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Tuesday Seminar on Topology
Seminar information archive ～05/16｜Next seminar｜Future seminars 05/17～
| 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
2026/05/19
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Joint with Lie Groups and Representation Theory Seminar. See our seminar webpage.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (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.
Yosuke Morita (Kyushu University)
Compact Clifford-Klein forms and homotopy theory of sphere bundles (JAPANESE)
[ Abstract ]
Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the 'vector fields on sphere' problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
[ Reference URL ]Let G/H be a homogeneous space of reductive type (such as the pseudo-Riemannian hyperbolic space H^{p,q}). If a discrete subgroup of G acts properly and freely on G/H, the quotient space becomes a manifold locally modelled on G/H and is called a Clifford-Klein form. In this talk, I will explain a new necessary condition on G/H for the existence of compact Clifford-Klein forms, formulated in terms of homotopy theory of sphere bundles. Our theorem and Adams's solution to the 'vector fields on sphere' problem (1962) together imply the following result: unless p is divisible by 2^{ν(q)}, there does not exist a compact complete pseudo-Riemannian manifolds of signature (p,q) with constant negative sectional curvature. Here, ν(q) is an explicit natural number roughly equal to q/2. This is joint work with Fanny Kassel and Nicolas Tholozan.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/05/26
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
On the large-scale geometry of k-multicurve graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kento Sakai (The University of Tokyo)
On the large-scale geometry of k-multicurve graphs (JAPANESE)
[ Abstract ]
Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
[ Reference URL ]Graphs whose vertices are isotopy classes of simple closed curves, or multicurves, on surfaces have been widely studied, since they admit natural actions of mapping class groups. The curve graph and the pants graph are two fundamental examples. These graphs have found many applications in low-dimensional topology, including the study of Teichmüller spaces, Kleinian groups, and topology of 3-manifolds. In particular, the Gromov hyperbolicity of the curve graph, established by Masur and Minsky, played an important role in the proof of the Ending Lamination Theorem.
The k-multicurve graph, introduced by Erlandsson and Fanoni, is a graph whose vertices are multicurves with k components. It provides a natural interpolation between the curve graph and the pants graph. In this talk, we will present results on large-scale geometric properties of k-multicurve graphs, including hyperbolicity, relative hyperbolicity, and quasi-flat rank. If time permits, we will also discuss some connections with mapping class groups and Teichmüller spaces. This talk is based on joint work with Erika Kuno (Shibaura Institute of Technology) and Rin Kuramochi (The University of Tokyo).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/06/02
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tomohiro Asano (Kyoto University)
Knot types of Lagrangian intersections and epimorphisms between knot groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tomohiro Asano (Kyoto University)
Knot types of Lagrangian intersections and epimorphisms between knot groups (JAPANESE)
[ Abstract ]
Lagrangian intersections in symplectic manifolds have been studied from various perspectives. In recent years, several works have also investigated the knot types of Lagrangian intersections.
In this talk, we discuss a problem posed by Okamoto. Starting from a knot in the 3-dimensional Euclidean space, we move its conormal bundle in the cotangent bundle by a compactly supported Hamiltonian isotopy. When its intersection with the zero-section is connected and clean, it gives rise to another knot. We ask how the knot type of this new knot is related to that of the original one.
I will explain a new constraint on this problem obtained by using microlocal sheaf theory, in terms of the fundamental groups of knot complements. This talk is based on joint work with Yukihiro Okamoto (Tokyo Metropolitan University).
[ Reference URL ]Lagrangian intersections in symplectic manifolds have been studied from various perspectives. In recent years, several works have also investigated the knot types of Lagrangian intersections.
In this talk, we discuss a problem posed by Okamoto. Starting from a knot in the 3-dimensional Euclidean space, we move its conormal bundle in the cotangent bundle by a compactly supported Hamiltonian isotopy. When its intersection with the zero-section is connected and clean, it gives rise to another knot. We ask how the knot type of this new knot is related to that of the original one.
I will explain a new constraint on this problem obtained by using microlocal sheaf theory, in terms of the fundamental groups of knot complements. This talk is based on joint work with Yukihiro Okamoto (Tokyo Metropolitan University).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/06/09
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Masato Tanabe (RIKEN iTHEMS)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masato Tanabe (RIKEN iTHEMS)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
[ Abstract ]
Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
[ Reference URL ]Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
