki's 3-cocycle is deduced with an easy computation. |
| 日時 | 2012年5月11日（金）16：00～17：00 |
| 講演者（所属） | 清水 理佳（広島大学） |
| タイトル | The half-twisted splice operation on reduced knot projections |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | We show that any nontrivial reduced knot projection can be obtained from a trefoil projection by a finite sequence of half-twisted splice operations and their inverses without becoming a reducible projection. This is a joint work with Noboru Ito. |
| 日時 | 2012年4月27日（金）16：00～17：00 |
| 講演者（所属） | 門上 晃久（East China Normal University） |
| タイトル | Integrality of Seifert surgery coefficient of twist knot, and Reidemeister torsion (joint work with Tsuyoshi Sakai (Nihon University)) |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | M. Brittenham and Y. Wu determined exceptional surgeries along every $2$-bridge knot by using a lamination structure of the knot complement. In particular, a $2$-bridge knot producing Seifert fibered spaces is a twist knot, which is denoted by $C(2n, 2)$\ $(n\in \mathbb{Z})$ in Conway's notation up to mirror images, and its Seifert surgery coefficients are $1$, $2$ and $3$ (and more for $n=0, \pm 1$). The speaker proved that the Alexander polynomial of a twist knot for $n\ne 0, -1$ restricts the positive numerators of Seifert surgery coefficients into $1$, $2$ or $3$. We try to prove that the denominators of Seifert surgery coefficients are $\pm 1$ (i.e.\ integrality) by using the Alexander polynomial of the knot and an invariant deduced from the Reidemeister torsion of the branched covering over the knot. We obtained necessary conditions as Diophantine equations, and partial answers for some cases. |
| 日時 | 2012年4月20日（金）16：00～17：00 |
| 講演者（所属） | Chad Musick（名古屋大学） |
| タイトル | Drawing Minimal Bridge Projections of Links |
| 場所 | 数学 第3セミナー室（3153） |
| アブストラクト | A method is given to achieve a minimal-bridge projection of a knot. This method relies on maze-solving and minimal path finding to shift all over-crossings off of extra underpasses. The method is proven correct by considering the knot as a fiber bundle from one end of a cylinder to the other end. |
