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 October 15, 2025
Information :
Kazuo Habiro
Nariya Kawazumi
Takahiro Kitayama
Takuya Sakasai
The seminar scheduled for October 23rd has been postponed.
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.