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トポロジー火曜セミナー
過去の記録 ～11/23｜次回の予定｜今後の予定 11/24～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也, 葉廣和夫 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
今後の予定
2025年11月25日(火)
17:00-18:00 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。
栗林 勝彦 氏 (信州大学)
Interleavings of persistence dg-modules and Sullivan models for maps (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。
栗林 勝彦 氏 (信州大学)
Interleavings of persistence dg-modules and Sullivan models for maps (JAPANESE)
[ 講演概要 ]
The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
[ 参考URL ]The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年12月02日(火)
17:30-18:30 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。
馬場 伸平 氏 (大阪大学)
Bending Teichmüller spaces and character varieties (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。
馬場 伸平 氏 (大阪大学)
Bending Teichmüller spaces and character varieties (JAPANESE)
[ 講演概要 ]
Let S be a closed oriented surface of genus at least two. The Teichmüller space of S can be regarded as the space of discrete faithful representations from the fundamental group of S into PSL(2, R). Given a simple closed curve on S with positive weight (or more generally, a measured lamination), we can "bend" the repsentation along the curve by an angle equal to the weight, and obtain a representation of the surface group into PSL(2, C). This bending deformation induces a mapping from the Teichmüller space into the space of representations of the surface group into PSL(2, C). We discuss some interesting properties of this mapping.
If time permits, we also discuss a complexification of this mapping.
[ 参考URL ]Let S be a closed oriented surface of genus at least two. The Teichmüller space of S can be regarded as the space of discrete faithful representations from the fundamental group of S into PSL(2, R). Given a simple closed curve on S with positive weight (or more generally, a measured lamination), we can "bend" the repsentation along the curve by an angle equal to the weight, and obtain a representation of the surface group into PSL(2, C). This bending deformation induces a mapping from the Teichmüller space into the space of representations of the surface group into PSL(2, C). We discuss some interesting properties of this mapping.
If time permits, we also discuss a complexification of this mapping.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年12月09日(火)
17:00-18:30 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。
久野 雄介 氏 (津田塾大学)
Emergent version of Drinfeld's associator equations (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。
久野 雄介 氏 (津田塾大学)
Emergent version of Drinfeld's associator equations (JAPANESE)
[ 講演概要 ]
In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
[ 参考URL ]In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
