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過去の記録
過去の記録 ～04/07｜本日 04/08 | 今後の予定 04/09～
2025年07月07日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
丸亀 泰二 氏 (電気通信大学)
Chains on twistor CR manifolds and conformal geodesics in dimension three (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
丸亀 泰二 氏 (電気通信大学)
Chains on twistor CR manifolds and conformal geodesics in dimension three (Japanese)
[ 講演概要 ]
任意の3次元共形多様体$(\Sigma, [g])$には，ツイスターCR多様体と呼ばれる5次元Lorentz CR多様体が付随する．$M$は，$\Sigma$上の計量$g$を固定すると，$(\Sigma, g)$の単位接球面束と同一視できる．この講演では，$M$に対するFefferman計量(CR多様体の$S^1$束上に自然に定まる共形計量)を，$(\Sigma, g)$のフレーム束上に具体的に構成し，$M$上の自然な曲線族であるchainの射影が，$\Sigma$上の共形測地線となることを説明する．応用として，3次元共形多様体の共形測地線が，全捩率汎関数の臨界曲線として特徴づけられることを述べる．
[ 参考URL ]任意の3次元共形多様体$(\Sigma, [g])$には，ツイスターCR多様体と呼ばれる5次元Lorentz CR多様体が付随する．$M$は，$\Sigma$上の計量$g$を固定すると，$(\Sigma, g)$の単位接球面束と同一視できる．この講演では，$M$に対するFefferman計量(CR多様体の$S^1$束上に自然に定まる共形計量)を，$(\Sigma, g)$のフレーム束上に具体的に構成し，$M$上の自然な曲線族であるchainの射影が，$\Sigma$上の共形測地線となることを説明する．応用として，3次元共形多様体の共形測地線が，全捩率汎関数の臨界曲線として特徴づけられることを述べる．
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
髙野 凌史 氏 (大阪大学)
A semigroup approach to the reconstruction theorem for singular modelled distributions and its application
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
髙野 凌史 氏 (大阪大学)
A semigroup approach to the reconstruction theorem for singular modelled distributions and its application
[ 講演概要 ]
In our recent research, we extended a semigroup approach used in Otto & Weber (2019) and Hoshino (2023) to provide an alternative proof of the reconstruction theorem for singular modelled distributions. As an application, we constructed a local-in-time solution to the two-dimensional parabolic Anderson model with a non-translation-invariant differential operator. In this talk, I will introduce the idea of constructing solutions to singular SPDEs based on the theory of regularity structures and highlight the differences between our approach and previous works. I will then present main results of our study. This talk is based on joint work with Masato Hoshino (Institute of Science Tokyo).
In our recent research, we extended a semigroup approach used in Otto & Weber (2019) and Hoshino (2023) to provide an alternative proof of the reconstruction theorem for singular modelled distributions. As an application, we constructed a local-in-time solution to the two-dimensional parabolic Anderson model with a non-translation-invariant differential operator. In this talk, I will introduce the idea of constructing solutions to singular SPDEs based on the theory of regularity structures and highlight the differences between our approach and previous works. I will then present main results of our study. This talk is based on joint work with Masato Hoshino (Institute of Science Tokyo).
2025年07月04日(金)
博士論文発表会
13:45-15:00 数理科学研究科棟(駒場) 128号室
今井 湖都 氏 (東京大学大学院数理科学研究科)
Ramification groups of Galois extensions over local fields of
positive characteristic with Galois group isomorphic to
the group of unitriangular matrices
(冪単三角行列の群と同型なGalois群を持つ正標数局所体上の
Galois拡大の分岐群)
今井 湖都 氏 (東京大学大学院数理科学研究科)
Ramification groups of Galois extensions over local fields of
positive characteristic with Galois group isomorphic to
the group of unitriangular matrices
(冪単三角行列の群と同型なGalois群を持つ正標数局所体上の
Galois拡大の分岐群)
2025年07月03日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
確率論セミナーと合同開催
Jessica Lin 氏 (McGill University)
Generalized Front Propagation for Stochastic Spatial Models (English)
確率論セミナーと合同開催
Jessica Lin 氏 (McGill University)
Generalized Front Propagation for Stochastic Spatial Models (English)
[ 講演概要 ]
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (University of Bath).
