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過去の記録
過去の記録 ～12/24｜本日 12/25 | 今後の予定 12/26～
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
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。
森藤 孝之 氏 (慶應義塾大学)
Bell polynomials and hyperbolic volume of knots (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。
森藤 孝之 氏 (慶應義塾大学)
Bell polynomials and hyperbolic volume of knots (JAPANESE)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie群論・表現論セミナー
15:30-16:30 数理科学研究科棟(駒場) 128号室
日仏数学拠点 FJ-LMI セミナーと合同．
Paolo Ciatti 氏 (University of Padua)
Spectral estimates on the Heisenberg group (English)
日仏数学拠点 FJ-LMI セミナーと合同．
Paolo Ciatti 氏 (University of Padua)
Spectral estimates on the Heisenberg group (English)
[ 講演概要 ]
In this talk we will discuss some estimates concerning the spectral projections of the sub-Laplacian on the Heisenberg group. We will also consider some open problems and formulate a conjecture, providing some motivation for it.
In this talk we will discuss some estimates concerning the spectral projections of the sub-Laplacian on the Heisenberg group. We will also consider some open problems and formulate a conjecture, providing some motivation for it.
代数幾何学セミナー
14:00-15:30 数理科学研究科棟(駒場) 122号室
いつもと日時・部屋が異なるのでご注意ください。
Meng Chen 氏 (Fudan University)
Some new methods in estimating the lower bound of the canonical volume of 3-folds of general type
いつもと日時・部屋が異なるのでご注意ください。
Meng Chen 氏 (Fudan University)
Some new methods in estimating the lower bound of the canonical volume of 3-folds of general type
[ 講演概要 ]
We introduce some new advance in estimating the lower bound of the canonical volume of 3-folds of general type with very small geometric genus. This topic covers a joint work with Jungkai A. Chen, Yong Hu and Chen Jiang.
We introduce some new advance in estimating the lower bound of the canonical volume of 3-folds of general type with very small geometric genus. This topic covers a joint work with Jungkai A. Chen, Yong Hu and Chen Jiang.
代数幾何学セミナー
16:00-17:30 数理科学研究科棟(駒場) 122号室
いつもと日時・部屋が異なるのでご注意ください。
Xun Yu 氏 (Tianjin University)
On the real forms of smooth complex projective varieties
いつもと日時・部屋が異なるのでご注意ください。
Xun Yu 氏 (Tianjin University)
On the real forms of smooth complex projective varieties
[ 講演概要 ]
The real form problem asks how many different ways one can describe a given complex variety by polynomial equations with real coefficients, up to isomorphisms over the real number field. In this talk, I will discuss some recent results about real forms of smooth complex projective varieties. This talk is based on my joint works with T.-C. Dinh, C. Gachet, G. van der Geer, H.-Y. Lin, K. Oguiso, and L. Wang.
The real form problem asks how many different ways one can describe a given complex variety by polynomial equations with real coefficients, up to isomorphisms over the real number field. In this talk, I will discuss some recent results about real forms of smooth complex projective varieties. This talk is based on my joint works with T.-C. Dinh, C. Gachet, G. van der Geer, H.-Y. Lin, K. Oguiso, and L. Wang.
東京名古屋代数セミナー
15:30-17:00 オンライン開催
Mohamad Haerizadeh 氏 (Univeristy of Tehran)
Generic decompositions of g-vectors (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Mohamad Haerizadeh 氏 (Univeristy of Tehran)
Generic decompositions of g-vectors (English)
[ 講演概要 ]
In this talk, we discuss the role of g-vectors in the representation theory of algebras. Specifically, we describe how generic decompositions of g-vectors yield decompositions of generically τ-reduced components of representation varieties and vice versa. This connection allows us to provide a partial answer to the Cerulli-Labardini-Schröer conjecture concerning the number of direct summands of generically τ-reduced components of representation varieties.
Furthermore, we examine the cones of g-vectors, demonstrating that they are both rational and simplicial. We establish that g-vectors satisfy the ray condition if they are sufficiently far from the origin. These results enable us to generalize several results by Asai and Iyama concerning TF-equivalence classes of g-vectors. Therefore, our consequences can be utilized to study the wall and chamber structures of finite-dimensional algebras. This is joint work with Siamak Yassemi.
