[English] [過去のプログラム]
17:00 -- 18:30 数理科学研究科棟(東京大学駒場キャンパス)
での対面開催と Zoom でのオンライン配信,
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17:00 -- 18:00 Zoom でのオンライン開催
Last updated September 16, 2025
世話係
河澄 響矢
北山 貴裕
逆井 卓也
葉廣 和夫
2025 年度の冬学期も
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10月7日 -- オンライン開催, 17:00 -- 18:00
菅原 朔見 (北海道大学)
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.
10月14日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
小木曾 啓示 (東京大学大学院数理科学研究科)
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.
10月23日（木）開催日時にご注意下さい -- 現地開催 (教室未定) & オンライン中継, 15:30 -- 17:00
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.