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (University of Bath).
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
教室は１２8です。応用解析セミナーとの合同セミナーです。 今日はTea Time はありません。
Jessica Lin 氏 (McGill University)
Generalized Front Propagation for Stochastic Spatial Models
教室は１２8です。応用解析セミナーとの合同セミナーです。 今日はTea Time はありません。
Jessica Lin 氏 (McGill University)
Generalized Front Propagation for Stochastic Spatial Models
[ 講演概要 ]
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (University of Bath).
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (University of Bath).
2025年07月02日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
藤井天守 氏 (東京大学大学院数理科学研究科)
Parametrization of supercuspidal representations of depth-zero for some simple adjoint groups (日本語)
藤井天守 氏 (東京大学大学院数理科学研究科)
Parametrization of supercuspidal representations of depth-zero for some simple adjoint groups (日本語)
[ 講演概要 ]
We construct a surjective map from the set of conjugacy classes of depth-zero enhanced L-parameters to that of isomorphism classes of depth-zero supercuspidal representations for simple adjoint groups, and check the bijectivity in various cases. We also prove that the Hiraga--Ichino--Ikeda conjecture on the formal degree of essentially square-integrable representations holds for this parametrization if it is bijective.
We construct a surjective map from the set of conjugacy classes of depth-zero enhanced L-parameters to that of isomorphism classes of depth-zero supercuspidal representations for simple adjoint groups, and check the bijectivity in various cases. We also prove that the Hiraga--Ichino--Ikeda conjecture on the formal degree of essentially square-integrable representations holds for this parametrization if it is bijective.
2025年07月01日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 117号室
星野真生 氏 (東大数理)
A tensor categorical aspect of quantum group actions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
星野真生 氏 (東大数理)
A tensor categorical aspect of quantum group actions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐藤 玄基 氏 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐藤 玄基 氏 (株式会社 fcuro)
Presentation of finite Reedy categories as localizations of finite direct categories (JAPANESE)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年06月30日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
Hugo Da Cunha 氏 (Université Lyon 1)
Boundary effects in the Facilitated Exclusion Process
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
Hugo Da Cunha 氏 (Université Lyon 1)
Boundary effects in the Facilitated Exclusion Process
[ 講演概要 ]
The Facilitated Exclusion Process (FEP) is a model of stochastic interacting particle system whose dynamics is subject to kinetic constraints, leading to a phase transition at the critical density 1/2: under this threshold, the system is completely frozen. In recent years, the FEP has been extensively studied on the periodic setting, but in this talk I will consider it with boundary conditions. I will focus first on open boundaries, with particles reservoirs at both ends allowing creation/annihilation of particles. If time allows, I will also consider the case of closed boundaries, when there are impermeable walls at both ends.
At the macroscopic level, the boundary dynamics impose some boundary conditions on the PDE describing the hydrodynamic limit, that can be of different types (such as Dirichlet, Neumann or Robin). These boundary conditions are not standard as they differ from what is usually found in other exclusion processes, and this is due to the two-phased nature of FEP.
This talk is based on joint works with Clément Erignoux, Marielle Simon and Lu Xu.
The Facilitated Exclusion Process (FEP) is a model of stochastic interacting particle system whose dynamics is subject to kinetic constraints, leading to a phase transition at the critical density 1/2: under this threshold, the system is completely frozen. In recent years, the FEP has been extensively studied on the periodic setting, but in this talk I will consider it with boundary conditions. I will focus first on open boundaries, with particles reservoirs at both ends allowing creation/annihilation of particles. If time allows, I will also consider the case of closed boundaries, when there are impermeable walls at both ends.
