本文印刷
全画面プリント
トポロジー火曜セミナー
過去の記録 ～01/15｜次回の予定｜今後の予定 01/16～
| 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
2026年01月20日(火)
17:00-18:00 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。
前川 拓海 氏 (東京大学大学院数理科学研究科)
A six-functor construction of the Bauer-Furuta invariant (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。
前川 拓海 氏 (東京大学大学院数理科学研究科)
A six-functor construction of the Bauer-Furuta invariant (JAPANESE)
[ 講演概要 ]
Building on the pioneering works of Verdier and Grothendieck, and later developed by Kashiwara-Schapira, the six-functor formalism for sheaves enables us to understand cohomological duality theorems and transfer maps in terms of certain (stable) ∞-categorical adjunction. Following Gaitsgory-Rozenblyum, these six operations fit into a single (∞,2)-functor out of the 2-category of correspondences. In this talk, we will recall these modern points of view on the six-functor formalism, and as an application, we will see that the stable homotopy theoretic refinement of the Seiberg-Witten invariant defined for a closed spin c four-manifold, introduced by Furuta and Bauer, does correspond to a 2-morphism in that (∞,2)-functoriality.
[ 参考URL ]Building on the pioneering works of Verdier and Grothendieck, and later developed by Kashiwara-Schapira, the six-functor formalism for sheaves enables us to understand cohomological duality theorems and transfer maps in terms of certain (stable) ∞-categorical adjunction. Following Gaitsgory-Rozenblyum, these six operations fit into a single (∞,2)-functor out of the 2-category of correspondences. In this talk, we will recall these modern points of view on the six-functor formalism, and as an application, we will see that the stable homotopy theoretic refinement of the Seiberg-Witten invariant defined for a closed spin c four-manifold, introduced by Furuta and Bauer, does correspond to a 2-morphism in that (∞,2)-functoriality.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年01月21日(水)
16:00-17:00 数理科学研究科棟(駒場) hybrid/118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。
Ingrid Irmer 氏 (南方科技大学)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
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。
Ingrid Irmer 氏 (南方科技大学)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
[ 講演概要 ]
The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
[ 参考URL ]The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年01月21日(水)
17:30-18:30 数理科学研究科棟(駒場) hybrid/118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。
Stavros Garoufalidis 氏 (南方科技大学)
What are Lie superalgebras good for? (ENGLISH)
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。
Stavros Garoufalidis 氏 (南方科技大学)
What are Lie superalgebras good for? (ENGLISH)
[ 講演概要 ]
I will try to answer, as honestly as I can, this question. Lie superalgebras are important in mathematical physics (supersymmetry), in representation theory, in categorification, in quantum topology, but also in classical topology. Namely, they may detect the genus of a smallest spanning surface of a knot. Come and listen about some theorems and experimental evidence, and decide for yourself if this is an accident, a conspiracy theory, or a manifestation of the truth!
[ 参考URL ]I will try to answer, as honestly as I can, this question. Lie superalgebras are important in mathematical physics (supersymmetry), in representation theory, in categorification, in quantum topology, but also in classical topology. Namely, they may detect the genus of a smallest spanning surface of a knot. Come and listen about some theorems and experimental evidence, and decide for yourself if this is an accident, a conspiracy theory, or a manifestation of the truth!
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
