| Speaker |
Riccardo Piergallini（University of Camerino） |
| Title |
Embedding branched covers as braided manifolds |
| Date |
January 12 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Inspired by Riemann surfaces and more generally complex hypersurfaces $S \subset C^n \times C$, a submanifold $M \subset X \times Y$ is said to be braided over $X$ if the projection over this factor restricts to a branched covering $M \to X$.
In the talk, we first present some different approaches to known results about the realization of a 3-manifold $M$ presented by a branched covering $M \to S^3$ as a braided submanifolds of $S^3 \times B^2$ (or $S^3 \times S^2$).
Then, we discuss the problem of finding analogous results for a 4-manifold $M$ presented by a branched covering $M \to S^4$. |
| Speaker |
Kanako Oshiro (Sophia University) |
| Title |
Biquandle (co)homology and handlebody-links |
| Date |
December 15 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In our previous paper, we introduced a multiple conjugation biquandle which is the universal algebra to define a semi-arc coloring invariant for handlebody-links. In this talk, we introduce a (co)homology theory of multiple conjugation biquandles and show that cocycle invariants of handlebody-links can be obtained by using them. This is a joint work with Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim and Shosaku Matsuzaki. |
| Speaker |
Kenta Hayano (Keio University) |
| Title |
On diagrams of simplified trisections and mapping class groups |
| Date |
December 8 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A trisection, introduced by Gay and Kirby, is a decomposition of a 4-manifold into three 4-dimensional handlebodies, which can be considered as a 4-dimensional counterpart of a Heegaard splitting of a 3-manifold. We can indeed obtain a 4-manifold with a trisection from a 3-tuple of systems of simple closed curves in a closed surface, which we call a trisection diagram.
In this talk, we give a criterion for a 3-tuple of curves to be a diagram of a simplified trisection (which is a special kind of trisection due to Baykur and Saeki) in terms of mapping class groups of surfaces. Baykur and Saeki recently gave an algorithmic construction of simplified trisections from broken Lefschetz fibrations. If time permits, we also explain an algorithm to obtain a diagram of a simplified trisection derived from Baykur and Saeki's construction. |
| Speaker |
Kengo Kishimoto（Osaka Institute of Technology） |
| Title |
Simple-ribbon concordance of knots |
| Date |
December 1 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A simple-ribbon fusion is a special kind of fusion of a knot and a trivial link. In this talk, we introduce a concordance relation generated by simple-ribbon fusions, and show that there are infinitely many ribbon knots which are not obtained from the trivial knot by a finite sequence of simple-ribbon fusions. This is a joint work with Tetsuo Shibuya and Tatsuya Tsukamoto. |
| Speaker |
Bruno Aarón Cisneros de la Cruz（Instituto de matemáticas de la UNAM and CONACyT） |
| Title |
Normal forms on virtual braid groups |
| Date |
November 10 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Virtual knots were defined by L. Kauffman on the nineties as a generalization of classic knots. They are defined by means of knot type diagrams and they are identified up to virtual Reidemeister moves. They have a topological counterpart as knots embedded in thickened surfaces, identified up to isotopy, compatibility and stability. Virtual braids are the braid version of virtual knots and generalize classical braids, but some nice properties of classical braids do not extend naturally to virtual braids (for example: solutions to word problem and normal forms).
In this talk I will show normal forms on virtual braid groups and how this is related to the genus problem on virtual braids. |
| Speaker |
Taizo Kanenobu（Osaka City University） |
| Title |
Coherent band-Gordian distances between knots and links |
| Date |
October 27 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A coherent band surgery is a local move for an oriented link. The coherent band-Gordian distance between two links is the minimum number of coherent band surgeries needed to transform one into the other. We introduce several methods to determine this number. Then we give a table of coherent band-Gordian distances between knots and 2-component links with up to seven crossings. This is a joint work with Hiromasa Moriuchi, Kindai University. |
| Speaker |
Migiwa Sakurai（National Institute of Technology, Ibaraki College） |
| Title |
Relationship between finite type invariants and forbidden moves |
| Date |
October 20 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Vassiliev introduced filtered invariants of knots using crossing changes
(1990), called finite type invariants. For Vassiliev invariants, Ohyama
introduced a notion of n-triviality (1990) and Taniyama generalized it
to obtain a notion of n-similarity (1992). Goussarov, Polyak, and Viro
introduced finite type invariants of virtual knots using virtualization
(2000). Noboru Ito and the speaker mimicked their ideas, and defined
finite type invariants of virtual knots and introduced a notion that
corresponds to n-similarity, using forbidden moves (2017, preprint). In
this talk, we consider a relationship between finite type invariants and
forbidden moves. |
| Speaker |
Shin’ya Okazaki（OCAMI） |
| Title |
Seifert complex for handlebody-knots |
| Date |
October 13 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A handlebody-knot is a handlebody embedded in the three sphere.