At the macroscopic level, the boundary dynamics impose some boundary conditions on the PDE describing the hydrodynamic limit, that can be of different types (such as Dirichlet, Neumann or Robin). These boundary conditions are not standard as they differ from what is usually found in other exclusion processes, and this is due to the two-phased nature of FEP.
This talk is based on joint works with Clément Erignoux, Marielle Simon and Lu Xu.
2025年06月27日(金)
東京無限可積分系セミナー
14:00-16:00 数理科学研究科棟(駒場) 056号室
Boris Feigin 氏 (Hebrew University)
W-algebra for supergroups, cosets and Langlands-type duality for supergroups
(English)
Boris Feigin 氏 (Hebrew University)
W-algebra for supergroups, cosets and Langlands-type duality for supergroups
(English)
[ 講演概要 ]
I try to explain what is known about the Langlands duality for superalgebras and also say something about center on a critical level for superalgebras.
I try to explain what is known about the Langlands duality for superalgebras and also say something about center on a critical level for superalgebras.
2025年06月26日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
Yang Yang 氏 (Johns Hopkins University)
A half-space Bernstein theorem for anisotropic minimal graphs (English)
Yang Yang 氏 (Johns Hopkins University)
A half-space Bernstein theorem for anisotropic minimal graphs (English)
[ 講演概要 ]
Anisotropic functionals are the natural generalization of the area functional. From a technical perspective, what distinguishes general anisotropic functionals from the area case is the absence of a monotonicity formula. In this talk, we will present a proof of a half-space Bernstein theorem for anisotropic minimal graphs with flat boundary condition. The proof uses only the maximal principle and ideas from fully nonlinear PDE theory in lieu of a monotonicity formula. This is joint work with W. Du, C. Moony, and J. Zhu.
Anisotropic functionals are the natural generalization of the area functional. From a technical perspective, what distinguishes general anisotropic functionals from the area case is the absence of a monotonicity formula. In this talk, we will present a proof of a half-space Bernstein theorem for anisotropic minimal graphs with flat boundary condition. The proof uses only the maximal principle and ideas from fully nonlinear PDE theory in lieu of a monotonicity formula. This is joint work with W. Du, C. Moony, and J. Zhu.
トポロジー火曜セミナー
15:30-17:00 数理科学研究科棟(駒場) hybrid/122号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Danny Calegari 氏 (The University of Chicago)
Universal circles and Zippers (2) (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Danny Calegari 氏 (The University of Chicago)
Universal circles and Zippers (2) (ENGLISH)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年06月24日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 117号室
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
George Elliott 氏 (Univ. Toronto)
Recent progress in the classification of $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Danny Calegari 氏 (The University of Chicago)
Universal circles and Zippers (1) (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Danny Calegari 氏 (The University of Chicago)
Universal circles and Zippers (1) (ENGLISH)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年06月23日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
菊池 翔太 氏 (鈴鹿工業高等専門学校)
Some properties of Azukawa pseudometrics for pluricomplex Green functions with poles along subvarieties (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
菊池 翔太 氏 (鈴鹿工業高等専門学校)
Some properties of Azukawa pseudometrics for pluricomplex Green functions with poles along subvarieties (Japanese)
[ 講演概要 ]
The Azukawa pseudometric is defined as the difference between the pluricomplex Green function and its logarithmic term along each complex lines passing through a pole. Therefore, the Azukawa pseudometric is useful to study the behavior of the pluricomplex Green function around a pole. It is also known that the Azukawa pseudometric is closely related to several important objects in complex analysis, including the Crath\'{e}odory-Reiffen pseudometric, the Kobayashi-Reiffen pseudometric, the Bergman kernel, among others.
In this talk, we present some properties and applications of an analogue of the Azukawa pseudometric for the pluricomplex Green function with poles along subvarieties.
If time permits, I will also explain my recent studies related to this topic.
