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過去の記録 ～06/12｜本日 06/13 | 今後の予定 06/14～
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.
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
猪奥倫左 氏 (東北大学)
半線形楕円型方程式の特異解の多重存在 (Japanese)
猪奥倫左 氏 (東北大学)
半線形楕円型方程式の特異解の多重存在 (Japanese)
[ 講演概要 ]
半線形楕円型方程式の特異解の構造は，空間3次元以上でのべき乗非線形項の場合にはよく理解されている．本講演では球対称解に対する既存の結果を概観したのち，単調増大する一般の非線形項に対して増大度の分類を導入し，それに基づく球対称特異解の構成方法について説明する．特に Sobolev 劣臨界に相当する場合の特異解の多重存在性について最近得られた結果を紹介する．本講演は藤嶋陽平氏（静岡大学）との共同研究に基づく．
半線形楕円型方程式の特異解の構造は，空間3次元以上でのべき乗非線形項の場合にはよく理解されている．本講演では球対称解に対する既存の結果を概観したのち，単調増大する一般の非線形項に対して増大度の分類を導入し，それに基づく球対称特異解の構成方法について説明する．特に Sobolev 劣臨界に相当する場合の特異解の多重存在性について最近得られた結果を紹介する．本講演は藤嶋陽平氏（静岡大学）との共同研究に基づく．
2025年06月03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
森孟彦 氏 (千葉大)
Application of Operator Theory for the Collatz Conjecture
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
森孟彦 氏 (千葉大)
Application of Operator Theory for the Collatz Conjecture
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
東京無限可積分系セミナー
15:00-16:00 数理科学研究科棟(駒場) 123号室
Veronica Fantini 氏 (Laboratoire Mathématique Orsay)
Modular resurgence (English)
https://sites.google.com/view/vfantini/home-page
Veronica Fantini 氏 (Laboratoire Mathématique Orsay)
Modular resurgence (English)
[ 講演概要 ]
Quantum modular forms were introduced by Zagier in 2010 to characterize the failure of modularity of certain q-series. Since then, different examples of quantum modular forms have also been studied in complex Chern-Simons theory and, more recently, in topological string theory on local Calabi-Yau 3folds. This talk aims to discuss the approach of resurgence to the study of a class of quantum modular forms. More precisely, I will present modular resurgence structures and illustrate their main properties. This is based on arXiv:2404.11550.
[ 参考URL ]Quantum modular forms were introduced by Zagier in 2010 to characterize the failure of modularity of certain q-series. Since then, different examples of quantum modular forms have also been studied in complex Chern-Simons theory and, more recently, in topological string theory on local Calabi-Yau 3folds. This talk aims to discuss the approach of resurgence to the study of a class of quantum modular forms. More precisely, I will present modular resurgence structures and illustrate their main properties. This is based on arXiv:2404.11550.
https://sites.google.com/view/vfantini/home-page
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。
諏訪 立雄 氏 (北海道大学)
Localized intersection product for maps and applications (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。
諏訪 立雄 氏 (北海道大学)
Localized intersection product for maps and applications (JAPANESE)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年06月02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。
Wai-Kit Lam 氏 (National Taiwan University)
Disorder monomer-dimer model and maximum weight matching
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。
Wai-Kit Lam 氏 (National Taiwan University)
Disorder monomer-dimer model and maximum weight matching
[ 講演概要 ]
Given a finite graph, one puts i.i.d. weights on the edges and i.i.d. weights on the vertices. For a (partial) matching on this graph, define the weight of the matching by adding all the weights of the edges in the matching together with the weights of the unmatched vertices. One would like to understand how the maximum weight behaves as the size of the graph becomes large. The talk will be divided into two parts. In the first part, we consider the "positive temperature" case (a.k.a. the disorder monomer-dimer model). We show that the model exhibits correlation decay, and from this one can prove a Gaussian central limit theorem for the associated free energy. In the second part, we will focus on the "zero temperature" case, the maximum weight matching. We show that if the edge weights are exponentially distributed, and if the vertex weights are absent, then there is also correlation decay for a certain class of graphs. This correlation decay allows us to define the maximum weight matching on some infinite graphs and also prove limit theorems for the maximum weight matching. Joint work with Arnab Sen (Minnesota).
Given a finite graph, one puts i.i.d. weights on the edges and i.i.d. weights on the vertices. For a (partial) matching on this graph, define the weight of the matching by adding all the weights of the edges in the matching together with the weights of the unmatched vertices. One would like to understand how the maximum weight behaves as the size of the graph becomes large. The talk will be divided into two parts. In the first part, we consider the "positive temperature" case (a.k.a. the disorder monomer-dimer model). We show that the model exhibits correlation decay, and from this one can prove a Gaussian central limit theorem for the associated free energy. In the second part, we will focus on the "zero temperature" case, the maximum weight matching. We show that if the edge weights are exponentially distributed, and if the vertex weights are absent, then there is also correlation decay for a certain class of graphs. This correlation decay allows us to define the maximum weight matching on some infinite graphs and also prove limit theorems for the maximum weight matching. Joint work with Arnab Sen (Minnesota).
