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Tuesday Seminar on Topology
Seminar information archive ～06/26｜Next seminar｜Future seminars 06/27～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
Future seminars
2026/06/30
16:00-17:30 Room #hybrid/123 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Sang-hyun Kim (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Sang-hyun Kim (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
[ Abstract ]
Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
[ Reference URL ]Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/07/07
16:00-17:00 Online
Pre-registration required. See our seminar webpage.
Tatsuhiko Yagasaki (Kyoto Institute of Technology)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsuhiko Yagasaki (Kyoto Institute of Technology)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
[ Abstract ]
This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
[ Reference URL ]This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/07/14
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Yuichiro Tanaka (The University of Tokyo)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Yuichiro Tanaka (The University of Tokyo)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
[ Abstract ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
[ Reference URL ]A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