In this talk, we introduce a Seifert complex and a C-complex of a handlebody-knot and calculate the Alexander invariant for a handlebody-knot by a C-complex.
We show that an equivalent class of a C-complex characterizes a handlebody-knot. |
| Speaker |
Kengo Kawamura（OCAMI） |
| Title |
No immersed $2$-knot with one self-intersection point has triple point number two or three |
| Date |
October 6 (Fri.) 16：00〜17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The triple point number of an embedded/immersed $2$-knot is the minimum number of triple points needed for its diagram into a $3$-space. Satoh proved that no embedded $2$-knot has triple point number two or three. In this talk, we introduce diagrams of an immersed surface-knot and show that no immersed $2$-knot with one self-intersection point has triple point number two or three. |
| Speaker |
Benjamin Bode（University of Bristol） |
| Title |
Constructing links of isolated singularities of real polynomials |
| Date |
July 28 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
In order to implement knotted configurations in physical systems it is often very useful to have an explicit function, ideally a polynomial, $f:R^3\to C$ with a zero level set of given knot type. In this talk I will introduce an algorithm that for every link $L$ constructs a polynomial $f:R^4\to R^2$ whose zero set on the unit three-sphere is $L$. Applying stereographic projection then makes these functions applicable to physical systems.
This constructive approach allows us to prove several results about the functions and their knotted zero level sets, for example under which conditions $f$ can be taken to have an isolated singularity or when $\arg f$ is a fibration of the link complement over $S^1$. |
| Speaker |
Kouki Sato（Tokyo Institute of Technology） |
| Title |
A partial order on $\nu^+$ equivalence classes |
| Date |
July 14 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The $\nu^+$ equivalence is an equivalence relation on the knot concordance
group. Hom proves that many concordance invariants derived from Heegaard
Floer homology are invariant under $\nu^+$ equivalence. In this work, we
introduce a partial order on $\nu^+$ equivalence classes, and study its
algebraic and geometrical properties. As an application, we prove that
any genus one knot is $\nu^+$ equivalent to one of the unknot, the trefoil
and its mirror. |
| Speaker |
Tomo Murao (University of Tsukuba) |
| Title |
The Gordian distance of handlebody-knots and Alexander biquandles |
| Date |
July 7 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A handlebody-knot is a handlebody embedded in the 3-sphere $S^3$. Any two handlebody-knots of the same genus can be related by a finite sequence of crossing changes. Then we define their Gordian distance by the minimal number of crossing changes needed to be deformed each other. In particular, for any handlebody-knot $H$ and the trivial handlebody-knot of the same genus, we call their Gordian distance the unknotting number of $H$. In this talk, we give evaluation formulas of the Gordian distance and the unknotting number of handlebody-knots by using Alexander biquandles and some examples. |
| Speaker |
Toshifumi Tanaka（Gifu University） |
| Title |
On the region index and the unknotting number of a knot |
| Date |
June 30 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
It is known that, for any knot, there exists a diagram such that we have
the unknot if we change all crossings on the boundary of some region of
the diagram. The minimal number of the crossing changes over all such diagrams
is called the region index of a knot. Clearly, the unknotting number is
less than or equal to the region index. In this talk, we show that there
exists a knot which has unknotting number $m$ and region index $m+1$ for
any positive integer $m$(>1) by using the Goeritz invariant. We also
show that there exists a knot which has unknotting number and region index
that are equal to $n$ for any positive integer $n$(>1) by using the
Rasmussen invariant. |
| Speaker |
Tsukasa Yashiro（Sultan Qaboos University） |
| Title |
Covering diagrams of surface-knots |
| Date |
June 23 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A surface-knot is a closed oriented surface embedded in 4-space. A surface-knot diagram of a surface-knot is the projected image in 3-space under the orthogonal projection with crossing information.
Every non-trivial surface-knot diagram is equipped with the double decker set (the union of closures of upper and lower decker sets). From the lower decker set and quandle coloring, pseudo-cycles are defined.
