Knotting Nagoya 2019-2023.
結び目の数理セミナー Knotting Nagoya 会合案内
- 2022年2月会合
- 「Knotting Nagoya and Madrid. 」
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日時(Date)：2022 Feb 18th（Fri）17:00 ~ 19:00 (Japan time)
場所(Place) : Nagoya Institute of Technology (on ZOOM, URL to be inquired)
予定(Schedule):
First 30 mins for general audience of knot theory,
followed by Q&A and comments
Next 60 mins for more details,
followed by further discussion
講演者(speaker): Benjamin Bode (INSTITUTO DE CIENCIAS MATEMATICAS，スペイン マドリッド)
タイトル(Title): Braided open book decompositions in S^3
アブストラクト(Abstract): We study four (a priori) different ways in which an open
book decomposition of the 3-sphere can be braided. These include
generalised exchangeability defined by Morton and Rampichini and
mutual braiding defined by Rudolph, which were shown to be equivalent
by Rampichini, as well as P-fiberedness (a property related to complex
polynomials) and a property related to simple branched covers of $S^3$
inspired by work of Montesinos and Morton. We prove that these four
notions of a braided open book are all equivalent to each other.
- 2021年8月会合
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日時(Date)：2021 Aug 7th（Sat）09:30 ~ 11:30 (Japan time)
場所(Place) : on ZOOM (URL to be inquired)
予定(Schedule):
Presentation for about an hour and following up discussion
講演者(speaker): 寺垣内 政一(Masakazu Teragaito, Hiroshima University)
タイトル(Title): Identifying non-pseudo-alternating knots by using
the free factor property of minimal genus Seifert surfaces
アブストラクト(Abstract): MaylandとMurasugiが1976年に導入した
pseudo-alternating knotという概念がある．それは，
alternating knotを含む広いクラスである．
primitive flat surfaceとよばれるSeifert surfaceを村杉和して得られる曲面の
境界として定義される．
したがって，pseudo-alternating knotを構成することは容易だが，
与えられた結び目がpseudo-alternatingかどうかを判定することは
一般には困難である．
この講演では，最小種数Seifert surfaceのもつfree factor propertyという
性質に着目して，ある種のpretzel knotがpseudo-alternatingでないことを
示す．これにより，特に，rationally homologically fibered knotではあるが
pseudo-alternatingではない結び目の存在を，任意の種数に対して確認できる．
議論の一端をになう最小種数Seifert surfaceの一意性については，
小林毅氏によるsutured manifold theoryを用いた議論を援用する．
（姫野圭佑氏（広島大学大学院先進理工系科学研究科）との共同研究）
Abstract:
Pseudo-alternating knots and links are defined constructively via their Seifert surfaces.
By performing Murasugi sums of primitive flat surfaces,
such a knot or link is obtained as the boundary of the resulting surface.
Conversely, it is hard to determine whether a given knot or link is pseudo-alternating or not.
A major difficulty is the lack of criteria to recognize whether a given Seifert surface is decomposable
as a Murasugi sum.
In this talk, we propose a new idea to identify non-pseudo-alternating knots.
Combining with the uniqueness of minimal genus Seifert surface obtained through sutured manifold theory,
we demonstrate that two infinite classes of pretzel knots are not
pseudo-alternating.
(This is a joint work with Keisuke Himeno.)
- 2021年4月会合
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「Knotting Nagoya and N.Y. 」
Date：2021 Apr 17th（Sat）10:00 ~ 11:00 (Japan time)
Place : on ZOOM (URL to be inquired)
Schedule:
10:00-10:05 Opening and introduction of the speaker
10:05-10:50 Talk by P. Ording
10:50-11:00 Q&A and discussion
After closing, open chat time for a while.
Speaker: Philip Ording (Sarah Lawrence College)
Title: A random walk through proof space
Abstract:
Abstract. Paul Erd\UTF{0151}s imagined that in heaven God has a book--"The Book"--and in it is written the best proof of any theorem. Putting theology aside there is some disagreement about whether the set of proofs admits such an ordering. For example John Conway and Joseph Shipman argued that we "shouldn’t speak of 'the best' proof, because different people will value proofs in different ways. Indeed one person’s value might oppose another’s." Instead they envisioned a multidimensional space of proofs. This informal talk will explore the proof space populated by the book 99 Variations on a Proof which appeared in a Japanese edition, 1つの定理を証明する99の方法, earlier this year.
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過去の会合の記録
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Knotting Nagoyaに関するお問い合わせは、平澤美可三
hirasawa.mikami アット nitech.ac.jp
までお願いします.
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Knotting Nagoyaは名古屋工業大学, 名古屋市立大学, 名城大学, 愛知教育大学, 名古屋大学の専門家にて共同運営しております.
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