Zoom ID 844 4810 7612 Password 275169
[ 参考URL ]In this talk, we discuss the role of g-vectors in the representation theory of algebras. Specifically, we describe how generic decompositions of g-vectors yield decompositions of generically τ-reduced components of representation varieties and vice versa. This connection allows us to provide a partial answer to the Cerulli-Labardini-Schröer conjecture concerning the number of direct summands of generically τ-reduced components of representation varieties.
Furthermore, we examine the cones of g-vectors, demonstrating that they are both rational and simplicial. We establish that g-vectors satisfy the ray condition if they are sufficiently far from the origin. These results enable us to generalize several results by Asai and Iyama concerning TF-equivalence classes of g-vectors. Therefore, our consequences can be utilized to study the wall and chamber structures of finite-dimensional algebras. This is joint work with Siamak Yassemi.
Zoom ID 844 4810 7612 Password 275169
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025年06月09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
本多 宣博 氏 (東京科学大学)
6次元球面とクレメンス3-fold上のファイブレーション構造 (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
本多 宣博 氏 (東京科学大学)
6次元球面とクレメンス3-fold上のファイブレーション構造 (Japanese)
[ 講演概要 ]
単連結コンパクト6次元多様体で2次元ベッチ数（正確には2次整数係数ホモロジー群）が消えているものは球面か3次元球面の直積かそれらの連結和に限ることが知られている。6次元球面上に複素構造が存在するかどうかは有名な未解決問題であり、3次元球面の直積とそれらの連結和の上には実際に複素構造が入ることが知られている。本講演ではこれらの複素多様体の基本的な性質を説明した後、複素曲面への全射正則写像の非存在に関する結果を説明する。これは6次元球面上の複素構造について新しい制約を与える。これはJeff Viaclovsky (UC Irvine)との共同研究である。
[ 参考URL ]単連結コンパクト6次元多様体で2次元ベッチ数（正確には2次整数係数ホモロジー群）が消えているものは球面か3次元球面の直積かそれらの連結和に限ることが知られている。6次元球面上に複素構造が存在するかどうかは有名な未解決問題であり、3次元球面の直積とそれらの連結和の上には実際に複素構造が入ることが知られている。本講演ではこれらの複素多様体の基本的な性質を説明した後、複素曲面への全射正則写像の非存在に関する結果を説明する。これは6次元球面上の複素構造について新しい制約を与える。これはJeff Viaclovsky (UC Irvine)との共同研究である。
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
17:00-18:30 数理科学研究科棟(駒場) 126号室
講演の開始が遅くなっています。今日はTea Time はありません。
角田 謙吉 氏 (九州大学)
粒子系に対する静的な揺らぎ
講演の開始が遅くなっています。今日はTea Time はありません。
角田 謙吉 氏 (九州大学)
粒子系に対する静的な揺らぎ
[ 講演概要 ]
非平衡定常状態は数理物理の問題として様々な文脈の中で研究されている。非平衡定常状態とはカレントは0でないが時間に対して不変な状態であり、相互作用粒子系においては系の定常測度として定義される。非平衡定常状態の解析で難しい問題点として、その明示的な具体形が知られていないことや定常測度が粒子系に対して可逆でないことなどがあげられる。そのため非平衡定常状態の解析は容易ではないが、一般的な手法として対応するdynamicsに対する解析を用いる方法がある。本講演では粒子数密度に対する揺らぎの問題について焦点を当て、境界で流入・流出のある排他過程やGlauber+Kawasaki過程に対してその手法を解説する。
非平衡定常状態は数理物理の問題として様々な文脈の中で研究されている。非平衡定常状態とはカレントは0でないが時間に対して不変な状態であり、相互作用粒子系においては系の定常測度として定義される。非平衡定常状態の解析で難しい問題点として、その明示的な具体形が知られていないことや定常測度が粒子系に対して可逆でないことなどがあげられる。そのため非平衡定常状態の解析は容易ではないが、一般的な手法として対応するdynamicsに対する解析を用いる方法がある。本講演では粒子数密度に対する揺らぎの問題について焦点を当て、境界で流入・流出のある排他過程やGlauber+Kawasaki過程に対してその手法を解説する。
2025年06月06日(金)
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
吉田 智輝 氏 (早稲田大学)
Bridgeland Stability of Sheaves on del Pezzo Surface of Picard Rank Three
吉田 智輝 氏 (早稲田大学)
Bridgeland Stability of Sheaves on del Pezzo Surface of Picard Rank Three
[ 講演概要 ]
Bridgeland stability is a notion of stability for objects in a triangulated category, particularly in the bounded derived category of coherent sheaves. Unlike classical sheaf stability, it is often unclear whether fundamental sheaves, such as line bundles, are (semi)stable with respect to a given Bridgeland stability condition. In this talk, we focus on the del Pezzo surface of Picard rank three and study the Bridgeland stability of its line bundles and certain torsion sheaves. More precisely, we first determine the maximal destabilizing objects for line bundles and then outline our proof strategy in the torsion case.