2025年05月30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
John A G Roberts 氏 (UNSW Sydney / 東京大学大学院数理科学研究科)
Arithmetic and geometric aspects of the (symbolic) dynamics of piecewise-linear maps (English)
John A G Roberts 氏 (UNSW Sydney / 東京大学大学院数理科学研究科)
Arithmetic and geometric aspects of the (symbolic) dynamics of piecewise-linear maps (English)
[ 講演概要 ]
We study a family of planar area-preserving maps, described by different $SL(2,\mathbb{R})$ matrices on the right and left half-planes. Such maps, studied extensively by Lagarias and Rains in 2005, can support periodic and quasiperiodic dynamics with a foliation of the plane by invariant curves. The parameter space is two dimensional (the parameters being the traces of the two matrices) and the set of parameters for which an initial condition on the half-plane boundary returns to it are algebraic “critical” curves, described by the symbolic dynamics of the itinerary between the boundaries. An important component of the planar dynamics is the rotational dynamics it induces on the unit circle. The study of the arithmetic, algebraic, and geometric aspects of the planar and circle (symbolic) dynamics has connections to various parts of number theory and geometry, which I will mention. These include: Farey sequences; continued fraction expansions and continuant polynomials; the character variety of group representations in $SL(2, \mathbb{C})$ and $PSL(2, \mathbb{C})$; and the group of polynomial diffeomorphisms of $\mathbb{C}^3$ preserving the Fricke-Vogt invariant $x^2 + y^2 + z^2 - xyz$.
This is joint work with Asaki Saito (Hakodate) and Franco Vivaldi (London).
We study a family of planar area-preserving maps, described by different $SL(2,\mathbb{R})$ matrices on the right and left half-planes. Such maps, studied extensively by Lagarias and Rains in 2005, can support periodic and quasiperiodic dynamics with a foliation of the plane by invariant curves. The parameter space is two dimensional (the parameters being the traces of the two matrices) and the set of parameters for which an initial condition on the half-plane boundary returns to it are algebraic “critical” curves, described by the symbolic dynamics of the itinerary between the boundaries. An important component of the planar dynamics is the rotational dynamics it induces on the unit circle. The study of the arithmetic, algebraic, and geometric aspects of the planar and circle (symbolic) dynamics has connections to various parts of number theory and geometry, which I will mention. These include: Farey sequences; continued fraction expansions and continuant polynomials; the character variety of group representations in $SL(2, \mathbb{C})$ and $PSL(2, \mathbb{C})$; and the group of polynomial diffeomorphisms of $\mathbb{C}^3$ preserving the Fricke-Vogt invariant $x^2 + y^2 + z^2 - xyz$.
This is joint work with Asaki Saito (Hakodate) and Franco Vivaldi (London).
2025年05月27日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
対面開催，通常とは場所が異なります
平良晃一 氏 (九州大学数理学研究院)
Semiclassical behaviors of matrix-valued operators (Japanese)
対面開催，通常とは場所が異なります
平良晃一 氏 (九州大学数理学研究院)
Semiclassical behaviors of matrix-valued operators (Japanese)
[ 講演概要 ]
半古典解析とは，微小なパラメータhを持つ微分方程式の解の漸近的性質を調べる理論である．物理的にはhがプランク定数を表しており，古典力学との対応関係を手がかりに量子力学的現象を理解する手段となる．数学的な応用として，シュレディンガー作用素やラプラス・ベルトラミ作用素の固有値，固有関数の漸近挙動を古典力学的，幾何学的に調べることができる．本講演では，簡単なモデルとして空間1次元の行列値作用素を取り上げ，主要項の特性曲線の幾何学的な交差によって，固有関数の漸近挙動が大きく変化する，という結果について紹介する．これは樋口健太氏（愛媛大学）とLouatron Vincent氏（立命館大学）との共同研究である．
半古典解析とは，微小なパラメータhを持つ微分方程式の解の漸近的性質を調べる理論である．物理的にはhがプランク定数を表しており，古典力学との対応関係を手がかりに量子力学的現象を理解する手段となる．数学的な応用として，シュレディンガー作用素やラプラス・ベルトラミ作用素の固有値，固有関数の漸近挙動を古典力学的，幾何学的に調べることができる．本講演では，簡単なモデルとして空間1次元の行列値作用素を取り上げ，主要項の特性曲線の幾何学的な交差によって，固有関数の漸近挙動が大きく変化する，という結果について紹介する．これは樋口健太氏（愛媛大学）とLouatron Vincent氏（立命館大学）との共同研究である．
2025年05月26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
松村 慎一 氏 (東北大学)
Fundamental groups of compact Kahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
松村 慎一 氏 (東北大学)
Fundamental groups of compact Kahler manifolds with semi-positive holomorphic sectional curvature (Japanese)
[ 講演概要 ]
この講演では, 非負の正則断面曲率をもつコンパクトKahler多様体の構造を論じ，そのような多様体がトーラスの有限エタール商への局所自明な有理連結射を持つことを説明する. この構造定理は，射影多様体に対して既に確立されていた結果をコンパクトKahler多様体へ拡張するものである. 証明の要所は，適切な意味で平坦な接ベクトルによって生成される葉層を解析し，Campanaによって導入された特殊型多様体に着目して，位相基本群が本質的にアーベルであることを示す点にある.
