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Tuesday Seminar on Topology
Seminar information archive ～06/27｜Next seminar｜Future seminars 06/28～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
Future seminars
2025/07/01
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Genki Sato (Fcuro, Inc.)
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
Pre-registration required. See our seminar webpage.
Genki Sato (Fcuro, Inc.)
Presentation of finite Reedy categories as localizations of finite direct categories (JAPANESE)
[ Abstract ]
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.
[ Reference 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
2025/07/08
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Hiroki Ishikura (The University of Tokyo)
Stallings-Swan’s Theorem for Borel graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hiroki Ishikura (The University of Tokyo)
Stallings-Swan’s Theorem for Borel graphs (JAPANESE)
[ Abstract ]
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.
[ Reference 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
2025/07/15
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Anastasiia Tsvietkova (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
Pre-registration required. See our seminar webpage.
Anastasiia Tsvietkova (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (ENGLISH)
[ Abstract ]
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.
[ Reference 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
2025/07/22
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Alexis Marchand (Kyoto University)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Alexis Marchand (Kyoto University)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
[ Abstract ]
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.
[ Reference 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
