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17:00 -- 18:30 �����Ȋw�����ȓ�(������w���L�����p�X)
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Last updated June 11, 2025
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Zoom �~�[�e�B���O�̊J�n�̓Z�~�i�[�J�n���� 15 ���قǑO�̗\��ł�.
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4��8�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
���� �� (������w��w�@�����Ȋw������)
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��15�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
��� ���l (������w��w�@�����Ȋw������)
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��22�� [Lie�Q�_�E�\���_�Z�~�i�[�ƍ���]
-- ���n�J�� (056����) & �I�����C�����p, 17:30 -- 18:30
���c ���K (�L����w)
Coarse coding theory and discontinuous groups on homogeneous spaces
Abstract: Let $M$ and $�_mathcal{I}$ be sets, and consider a surjective map
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R : M �_times M �_to �_mathcal{I}.
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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��13�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
�r �S�� (������w��w�@�����Ȋw������)
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��3�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
�z�K ���Y (�k�C����w)
Localized intersection product for maps and applications
Abstract: ���l�̂ɂ�����Ǐ������ς�g�ݍ��킹�g�|���W�[��p���Ē�`����B
����� Alexander �o�ΐ�����đ��R�z�����W�[�̃J�b�v�ςɑΉ�����B
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���� Cech-de Rham �R�z�����W�[�_�Ƒg�ݍ��킹�邱�ƂŁA
�x�N�g������A�ڑw�̗������_�ɂ����Č��ʓI�ɗp������B
���p�Ƃ��āA����������ł̓��ٕ��f��͓I�t�w�\���� Baum-Bott �����̊֎萫������A
����͓��ٗt�w�\���E���f�|�A�\���\���Ɋւ��ėl�X�Ȑl����N��������\�z�ɑ����^����B
����� M. Correa �Ƃ̋����������܂ށB
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[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��10�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
�X�� �F�V (�c��`�m��w)
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��17�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
���� �x�l (�����w������ �����n�������Z���^�[)
Rasmussen �s�ϗʂ̃R�{���f�B�Y���I���߂Ɛ}���I�Ȍv�Z
Abstract: Rasmussen �� s-�s�ϗʂ� Khovanov �z�����W�[���瓾���鐮���l�̌��іڕs�ϗʂŁC
Milnor �\�z�̑g�����I�ȍďؖ���^����Ȃǃg�|���W�[�ւ̖ڊo�܂������p�����D
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�{�u���ł́CBar-Natan �ɂ�� Khovanov �z�����W�[�̃^���O���ƃR�{���f�B�Y����p�����莮���Ɋ�Â��āCs-�s�ϗʂɂ��R�{���f�B�Y���I�ȉ��߂�^����D
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�v���v�����g: https://arxiv.org/abs/2503.05414
6��24�� -- ���n�J�� (056����) & �I�����C�����p, 17:00 -- 18:30
6��26�� �i�j�J�Ó����Əꏊ�ɂ����Ӊ�����
-- ���n�J�� (122����) & �I�����C�����p, 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.