[ 参考URL ]この講演では, 非負の正則断面曲率をもつコンパクトKahler多様体の構造を論じ，そのような多様体がトーラスの有限エタール商への局所自明な有理連結射を持つことを説明する. この構造定理は，射影多様体に対して既に確立されていた結果をコンパクトKahler多様体へ拡張するものである. 証明の要所は，適切な意味で平坦な接ベクトルによって生成される葉層を解析し，Campanaによって導入された特殊型多様体に着目して，位相基本群が本質的にアーベルであることを示す点にある.
https://forms.gle/gTP8qNZwPyQyxjTj8
2025年05月23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
宮本 拓哉 氏 (東京大学)
Pathology of formal locally-trivial
deformations in positive characteristic
宮本 拓哉 氏 (東京大学)
Pathology of formal locally-trivial
deformations in positive characteristic
[ 講演概要 ]
An infinitesimal deformation of an algebraic variety X is called (formally) locally trivial if it is Zariski-locally isomorphic to the trivial deformation. The locally trivial deformation functor of X is the subfunctor of the usual deformation functor associated with X consisting of locally trivial deformations. In this talk, I will construct an explicit example that is an algebraic curve in positive characteristic whose locally trivial deformation functor does not satisfy Schlessinger’s first condition (H_1), in contrast to the complex/characteristic 0 case. In particular, this provides a negative answer to a question posed by H. Flenner and S. Kosarew. I will also mention recent progress on the structure of fibers of locally trivial deformation functors.
An infinitesimal deformation of an algebraic variety X is called (formally) locally trivial if it is Zariski-locally isomorphic to the trivial deformation. The locally trivial deformation functor of X is the subfunctor of the usual deformation functor associated with X consisting of locally trivial deformations. In this talk, I will construct an explicit example that is an algebraic curve in positive characteristic whose locally trivial deformation functor does not satisfy Schlessinger’s first condition (H_1), in contrast to the complex/characteristic 0 case. In particular, this provides a negative answer to a question posed by H. Flenner and S. Kosarew. I will also mention recent progress on the structure of fibers of locally trivial deformation functors.
2025年05月21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
Toni Annala 氏 (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
https://tannala.com/
Toni Annala 氏 (University of Chicago)
A¹-Colocalization and Logarithmic Cohomology Theories
[ 講演概要 ]
In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
[ 参考URL ]In recent joint work with Hoyois and Iwasa, we discovered that non-A¹-invariant motivic homotopy theory offers a new lens for understanding logarithmic cohomology theories. Central to this perspective is A¹-colocalization, which produces a cohomology theory whose value on a smooth scheme U agrees with the "logarithmic cohomology" of a good compactification (X,D). In many examples, including de Rham and crystalline cohomology, the quotation marks can be dropped, as A¹-colocalization recovers the classical logarithmic cohomology groups. I will explain this connection and, time permitting, sketch a proof of the duality theorem underlying this phenomenon, which states that smooth projective schemes have a dualizable motive.
https://tannala.com/
2025年05月20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
佐藤ふたば 氏 (東大数理)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
佐藤ふたば 氏 (東大数理)
Heat semigroups on quantum automorphism groups of finite dimensional C$^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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
北川宜稔 氏 (九州大学 マス・フォア・インダストリ研究所)
簡約リー群の分岐則におけるgood filtrationの制限について (Japanese)
北川宜稔 氏 (九州大学 マス・フォア・インダストリ研究所)
簡約リー群の分岐則におけるgood filtrationの制限について (Japanese)
[ 講演概要 ]
arXiv:2405.10382において、簡約リー群の分岐則と関係するカルタン部分代数を定義した。
これは既約分解の連続スペクトルの大きさや形を統制するものと考えられ、普遍包絡環の中心の作用の台を使って定義される。特別な場合を除き、このカルタン部分代数の定義からの直接計算は困難である。
本講演では、good filtrationの制限に関する結果を述べ、表現の随伴多様体とカルタン部分代数を関連付ける結果を示す。
また、小林俊行氏による離散分解性の必要条件と関連する予想への応用についても紹介する。
arXiv:2405.10382において、簡約リー群の分岐則と関係するカルタン部分代数を定義した。
これは既約分解の連続スペクトルの大きさや形を統制するものと考えられ、普遍包絡環の中心の作用の台を使って定義される。特別な場合を除き、このカルタン部分代数の定義からの直接計算は困難である。
本講演では、good filtrationの制限に関する結果を述べ、表現の随伴多様体とカルタン部分代数を関連付ける結果を示す。
また、小林俊行氏による離散分解性の必要条件と関連する予想への応用についても紹介する。
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