[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 April 22, 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.
各回の開催の形式については本ページにてご案内いたします.
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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.