[ 参考URL ]The Azukawa pseudometric is defined as the difference between the pluricomplex Green function and its logarithmic term along each complex lines passing through a pole. Therefore, the Azukawa pseudometric is useful to study the behavior of the pluricomplex Green function around a pole. It is also known that the Azukawa pseudometric is closely related to several important objects in complex analysis, including the Crath\'{e}odory-Reiffen pseudometric, the Kobayashi-Reiffen pseudometric, the Bergman kernel, among others.
In this talk, we present some properties and applications of an analogue of the Azukawa pseudometric for the pluricomplex Green function with poles along subvarieties.
If time permits, I will also explain my recent studies related to this topic.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025年06月20日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室(auditorium)号室
池祐一 氏 (東京大学大学院数理科学研究科)
正方形杭問題と超局所層理論 (JAPANESE)
池祐一 氏 (東京大学大学院数理科学研究科)
正方形杭問題と超局所層理論 (JAPANESE)
[ 講演概要 ]
正方形杭問題（square peg problem）とは「平面内の単純閉曲線が与えられたとき，その上に正方形の4頂点となる異なる4点が存在するかどうか」を問うもので，1911年にToeplitzによって提起されたが現在も未解決である．この問題はより一般に，辺の比が指定された長方形の存在を問う長方形杭問題に拡張できる．GreeneとLobbは，シンプレクティック幾何を用いて滑らかな曲線に対する長方形杭問題を肯定的に解決し，後にFloer理論におけるスペクトル不変量を用いて結果を改良した．本講演では，超局所層理論を用いると，長さ有限の単純閉曲線に対する長方形杭問題を肯定的に解決できることを紹介する．これは浅野知紘氏との共同研究に基づく．
正方形杭問題（square peg problem）とは「平面内の単純閉曲線が与えられたとき，その上に正方形の4頂点となる異なる4点が存在するかどうか」を問うもので，1911年にToeplitzによって提起されたが現在も未解決である．この問題はより一般に，辺の比が指定された長方形の存在を問う長方形杭問題に拡張できる．GreeneとLobbは，シンプレクティック幾何を用いて滑らかな曲線に対する長方形杭問題を肯定的に解決し，後にFloer理論におけるスペクトル不変量を用いて結果を改良した．本講演では，超局所層理論を用いると，長さ有限の単純閉曲線に対する長方形杭問題を肯定的に解決できることを紹介する．これは浅野知紘氏との共同研究に基づく．
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
岡村 郁弥 氏 (中央大学)
Moduli spaces of rational curves on Artin-Mumford double solids
岡村 郁弥 氏 (中央大学)
Moduli spaces of rational curves on Artin-Mumford double solids
[ 講演概要 ]
Artin-Mumford double solids were originally constructed as examples of unirational but irrational varieties. Their method showed that the Brauer group gives an obstruction to rationality. Later, Voisin observed that this obstruction measures the difference between algebraic and numerical equivalence for 1-cycles.
In this talk, we study the moduli spaces of rational curves on Artin-Mumford double solids. First, we discuss the relation between the spaces of lines on these varieties and certain Enriques surfaces known as Reye congruences. Then, we classify all irreducible components of the moduli spaces of rational curves of each degree, and prove Geometric Manin's Conjecture in this setting.
Artin-Mumford double solids were originally constructed as examples of unirational but irrational varieties. Their method showed that the Brauer group gives an obstruction to rationality. Later, Voisin observed that this obstruction measures the difference between algebraic and numerical equivalence for 1-cycles.
In this talk, we study the moduli spaces of rational curves on Artin-Mumford double solids. First, we discuss the relation between the spaces of lines on these varieties and certain Enriques surfaces known as Reye congruences. Then, we classify all irreducible components of the moduli spaces of rational curves of each degree, and prove Geometric Manin's Conjecture in this setting.
