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トポロジー火曜セミナー
過去の記録 ～10/18｜次回の予定｜今後の予定 10/19～
| 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10月20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。
大鹿 健一 氏 (学習院大学)
Structures of unit tangent spheres of Thurston’s metric (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。
大鹿 健一 氏 (学習院大学)
Structures of unit tangent spheres of Thurston’s metric (JAPANESE)
[ 講演概要 ]
Thurston introduced in the 1980s a new metric on Teichmüller space using best Lipschitz maps instead of best quasi-conformal maps. Thurston’s metric is Finsler, and so we can consider the associated norm on tangent spaces of Teichmüller space. In this talk, we show how the unit sphere of this norm looks, regarded as a convex sphere. We in particular give a formula for dimensions of faces. This is a part of joint work with A. Papadopoulos.
[ 参考URL ]Thurston introduced in the 1980s a new metric on Teichmüller space using best Lipschitz maps instead of best quasi-conformal maps. Thurston’s metric is Finsler, and so we can consider the associated norm on tangent spaces of Teichmüller space. In this talk, we show how the unit sphere of this norm looks, regarded as a convex sphere. We in particular give a formula for dimensions of faces. This is a part of joint work with A. Papadopoulos.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年11月10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。
キムミンギュ 氏 (Korea Institute for Advanced Study)
Symmetric powers and double loop spaces of odd spheres
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。
キムミンギュ 氏 (Korea Institute for Advanced Study)
Symmetric powers and double loop spaces of odd spheres
[ 講演概要 ]
Functors from free groups to abelian groups form a natural setting in algebra and topology, and Ext-groups between such functors govern, for instance, the stable homology of automorphism groups of free groups with twisted coefficients. Over the rationals, these Ext-groups are by now well understood for a wide range of polynomial functors, thanks to work of Christine Vespa. Gregory Arone recently extended Vespa's results to integral coefficients using a new homotopical approach. One case, however, has remained particularly delicate: the Ext-groups from the abelianization functor ab to its symmetric powers S^n. These vanish rationally, but in recent joint work with Vespa, we determined Ext^1 and Ext^2 and found that they contain substantial torsion.
In this talk, I will present an unexpected result obtained recently in joint work with Arone and Vespa: the integral Ext-groups Ext*(ab, S^n) can be expressed in terms of the homology of the double loop space of a sphere of odd dimension at least 3. This identification not only determines the groups in all degrees, but also connects them to the homology of braid groups via classical results in the topology of configuration spaces.
[ 参考URL ]Functors from free groups to abelian groups form a natural setting in algebra and topology, and Ext-groups between such functors govern, for instance, the stable homology of automorphism groups of free groups with twisted coefficients. Over the rationals, these Ext-groups are by now well understood for a wide range of polynomial functors, thanks to work of Christine Vespa. Gregory Arone recently extended Vespa's results to integral coefficients using a new homotopical approach. One case, however, has remained particularly delicate: the Ext-groups from the abelianization functor ab to its symmetric powers S^n. These vanish rationally, but in recent joint work with Vespa, we determined Ext^1 and Ext^2 and found that they contain substantial torsion.
In this talk, I will present an unexpected result obtained recently in joint work with Arone and Vespa: the integral Ext-groups Ext*(ab, S^n) can be expressed in terms of the homology of the double loop space of a sphere of odd dimension at least 3. This identification not only determines the groups in all degrees, but also connects them to the homology of braid groups via classical results in the topology of configuration spaces.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
