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トポロジー火曜セミナー
過去の記録 ～04/11｜次回の予定｜今後の予定 04/12～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 池 祐一, 今野 北斗, 逆井卓也 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
今後の予定
2026年04月14日(火)
16:00-17:30 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
岡本 幸大 氏 (東京都立大学)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
岡本 幸大 氏 (東京都立大学)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
[ 講演概要 ]
The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
[ 参考URL ]The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年04月21日(火)
16:00-17:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
[ 講演概要 ]
Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
[ 参考URL ]Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年04月28日(火)
16:00-17:30 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐野 岳人 氏 (理化学研究所)
A y-ification of Khovanov homology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐野 岳人 氏 (理化学研究所)
A y-ification of Khovanov homology (JAPANESE)
[ 講演概要 ]
In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
[ 参考URL ]In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年05月12日(火)
16:00-17:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
Sanghoon Kwak 氏 (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
Sanghoon Kwak 氏 (Seoul National University)
Mapping class group of Infinite graph: 'Big' Out(Fn) (ENGLISH)
[ 講演概要 ]
Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
[ 参考URL ]Algom-Kfir and Bestvina introduced the mapping class groups of locally finite, infinite graphs in 2021. Since Out(Fn) can be realized as the mapping group of a finite graph, their construction may be viewed as a "big" version of Out(Fn). In this talk, we survey the algebraic and coarse geometric properties of these groups and discuss a relationship with mapping class groups of infinite-type surfaces ("big mapping class groups"). This talk is based on joint work with Ryan Dickmann, George Domat, and Hannah Hoganson, in various collaborations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
