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 April 22, 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, 2024.
The zoom meeting will be opened 15 minutes before start.
Making audio and video recordings is prohibited.
April 8, 17:00-18:30 -- Room 056 with live streaming on Zoom
Asuka Takatsu (The University of Tokyo)
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.
April 15, 17:00-18:30 -- Room 056 with live streaming on Zoom
Kento Sakai (The University of Tokyo)
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.
April 22, 17:30-18:30 [Joint with Lie Groups and Representation Theory Seminar]
-- Room 056 with live streaming on Zoom
Takayuki Okuda (Hiroshima University)
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 $X = G/H$.
May 13, 17:00-18:30 -- Room 056 with live streaming on Zoom
Yuichi Ike (The University of Tokyo)
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.