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Tuesday Seminar on Topology
Seminar information archive ～10/31｜Next seminar｜Future seminars 11/01～
| 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
2025/11/04
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Kazuto Takao (Tohoku University)
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kazuto Takao (Tohoku University)
Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups (JAPANESE)
[ Abstract ]
Casson-Gordon gave a criterion for Heegaard splittings of 3-manifolds to be strongly irreducible. By strengthening it, Lustig-Moriah gave a criterion for Goeritz groups of Heegaard splittings to be finite. Their criteria are based on Heegaard diagrams formed by maximal disk systems of the handlebodies. We generalize them for arbitrary disk systems, including minimal ones. As an application, we give Heegaard splittings with non-minimal genera and finite Goeritz groups. This is based on joint work with Yuya Koda.
[ Reference URL ]Casson-Gordon gave a criterion for Heegaard splittings of 3-manifolds to be strongly irreducible. By strengthening it, Lustig-Moriah gave a criterion for Goeritz groups of Heegaard splittings to be finite. Their criteria are based on Heegaard diagrams formed by maximal disk systems of the handlebodies. We generalize them for arbitrary disk systems, including minimal ones. As an application, we give Heegaard splittings with non-minimal genera and finite Goeritz groups. This is based on joint work with Yuya Koda.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/11/11
9:30-10:30 Online
Pre-registration required. See our seminar webpage.
Richard Hain (Duke University)
Mapping class group actions on the homology of configuration spaces (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Richard Hain (Duke University)
Mapping class group actions on the homology of configuration spaces (ENGLISH)
[ Abstract ]
The action of the mapping class group of a surface S on the homology of the space F_n(S) of ordered configurations of n points in S is well understood when S has genus 0, but is not very well understood when S has positive genus. In this talk I will report on joint work with Clément Dupont (Montpellier) in the case where S is a surface of finite type of genus at least 2. We give a strong lower bound on the size of the Zariski closure of the image of the Torelli and mapping class groups in the automorphism group of the degree n cohomology of F_n(S). Our main tools are Hodge theory and the Goldman Lie algebra of the surface, which is the free abelian group generated by the conjugacy classes in the fundamental group of S.
[ Reference URL ]The action of the mapping class group of a surface S on the homology of the space F_n(S) of ordered configurations of n points in S is well understood when S has genus 0, but is not very well understood when S has positive genus. In this talk I will report on joint work with Clément Dupont (Montpellier) in the case where S is a surface of finite type of genus at least 2. We give a strong lower bound on the size of the Zariski closure of the image of the Torelli and mapping class groups in the automorphism group of the degree n cohomology of F_n(S). Our main tools are Hodge theory and the Goldman Lie algebra of the surface, which is the free abelian group generated by the conjugacy classes in the fundamental group of S.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/11/11
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Serban Matei Mihalache (The University of Tokyo)
Constructing solution of Polygon and Simplex equation (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Serban Matei Mihalache (The University of Tokyo)
Constructing solution of Polygon and Simplex equation (JAPANESE)
[ Abstract ]
The Polygon equation, formulated by Dimakis and Müller-Hoissen, can be interpreted as an algebraic equation corresponding to the Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-move on triangulations of n-dimensional PL manifolds, and is expected that this can be used to construct invariants of PL manifolds. In this talk, we show that solutions of higher-dimensional Polygon equations can be constructed from collections of "commutative" solutions of lower-dimensional Polygon equations, and we present explicit examples of such solutions. Furthermore, when a pair of solutions of the Polygon equation satisfies a condition called the mixed relation, we show that it gives rise to a solution of the Simplex equation, which is a higher-dimensional analogue of the Yang–Baxter equation. This talk is based on joint work with Tomoro Mochida.
[ Reference URL ]The Polygon equation, formulated by Dimakis and Müller-Hoissen, can be interpreted as an algebraic equation corresponding to the Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-move on triangulations of n-dimensional PL manifolds, and is expected that this can be used to construct invariants of PL manifolds. In this talk, we show that solutions of higher-dimensional Polygon equations can be constructed from collections of "commutative" solutions of lower-dimensional Polygon equations, and we present explicit examples of such solutions. Furthermore, when a pair of solutions of the Polygon equation satisfies a condition called the mixed relation, we show that it gives rise to a solution of the Simplex equation, which is a higher-dimensional analogue of the Yang–Baxter equation. This talk is based on joint work with Tomoro Mochida.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/11/25
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Interleavings of persistence dg-modules and Sullivan models for maps (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsuhiko Kuribayashi (Shinshu University)
Interleavings of persistence dg-modules and Sullivan models for maps (JAPANESE)
[ Abstract ]
The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
[ Reference URL ]The cohomology interleaving distance (CohID) is introduced and considered in the category of persistence differential graded modules. As a consequence, we show that, in the category, the distance coincides with the the homotopy commutative interleaving distance, the homotopy interleaving distance originally due to Blumberg and Lesnick, and the interleaving distance in the homotopy category (IDHC) in the sense of Lanari and Scoccola. Moreover, by applying the CohID to spaces over the classifying space of the circle group via the singular cochain functor, we have a numerical two-variable homotopy invariant for such spaces. In the latter half of the talk, we consider extended tame persistence commutative differential graded algebras (CDGA) associated with relative Sullivan algebras. Then, the IDHC enables us to introduce an extended pseudodistance between continuous maps with such persistence objects. By examining the pseudodistance, we see that the persistence CDGA is more `sensitive' than the persistence homology. This talk is based on joint work with Naito, Sekizuka, Wakatsuki and Yamaguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
