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 May 21, 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.
June 3, 17:00-18:30 -- Room 056 with live streaming on Zoom
Tatsuo Suwa (Hokkaido University)
Localized intersection product for maps and applications
Abstract: We define localized intersection product in manifolds using combinatorial topology,
which corresponds to the cup product in relative cohomology via the Alexander duality.
It is extended to localized intersection product for maps.
Combined with the relative Cech-de Rham cohomology,
it is effectively used in the residue theory of vector bundles and coherent sheaves.
As an application, we have the functoriality of Baum-Bott residues of singular holomorphic foliations under certain conditions,
which yields answers to problems and conjectures posed by various authors concerning singular holomorphic foliations and complex Poisson structures.
This includes a joint work with M. Correa.
References
[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.
June 10, 17:00-18:30 -- Room 056 with live streaming on Zoom
Takayuki Morifuji (Keio University)
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.
June 17, 17:00-18:30 -- Room 056 with live streaming on Zoom
Taketo Sano (RIKEN iTHEMS)
A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms
Abstract: Rasmussen's s-invariant is an integer-valued knot invariant derived from Khovanov homology,
and it has remarkable applications in topology, such as providing a combinatorial reproof of the Milnor conjecture.
Although the s-invariant is defined using the quantum filtration of the homology group, it is difficult to interpret it geometrically.
In this talk, we give a cobordism-based interpretation of the s-invariant based on Bar-Natan's reformulation of Khovanov homology via tangles and cobordisms.
This interpretation allows for the computation of the s-invariant from a tangle decomposition of the knot.
As an application, we demonstrate that the s-invariants of a certain infinite family of pretzel knots can be determined by hand.
Preprint: https://arxiv.org/abs/2503.05414