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トポロジー火曜セミナー
過去の記録 ～06/30｜次回の予定｜今後の予定 07/01～
| 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07月01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。
佐藤 玄基 氏 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories (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。
佐藤 玄基 氏 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories (JAPANESE)
[ 講演概要 ]
In this talk, we present a novel construction that, for a given Reedy category $C$, produces a direct category $\operatorname{Down}(C)$ and a functor $\operatorname{Down}(C) \to C$, exhibiting $C$ as an $(\infty,1)$-categorical localization of $\operatorname{Down}(C)$. This result refines previous constructions in the literature by ensuring that $\operatorname{Down}(C)$ is finite whenever $C$ is finite—a property not guaranteed by existing approaches, such as those by Lurie or by Barwick and Kan. As an intended future application, this finiteness property is expected to be useful for embedding the construction into the syntax of a (non-infinitary) logic. In particular, I expect that the construction may be used to develop a meta-theory of finitely truncated simplicial types and other finite Reedy presheaves for homotopy type theory, thereby extending Kraus and Sattler's unfinished approach. This talk is based on arXiv:2502.05096.
[ 参考URL ]In this talk, we present a novel construction that, for a given Reedy category $C$, produces a direct category $\operatorname{Down}(C)$ and a functor $\operatorname{Down}(C) \to C$, exhibiting $C$ as an $(\infty,1)$-categorical localization of $\operatorname{Down}(C)$. This result refines previous constructions in the literature by ensuring that $\operatorname{Down}(C)$ is finite whenever $C$ is finite—a property not guaranteed by existing approaches, such as those by Lurie or by Barwick and Kan. As an intended future application, this finiteness property is expected to be useful for embedding the construction into the syntax of a (non-infinitary) logic. In particular, I expect that the construction may be used to develop a meta-theory of finitely truncated simplicial types and other finite Reedy presheaves for homotopy type theory, thereby extending Kraus and Sattler's unfinished approach. This talk is based on arXiv:2502.05096.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年07月08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。
石倉 宙樹 氏 (東京大学大学院数理科学研究科)
Stallings-Swan’s Theorem for Borel 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。
石倉 宙樹 氏 (東京大学大学院数理科学研究科)
Stallings-Swan’s Theorem for Borel graphs (JAPANESE)
[ 講演概要 ]
A Borel graph is a simplicial graph on a standard Borel space X such that the edge set is a Borel subset of X^2. Such objects have been studied in the context of countable Borel equivalence relations, and recently there are many attempts to apply the ideas of geometric group theory to them. Stallings-Swan's theorem states that groups of cohomological dimension 1 are free groups. We will talk about an analog of this theorem for Borel graphs: A Borel graph on X with uniformly bounded degrees of cohomological dimension 1 is Lipschitz equivalent to a Borel acyclic graph on X. This is proved by establishing a criterion for certain decomposition of Borel graphs, which is inspired by Dunwoody's work on accessibility of groups.
[ 参考URL ]A Borel graph is a simplicial graph on a standard Borel space X such that the edge set is a Borel subset of X^2. Such objects have been studied in the context of countable Borel equivalence relations, and recently there are many attempts to apply the ideas of geometric group theory to them. Stallings-Swan's theorem states that groups of cohomological dimension 1 are free groups. We will talk about an analog of this theorem for Borel graphs: A Borel graph on X with uniformly bounded degrees of cohomological dimension 1 is Lipschitz equivalent to a Borel acyclic graph on X. This is proved by establishing a criterion for certain decomposition of Borel graphs, which is inspired by Dunwoody's work on accessibility of groups.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年07月15日(火)
17:00-18:30 数理科学研究科棟(駒場) 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。
Anastasiia Tsvietkova 氏 (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (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。
Anastasiia Tsvietkova 氏 (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (ENGLISH)
[ 講演概要 ]
For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
[ 参考URL ]For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年07月22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。
Alexis Marchand 氏 (京都大学)
Sharp spectral gaps for scl from negative curvature (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。
Alexis Marchand 氏 (京都大学)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
[ 講演概要 ]
Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
[ 参考URL ]Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