2025年06月18日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
劉 元旻 氏 (東京大学大学院数理科学研究科)
p-Adic cohomology over Laurent series rings and weight spectral sequences of strictly semistable schemes (日本語 (Japanese))
劉 元旻 氏 (東京大学大学院数理科学研究科)
p-Adic cohomology over Laurent series rings and weight spectral sequences of strictly semistable schemes (日本語 (Japanese))
[ 講演概要 ]
Let $k$ be a field of characteristic $p > 0$. Berthelot defined the rigid cohomology for varieties over $k$ after the work of Monsky-Washnitzer and Dwork. He also consider the theory of arithmetic D-modules which should be the coefficients for rigid cohomology. His work is generalized by Lazda-Pál and Caro to theories over $k((t))$. I will talk about their generalization and the construction of weight spectral sequence of strictly semistable schemes using arithmetic D-modules.
Let $k$ be a field of characteristic $p > 0$. Berthelot defined the rigid cohomology for varieties over $k$ after the work of Monsky-Washnitzer and Dwork. He also consider the theory of arithmetic D-modules which should be the coefficients for rigid cohomology. His work is generalized by Lazda-Pál and Caro to theories over $k((t))$. I will talk about their generalization and the construction of weight spectral sequence of strictly semistable schemes using arithmetic D-modules.
2025年06月17日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 117号室
粟津光 氏 (東大数理)
Amenability of group actions on compact spaces and the associated Banach algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
粟津光 氏 (東大数理)
Amenability of group actions on compact spaces and the associated Banach algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) ハイブリッド開催/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐野 岳人 氏 (理化学研究所 数理創造研究センタ)
Rasmussen 不変量のコボルディズム的解釈と図式的な計算 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
佐野 岳人 氏 (理化学研究所 数理創造研究センタ)
Rasmussen 不変量のコボルディズム的解釈と図式的な計算 (JAPANESE)
[ 講演概要 ]
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．
[ 参考URL ]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
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年06月16日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
高倉 真和 氏 (東京都立大学)
On the sharp $L^2$-estimate of Skoda division theorem (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
高倉 真和 氏 (東京都立大学)
On the sharp $L^2$-estimate of Skoda division theorem (Japanese)
[ 講演概要 ]
割算問題とは、与えられた正則関数の組 $f, g_1, \dots, g_r$ に対して、$\sum h_i g_i = f$ を満たす正則関数の組 $h_1, \dots, h_r$ が存在するかを問う問題である。Skoda はこの問題を Hörmander の $L^2$ 存在定理を用いて研究し、$L^2$ 評価付きの解の存在定理を与えた。
本講演では、Skoda の割算定理を乗数イデアル層に対する割算定理として一般化し、その最良の $L^2$ 評価を与える。また、この評価が多重劣調和関数の特徴付けになっていることを説明する。さらに、Guan–Zhou による最良評価付き $L^2$ 拡張定理や強開性定理が、この割算定理の系として導かれることを紹介する。
[ 参考URL ]割算問題とは、与えられた正則関数の組 $f, g_1, \dots, g_r$ に対して、$\sum h_i g_i = f$ を満たす正則関数の組 $h_1, \dots, h_r$ が存在するかを問う問題である。Skoda はこの問題を Hörmander の $L^2$ 存在定理を用いて研究し、$L^2$ 評価付きの解の存在定理を与えた。
本講演では、Skoda の割算定理を乗数イデアル層に対する割算定理として一般化し、その最良の $L^2$ 評価を与える。また、この評価が多重劣調和関数の特徴付けになっていることを説明する。さらに、Guan–Zhou による最良評価付き $L^2$ 拡張定理や強開性定理が、この割算定理の系として導かれることを紹介する。
https://forms.gle/gTP8qNZwPyQyxjTj8
2025年06月11日(水)
Lie群論・表現論セミナー
14:00-15:00 数理科学研究科棟(駒場) 056号室
日仏数学拠点 FJ-LMI セミナーと合同．
Valentina Casarino 氏 (University of Padua)
Variational inequalities in a nonsymmetric Gaussian framework (English)
日仏数学拠点 FJ-LMI セミナーと合同．
Valentina Casarino 氏 (University of Padua)
Variational inequalities in a nonsymmetric Gaussian framework (English)
[ 講演概要 ]
In this talk we introduce variation seminorms and consider the variation operator of a nonsymmetric Ornstein--Uhlenbeck semigroup (H_t)_(t> 0), taken with respect to t, in R^n. We prove that this seminorm defines an operator of weak type (1, 1) for the invariant measure.
