[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,
もしくは
17:00 -- 18:00 Zoom でのオンライン開催
Last updated June 25, 2025
世話係
河澄 響矢
北山 貴裕
逆井 卓也
葉廣 和夫
2025 年度の夏学期も
「対面開催 & オンライン中継形式」(90 分 or 60 分) と「完全オンライン形式」(60 分)
を併用してセミナーを行います.
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4月8日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
高津 飛鳥 (東京大学大学院数理科学研究科)
Concavity and Dirichlet heat flow
Abstract: In a convex domain of Euclidean space,
the Dirichlet heat flow transmits log-concavity from the initial time to any time.
I first introduce a notion of generalized concavity and specify a concavity preserved by the Dirichlet heat flow.
Then I show that in a totally convex domain of a Riemannian manifold,
if some concavity is preserved by the Dirichlet heat flow,
then the sectional curvature must vanish on the domain.
The first part is based on joint work with Kazuhiro Ishige and Paolo Salani,
and the second part is based on joint work with Kazuhiro Ishige and Haruto Tokunaga.
4月15日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
坂井 健人 (東京大学大学院数理科学研究科)
Harmonic maps and uniform degeneration of hyperbolic surfaces with boundary
Abstract: If holomorphic quadratic differentials on a punctured Riemann surface have poles of order >1 at the punctures,
they correspond to hyperbolic surfaces with geodesic boundary via harmonic maps.
This correspondence is known as the harmonic map parametrization of hyperbolic surfaces.
In this talk, we use this parametrization to describe the degeneration of hyperbolic surfaces via Gromov-Hausdorff convergence.
As an application, we study the limit of a one-parameter family of hyperbolic surfaces in the Thurston boundary of Teichmüller space.
4月22日 [Lie群論・表現論セミナーと合同]
-- 現地開催 (056号室) & オンライン中継, 17:30 -- 18:30
奥田 隆幸 (広島大学)
Coarse coding theory and discontinuous groups on homogeneous spaces
Abstract: Let $M$ and $＼mathcal{I}$ be sets, and consider a surjective map
＼[
R : M ＼times M ＼to ＼mathcal{I}.
＼]
For each subset $＼mathcal{A} ＼subseteq ＼mathcal{I}$, we define $＼mathcal{A}$-free codes on $M$ as subsets $C ＼subseteq M$ satisfying
＼[
R(C ＼times C) ＼cap ＼mathcal{A} = ＼emptyset.
＼]
This definition encompasses various types of codes, including error-correcting codes, spherical codes, and those defined on association schemes or homogeneous spaces.
In this talk, we introduce a "pre-bornological coarse structure" on $＼mathcal{I}$ and define the notion of coarsely $＼mathcal{A}$-free codes on $M$.
This extends the concept of $＼mathcal{A}$-free codes introduced above. As a main result, we establish relationships between coarse coding theory on Riemannian homogeneous spaces $M = G/K$ and discontinuous group theory on non-Riemannian homogeneous spaces $X = G/H$.
5月13日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
池 祐一 (東京大学大学院数理科学研究科)
Interleaving distance for sheaves and its application to symplectic geometry
Abstract: The Interleaving distance was first introduced in the context of the stability of persistent homology
and is now used in various fields. It was adapted to sheaves by the pioneering work of Curry,
and later in the derived setting by Kashiwara and Schapira.
In this talk, I will explain that the interleaving distance for sheaves is related to the energy of Hamiltonian actions on cotangent bundles.
Moreover, I will show that the derived interleaving distance is complete,
which enables us to treat non-smooth objects in symplectic geometry using sheaf-theoretic methods.
This is based on joint work with Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, and Claude Viterbo.
6月3日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
諏訪 立雄 (北海道大学)
Localized intersection product for maps and applications
Abstract: 多様体における局所交叉積を組み合わせトポロジーを用いて定義する。
これは Alexander 双対性を介して相対コホモロジーのカップ積に対応する。
さらにこれは写像の局所交叉積にも拡張され、
相対 Cech-de Rham コホモロジー論と組み合わせることで、
ベクトル束や連接層の留数理論において効果的に用いられる。
応用として、ある条件下での特異複素解析的葉層構造の Baum-Bott 留数の関手性があり、
これは特異葉層構造・複素ポアソン構造に関して様々な人が提起した問題や予想に対する解答を与える。
これは M. Correa との共同研究を含む。
参考文献
[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.
6月10日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
森藤 孝之 (慶應義塾大学)
Bell polynomials and hyperbolic volume of knots
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.
