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Tuesday Seminar on Topology
Seminar information archive ～05/20｜Next seminar｜Future seminars 05/21～
| 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
2025/06/03
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tatsuo Suwa (Hokkaido University)
Localized intersection product for maps and applications (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsuo Suwa (Hokkaido University)
Localized intersection product for maps and applications (JAPANESE)
[ Abstract ]
We define localized intersection product in manifolds using combinatorial topology, which corresponds to the cup product in relative cohomology via the Alexander duality. It is extended to localized intersection product for maps. Combined with the relative Cech-de Rham cohomology, it is effectively used in the residue theory of vector bundles and coherent sheaves. As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions, which yields answers to problems and conjectures posed by various authors concerning singular holomorphic foliations and complex Poisson structures. This includes a joint work with M. Correa.
References
[1] M. Correa and T. Suwa, On functoriality of Baum-Bott residues, arXiv:2501.15133.
[2] T. Suwa, Complex Analytic Geometry - From the Localization Viewpoint,
World Scientific, 2024.
[ Reference URL ]We define localized intersection product in manifolds using combinatorial topology, which corresponds to the cup product in relative cohomology via the Alexander duality. It is extended to localized intersection product for maps. Combined with the relative Cech-de Rham cohomology, it is effectively used in the residue theory of vector bundles and coherent sheaves. As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions, which yields answers to problems and conjectures posed by various authors concerning singular holomorphic foliations and complex Poisson structures. This includes a joint work with M. Correa.
References
[1] M. Correa and T. Suwa, On functoriality of Baum-Bott residues, arXiv:2501.15133.
[2] T. Suwa, Complex Analytic Geometry - From the Localization Viewpoint,
World Scientific, 2024.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/06/10
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Takayuki Morifuji (Keio University)
Bell polynomials and hyperbolic volume of knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Takayuki Morifuji (Keio University)
Bell polynomials and hyperbolic volume of knots (JAPANESE)
[ Abstract ]
In this talk, we introduce two volume formulas for hyperbolic knot complements using Bell polynomials. The first applies to hyperbolic fibered knots and expresses the volume of the complement in terms of the trace of the monodromy matrix. The second provides a formula for the volume of general hyperbolic knot complements based on a weighted adjacency matrix. This talk is based on joint work with Hiroshi Goda.
[ Reference URL ]In this talk, we introduce two volume formulas for hyperbolic knot complements using Bell polynomials. The first applies to hyperbolic fibered knots and expresses the volume of the complement in terms of the trace of the monodromy matrix. The second provides a formula for the volume of general hyperbolic knot complements based on a weighted adjacency matrix. This talk is based on joint work with Hiroshi Goda.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/06/17
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN iTHEMS)
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Taketo Sano (RIKEN iTHEMS)
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms (JAPANESE)
[ Abstract ]
Rasmussen's s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of a certain infinite family of pretzel knots can be determined by hand.
[ Reference URL ]Rasmussen's s-invariant is an integer-valued knot invariant derived from Khovanov homology, and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture. Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically. In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan’s reformulation of Khovanov homology via tangles and cobordisms. This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot. As an application, we demonstrate that the s-invariants of a certain infinite family of pretzel knots can be determined by hand.
Preprint: https://arxiv.org/abs/2503.05414
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
