Tuesday Seminar on Topology

[Japanese]   [Past Programs]
17:00 -- 18:30 Graduate School of Mathematical Sciences, The University of Tokyo (with live streaming on Zoom)
or
17:00 -- 18:00 Online seminar on Zoom.

Last updated November 4, 2025
Information :
Kazuo Habiro
Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai

Pre-registration is required.
Once you register, you can attend all our seminars until the end of March, 2026.
The zoom meeting will be opened 15 minutes before start.

Making audio and video recordings is prohibited.

October 7, 17:00-18:30 -- Online on Zoom

Sakumi Sugawara (Hokkaido University)

Topology of hyperplane arrangements and related 3-manifolds

Abstract: One of the central questions in the topology of hyperplane arrangements is whether several topological invariants are combinatorially determined. While the cohomology ring of the complement has a combinatorial description, it remains open whether even the first Betti number of the Milnor fiber is. In contrast, the homeomorphism types of 3-manifolds appearing as the boundary manifold of projective line arrangements and the Milnor fiber boundary of arrangements in a 3-dimensional space are combinatorially determined. In this talk, we focus on these 3-manifolds. In particular, we will present the cohomology ring structure for the boundary manifold, originally due to Cohen-Suciu, and an explicit formula for the homology group of the Milnor fiber boundary of generic arrangements.

October 14, 17:00-18:30 -- Room 056 with live streaming on Zoom

Keiji Oguiso (The University of Tokyo)

On K3 surfaces with non-elementary hyperbolic automorphism group

Abstract: This talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).
Main result of this talk is the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic, under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling basic facts and some special nice properties of K3 surfaces, the notion of hyperbolicity of group due to Gromov, and their importance and interest (in our view), I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Néron-Severi lattices and then how one can deduce the above-mentioned finiteness, via a recent important observation by Professors Kikuta and Takatsu (independently) on geometrically finiteness, with a new algebro-geometric study of genus one fibrations on K3 surfaces by us.

October 28, 17:00-18:30 -- Room 056 with live streaming on Zoom

Ayumu Inoue (Tsuda University)

On a relationship between quandle homology and relative group homology, from the view point of Seifert surfaces

Abstract: Quandles and their homology are known to have good chemistry with knot theory. Associated with a triple of a group G, its automorphism, and its subgroup H satisfying a certain condition, we have a quandle. In this talk, we see that we have a chain map from the quandle chain complex of the quandle to the (Adamson/Hochschild) relative group chain complex of (G, H). We also see that this chain map has good chemistry with a triangulation of Seifert surface of a knot.

November 4, 17:00-18:00 -- Online on Zoom

Kazuto Takao (Tohoku University)

Diagrammatic criteria for strong irreducibility of Heegaard splittings and finiteness of Goeritz groups

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.

November 11

(1) 9:30-10:30 -- Online on Zoom

Richard Hain (Duke University)

Mapping class group actions on the homology of configuration spaces

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.


(2) 17:00-18:30 -- Room 056 with live streaming on Zoom

Serban Matei Mihalache (The University of Tokyo)

Constructing solution of Polygon and Simplex equation

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.

November 18, 17:30-18:30 -- Room 056 with live streaming on Zoom

Masaki Tsukamoto (Kyoto University)

Rate distortion dimension of random Brody curves

Abstract: Brody curves are one-Lipschtiz holomorphic maps from the complex plane to the complex projective space. Entire holomorphic curves have been studied over a century since Nevanlinna and H. Cartan, but there still remain many fundamental questions. In this talk we explain that ideas of ergodic theory and geometric measure theory provide a radically new approach on them. Roughly speaking, we show that Brody curves have an ergodic theoretic structure somehow analogous to that of Axiom A diffeomorphisms. In particular we establish "Ruelle inequality" and "existence of equilibrium measures" for Brody curves.

November 25, 17:00-18:00 -- Online on Zoom

Katsuhiko Kuribayashi (Shinshu University)

Interleavings of persistence dg-modules and Sullivan models for maps

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.