The talk is based on joint work with Paolo Ciatti (University of Padua)and Peter Sjögren (Chalmers University).
In this talk we introduce variation seminorms and consider the variation operator of a nonsymmetric Ornstein--Uhlenbeck semigroup (H_t)_(t> 0), taken with respect to t, in R^n. We prove that this seminorm defines an operator of weak type (1, 1) for the invariant measure.
The talk is based on joint work with Paolo Ciatti (University of Padua)and Peter Sjögren (Chalmers University).
離散数理モデリングセミナー
17:00-18:00 数理科学研究科棟(駒場) 118号室
Andy Hone 氏 (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
Andy Hone 氏 (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
[ 講演概要 ]
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Bruno Kahn 氏 (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
https://webusers.imj-prg.fr/~bruno.kahn/
Bruno Kahn 氏 (FJ-LMI)
Zeta and $L$-functions of Voevodsky motives
[ 講演概要 ]
We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
[ 参考URL ]We associate an $L$-function $L^{\text{near}}(M,s)$ to any geometric motive over a global field $K$ in the sense of Voevodsky. This is a Dirichlet series which converges in some half-plane and has an Euler product factorisation. When $M$ is the dual of $M(X)$ for $X$ a smooth projective variety, $L^{\text{near}}(M,s)$ differs from the alternating product of the zeta functions defined by Serre in 1969 only at places of bad reduction; in exchange, it is multiplicative with respect to exact triangles. If $K$ is a function field over $\mathbb{F}_q$, $L^{\text{near}}(M,s)$ is a rational function in $q^{-s}$ and enjoys a functional equation. The techniques use the full force of Ayoub's six (and even seven) operations.
https://webusers.imj-prg.fr/~bruno.kahn/
2025年06月10日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
大島伸行 氏 (北海道大学大学院工学研究院)
壁境界が埋め込まれた流れ方程式とその応用 (Japanese)
大島伸行 氏 (北海道大学大学院工学研究院)
壁境界が埋め込まれた流れ方程式とその応用 (Japanese)
[ 講演概要 ]
界面を表現するレベルセット法やフェーズフィールド法を流れ解析へ導入・応用する研究の一環として、壁境界が埋め込まれた流れ方程式（Immersed-boundary Navier-Stokes）を提案した。その導出の考え方、数値検証例を示すとともに、工学応用事例として画像データが駆動する流れシミュレーション（image-data driven flow simulation）の構築について紹介する。
参考：
1. N.Oshima, J. Fluid Sci. Tech., Vol.19, No.3, (2024) 10.1299/jfst.2024jfst0026, Vol.18, No.4, (2023) 10.1299/fst.2023jfsr0034
2. N. Nakamichi, et al., Mech. Eng. J. , Vol.11, No.6, (2024) 10.1299/mej.24-00196
界面を表現するレベルセット法やフェーズフィールド法を流れ解析へ導入・応用する研究の一環として、壁境界が埋め込まれた流れ方程式（Immersed-boundary Navier-Stokes）を提案した。その導出の考え方、数値検証例を示すとともに、工学応用事例として画像データが駆動する流れシミュレーション（image-data driven flow simulation）の構築について紹介する。
参考：
1. N.Oshima, J. Fluid Sci. Tech., Vol.19, No.3, (2024) 10.1299/jfst.2024jfst0026, Vol.18, No.4, (2023) 10.1299/fst.2023jfsr0034
2. N. Nakamichi, et al., Mech. Eng. J. , Vol.11, No.6, (2024) 10.1299/mej.24-00196
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