This talk is based on arXiv:2502.18894, which is joint work with Yuki Mizuno.
Bridgeland stability is a notion of stability for objects in a triangulated category, particularly in the bounded derived category of coherent sheaves. Unlike classical sheaf stability, it is often unclear whether fundamental sheaves, such as line bundles, are (semi)stable with respect to a given Bridgeland stability condition. In this talk, we focus on the del Pezzo surface of Picard rank three and study the Bridgeland stability of its line bundles and certain torsion sheaves. More precisely, we first determine the maximal destabilizing objects for line bundles and then outline our proof strategy in the torsion case.
This talk is based on arXiv:2502.18894, which is joint work with Yuki Mizuno.
2025年06月05日(木)
幾何解析セミナー
14:00-16:30 数理科学研究科棟(駒場) 122号室
Chao Li 氏 (New York University) 14:00-15:00
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
Poincar\'e-Einstein manifolds: conformal structure meets metric geometry (英語)
Chao Li 氏 (New York University) 14:00-15:00
On the topology of stable minimal hypersurfaces in a homeomorphic $S^4$ (英語)
[ 講演概要 ]
Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
Ruobing Zhang 氏 (University of Wisconsin–Madison) 15:30-16:30Given an $n$-dimensional manifold (with $n$ at least $4$), it is generally impossible to control the topology of a homologically minimizing hypersurface $M$. In this talk, we construct stable (or locally minimizing) hypersurfaces with optimal restrictions on its topology in a $4$-manifold $X$ with natural curvature conditions (e.g. positive scalar curvature), provided that $X$ admits certain embeddings into a homeomorphic $S^4$. As an application, we obtain black hole topology theorems in such $4$-dimensional asymptotically flat manifolds with nonnegative scalar curvature. This is based on joint work with Boyu Zhang.
Poincar\'e-Einstein manifolds: conformal structure meets metric geometry (英語)
[ 講演概要 ]
A Poincar\'e-Einstein manifold is a complete non-compact Einstein manifold with negative scalar curvature which can be conformally deformed to a compact manifold with boundary, called the conformal boundary or conformal infinity. Naturally, such a space is associated with a conformal structure on the conformal infinity. A fundamental theme in studying these geometric objects is to relate the Riemannian geometric data of the Einstein metric to the conformal geometric data at infinity which is also called the AdS/CFT correspondence in theoretical physics.
In this talk, we will explore some new techniques from the metric geometric point of view, by which one can establish some new rigidity, quantitative rigidity, and regularity results.
A Poincar\'e-Einstein manifold is a complete non-compact Einstein manifold with negative scalar curvature which can be conformally deformed to a compact manifold with boundary, called the conformal boundary or conformal infinity. Naturally, such a space is associated with a conformal structure on the conformal infinity. A fundamental theme in studying these geometric objects is to relate the Riemannian geometric data of the Einstein metric to the conformal geometric data at infinity which is also called the AdS/CFT correspondence in theoretical physics.
In this talk, we will explore some new techniques from the metric geometric point of view, by which one can establish some new rigidity, quantitative rigidity, and regularity results.
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