6月17日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
佐野 岳人 (理化学研究所 数理創造研究センター)
Rasmussen 不変量のコボルディズム的解釈と図式的な計算
Abstract: Rasmussen の s-不変量は Khovanov ホモロジーから得られる整数値の結び目不変量で，
Milnor 予想の組合せ的な再証明を与えるなどトポロジーへの目覚ましい応用を持つ．
s-不変量は量子次数によるホモロジー群のフィルトレーションを用いて定義されるものであるが，そこから幾何的な意味を読み取るのは難しい．
本講演では，Bar-Natan による Khovanov ホモロジーのタングルとコボルディズムを用いた定式化に基づいて，s-不変量にもコボルディズム的な解釈を与える．
この解釈によって，s-不変量は結び目のタングル分解から計算ができるようになる．
応用として，特定のプレッツェル結び目の無限族の s-不変量が手計算によって決定できることを示す．
プレプリント: https://arxiv.org/abs/2503.05414
6月24日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
6月26日 （木）開催日時と場所にご注意下さい
-- 現地開催 (122号室) & オンライン中継, 15:30 -- 17:00
Danny Calegari (The University of Chicago)
Universal circles and Zippers
Abstract: If M is a hyperbolic 3-manifold fibering over the circle,
then the fundamental group of M acts faithfully by homeomorphisms on a circle―the circle at infinity of the universal cover of the fiber―preserving a pair of invariant (stable and unstable) laminations.
Many different kinds of dynamical structures including taut foliations and quasigeodesic or pseudo-Anosov flows are known to give rise to universal circles―a circle with a faithful action of the fundamental group preserving a pair of invariant laminations―and those universal circles play a key role in relating the dynamical structure to the geometry of M.
In these two talks, I will introduce the idea of *zippers*, which give a new and direct way to construct universal circles, streamlining the known constructions in many cases, and giving a host of new constructions in others.
In particular, zippers―and their associated universal circles―may be constructed directly from homological objects (uniform quasimorphisms), causal structures (uniform left orders),
and many other structures. This is joint work with Ino Loukidou.
7月1日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:00
佐藤 玄基 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories
Abstract: In this talk, we present a novel construction that,
for a given Reedy category $C$,
produces a direct category $＼operatorname{Down}(C)$ and a functor $＼operatorname{Down}(C) ＼to C$,
exhibiting $C$ as an $(＼infty,1)$-categorical localization of $＼operatorname{Down}(C)$.
This result refines previous constructions in the literature by ensuring that $＼operatorname{Down}(C)$ is finite whenever $C$ is finite-a property not guaranteed by existing approaches,
such as those by Lurie or by Barwick and Kan.
As an intended future application,
this finiteness property is expected to be useful for embedding the construction into the syntax of a (non-infinitary) logic. In particular,
I expect that the construction may be used to develop a meta-theory of finitely truncated simplicial types and other finite Reedy presheaves for homotopy type theory,
thereby extending Kraus and Sattler's unfinished approach.
This talk is based on arXiv:2502.05096.
7月8日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
石倉 宙樹 (東京大学大学院数理科学研究科)
Stallings-Swan's Theorem for Borel graphs
Abstract: A Borel graph is a simplicial graph on a standard Borel space X such that the edge set is a Borel subset of X^2.
Such objects have been studied in the context of countable Borel equivalence relations,
and recently there are many attempts to apply the ideas of geometric group theory to them.
Stallings-Swan's theorem states that groups of cohomological dimension 1 are free groups.
We will talk about an analog of this theorem for Borel graphs:
A Borel graph on X with uniformly bounded degrees of cohomological dimension 1 is Lipschitz equivalent to a Borel acyclic graph on X.
This is proved by establishing a criterion for certain decomposition of Borel graphs,
which is inspired by Dunwoody's work on accessibility of groups.
7月15日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
Anastasiia Tsvietkova (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold
Abstract: For a low-dimensional manifold,
one often tries to understand its intrinsic topology through its submanifolds,
in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold.
However to construct, classify or count such surfaces is a non-trivial task.
We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold,
polynomial in hyperbolic volume.
The surfaces are all closed essential surfaces, oriented and connected.
This is joint work with Marc Lackenby.
7月22日 -- 現地開催 (056号室) & オンライン中継, 17:00 -- 18:30
Alexis Marchand (京都大学)
Sharp spectral gaps for scl from negative curvature
Abstract: Stable commutator length is a measure of homological complexity of group elements,
with connections to many topics in geometric topology,
including quasimorphisms, bounded cohomology, and simplicial volume.
The goal of this talk is to shed light on some of its relations with negative curvature.
We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups.
Our proof relates letter-quasimorphisms
(which are analogues of real-valued quasimorphisms with image in free groups)
to negatively curved angle structures for surfaces estimating scl.