In this talk, we will introduce a covering diagram over a surface-knot diagram and we will show that a lower bound of the triple point number of the covering diagram is obtained. |
| Speaker |
Sam Nelson（Claremont McKenna College） |
| Title |
Biquandle Brackets |
| Date |
June 9 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A biquandle bracket is a skein invariant of biquandle-colored oriented knots and links. We define an enhancement of the biquandle counting invariant by collecting the values of a biquandle bracket over the complete set of colorings of an oriented knot or link diagram. This class of invariants includes the classical skein invariants (HOMFLYpt, Jones, Alexander-Conway and Kauffman polynomials) as well as the biquandle 2-cocycle invariants as special cases, as well as new invariants. |
| Speaker |
Kodai Wada（Waseda University） |
| Title |
Invariants of welded links derived from multiplexing of crossings |
| Date |
June 2 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
For a link diagram $L$, we construct a virtual link diagram $L(m)$ which is obtained from $L$ by multiplexing of the crossings of $L$, where $m$ is a positive integer. If two link diagrams $L$ and $L'$ are equivalent, then $L(m)$ and $L'(m)$ are equivalent as welded links. Since an invariant of $L(m)$ is that of $L$, we try to find new invariants of $L$ via $L(m)$. This is a joint work with Haruko A. Miyazawa (Tsuda University) and Akira Yasuhara (Tsuda University). |
| Speaker |
Anh Tran (The University of Texas at Dallas) |
| Title |
Introduction to the AJ conjecture |
| Date |
May 19 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
The AJ conjecture was proposed by Garoufalidis about 15 years ago. It predicts a strong connection between two important knot invariants derived from very different background, namely the colored Jones function (a quantum invariant) and the A-polynomial (a geometric invariant). The colored Jones function is a sequence of Laurent polynomials which is known to satisfy a linear q-difference equation. The AJ conjecture states that by writing the linear q-difference equation into an operator form and setting q=1, one gets the A-polynomial. In this talk, I will give an introduction to this conjecture. |
| Speaker |
Ryo Nikkuni (Tokyo Woman's Christian University) |
| Title |
A regular isotopy between two spatial graphs which are ambient isotopic |
| Date |
May 12 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Trace showed that two knot diagrams representing the same knot are transformed into each other by Reidemeister moves II and III if and only if they have the same writhe and rotation number, and this was extended to singular knots by Tsau. In this talk, for a graph each of whose components is the circle, theta graph or complete graph on four vertices, we give a necessary and sufficient condition for two diagrams of the graph representing the same spatial graph to be transformed into each other by Reidemeister moves II, III and IV. This is also extended to singular spatial graphs. |
| Speaker |
Yuka Kotorii (RIKEN/OCAMI) |
| Title |
On link-homotopy classes of handlebody-links |
| Date |
April 28 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and link-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of link-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of link-homotopy classes of $n$-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa.
|
| Speaker |
Hideo Takioka (OCAMI) |
| Title |
Infinitely many knots with the trivial $(2,1)$-cable $\Gamma$-polynomial |
| Date |
April 21 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
For coprime integers $p(>0)$ and $q$, the $(p,q)$-cable $\Gamma$-polynomial
of a knot is the $\Gamma$-polynomial of the $(p,q)$-cable knot of the knot,
where the $\Gamma$-polynomial is the common zeroth coefficient polynomial
of both the HOMFLYPT and Kauffman polynomials. In this talk, we show that
there exist infinitely many knots with the trivial $(2,1)$-cable $\Gamma$-polynomial,
that is, the $(2,1)$-cable $\Gamma$-polynomial of the unknot. Moreover,
we show that the knots have the trivial $\Gamma$-polynomial, the trivial
first coefficient HOMFLYPT polynomial, and the distinct Conway polynomials.
|
| Speaker |
Megumi Hashizume (OCAMI) |
| Title |
Link version of Inoue-Shimizu's result on region crossing |
| Date |
April 14 (Fri.) 16：00～17：00 |
| Place |
Dept. of Mathematics, Sci. Bldg., F415 |
| Abstract |
Recently, a new local transformation on link diagram called region freeze crossing change is proposed as a mutant of region crossing change. It is known that any change of crossings on any knot diagram can be realized as a region crossing change. Inoue-Shimizu showed there is a knot diagram such that some change of crossings can NOT be realized by region freeze crossing change. They showed necessary and sufficient condition for the exchangeability of any given crossing of the knot diagram via region freeze crossing change. In this talk, we discuss about a generalization of this result for links. |
Last Modified on 2017.12.19
