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トポロジー火曜セミナー
過去の記録 ～05/20｜次回の予定｜今後の予定 05/21～
| 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05月26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。
坂井 健人 氏 (東京大学大学院数理科学研究科)
On the large-scale geometry of k-multicurve graphs (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。
坂井 健人 氏 (東京大学大学院数理科学研究科)
On the large-scale geometry of k-multicurve graphs (JAPANESE)
[ 講演概要 ]
Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
[ 参考URL ]Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年06月02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。
浅野 知紘 氏 (京都大学)
Knot types of Lagrangian intersections and epimorphisms between knot groups (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。
浅野 知紘 氏 (京都大学)
Knot types of Lagrangian intersections and epimorphisms between knot groups (JAPANESE)
[ 講演概要 ]
Lagrangian intersections in symplectic manifolds have been studied from various perspectives. In recent years, several works have also investigated the knot types of Lagrangian intersections.
In this talk, we discuss a problem posed by Okamoto. Starting from a knot in the 3-dimensional Euclidean space, we move its conormal bundle in the cotangent bundle by a compactly supported Hamiltonian isotopy. When its intersection with the zero-section is connected and clean, it gives rise to another knot. We ask how the knot type of this new knot is related to that of the original one.
I will explain a new constraint on this problem obtained by using microlocal sheaf theory, in terms of the fundamental groups of knot complements. This talk is based on joint work with Yukihiro Okamoto (Tokyo Metropolitan University).
[ 参考URL ]Lagrangian intersections in symplectic manifolds have been studied from various perspectives. In recent years, several works have also investigated the knot types of Lagrangian intersections.
In this talk, we discuss a problem posed by Okamoto. Starting from a knot in the 3-dimensional Euclidean space, we move its conormal bundle in the cotangent bundle by a compactly supported Hamiltonian isotopy. When its intersection with the zero-section is connected and clean, it gives rise to another knot. We ask how the knot type of this new knot is related to that of the original one.
I will explain a new constraint on this problem obtained by using microlocal sheaf theory, in terms of the fundamental groups of knot complements. This talk is based on joint work with Yukihiro Okamoto (Tokyo Metropolitan University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年06月09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。
田邊 真郷 氏 (理化学研究所数理創造研究センター)
Thom polynomials relative to maps prescribed near the boundary (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。
田邊 真郷 氏 (理化学研究所数理創造研究センター)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
[ 講演概要 ]
Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
[ 参考URL ]Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
