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過去の記録
過去の記録 ～07/27｜本日 07/28 | 今後の予定 07/29～
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。
2025年05月19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
安福 悠 氏 (早稲田大学 )
高次元代数多様体での同時個数関数の上界について (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
安福 悠 氏 (早稲田大学 )
高次元代数多様体での同時個数関数の上界について (Japanese)
[ 講演概要 ]
最大公約数のNevanlinna理論類似は，複数の因子に対するいわば同時個数関数となる．Ru--Vojtaは，大域切断の次元の漸近的性質に基づく不変量を導入し，Cartanの定理を効果的に適用することで，幾何学的に一般の位置にある因子に対する接近関数を上から抑えた．n次元射影空間をブローアップした多様体にRu--Vojta理論を活用することで，同時個数関数の上界を得ることができたので，本講演で紹介する．応用として，Borelの定理型の主張を，個数関数を多少持つような整関数の場合で考察する．
[ 参考URL ]最大公約数のNevanlinna理論類似は，複数の因子に対するいわば同時個数関数となる．Ru--Vojtaは，大域切断の次元の漸近的性質に基づく不変量を導入し，Cartanの定理を効果的に適用することで，幾何学的に一般の位置にある因子に対する接近関数を上から抑えた．n次元射影空間をブローアップした多様体にRu--Vojta理論を活用することで，同時個数関数の上界を得ることができたので，本講演で紹介する．応用として，Borelの定理型の主張を，個数関数を多少持つような整関数の場合で考察する．
https://forms.gle/gTP8qNZwPyQyxjTj8
2025年05月16日(金)
統計数学セミナー
13:30-14:30 数理科学研究科棟(駒場) 128 号室
ハイブリッド開催
Maud Delattre 氏 (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
ハイブリッド開催
Maud Delattre 氏 (INRAE)
Efficient precondition stochastic gradient descent for estimation in latent variables models (English)
[ 講演概要 ]
Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
[ 参考URL ]Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this work, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm.
Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variable models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed-effects model.
https://u-tokyo-ac-jp.zoom.us/meeting/register/yixIylc3S8uJqOQ_Vqm_3Q
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
後藤 慶太 氏 (東京大学)
Berkovich geometry and SYZ fibration
後藤 慶太 氏 (東京大学)
Berkovich geometry and SYZ fibration
[ 講演概要 ]
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
The SYZ fibration refers to a special Lagrangian torus fibration on a Calabi–Yau manifold and has been extensively studied in the context of mirror symmetry.
In particular, for a degenerating family of Calabi--Yau manifolds, a family of SYZ fibrations defined on each fiber, away from a subset of sufficiently small measure, plays a central role.
However, the existence of such fibrations remains an open problem, known as the metric SYZ conjecture.
To approach this problem, formal analytic techniques are particularly effective, and Berkovich geometry lies at their foundation.
In this talk, I will explain Yang Li’s "comparison property," a sufficient condition for the conjecture, and present some related results I have been involved in. Along the way, I will also introduce some foundational ideas in Berkovich geometry.
2025年05月15日(木)
幾何解析セミナー
15:30-16:30 数理科学研究科棟(駒場) 123号室
Kobe Marshall-Stevens 氏 (Johns Hopkins University)
Gradient flow of phase transitions with fixed contact angle (英語)
Kobe Marshall-Stevens 氏 (Johns Hopkins University)
Gradient flow of phase transitions with fixed contact angle (英語)
[ 講演概要 ]
The Allen-Cahn equation is closely related to the area functional on hypersurfaces and provides a means to investigate both its critical points (minimal hypersurfaces) and gradient flow (mean curvature flow). I will discuss various properties of the gradient flow of the Allen-Cahn equation with a fixed boundary contact angle condition, which is used to gain insight into an appropriate formulation for mean curvature flow with fixed boundary contact angle. This is based on joint work with M. Takada, Y. Tonegawa, and M. Workman.
The Allen-Cahn equation is closely related to the area functional on hypersurfaces and provides a means to investigate both its critical points (minimal hypersurfaces) and gradient flow (mean curvature flow). I will discuss various properties of the gradient flow of the Allen-Cahn equation with a fixed boundary contact angle condition, which is used to gain insight into an appropriate formulation for mean curvature flow with fixed boundary contact angle. This is based on joint work with M. Takada, Y. Tonegawa, and M. Workman.
2025年05月14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
Eamon Quinlan 氏 (University of Utah)
Introduction to the Bernstein-Sato polynomial in positive characteristic
https://eamonqg.github.io/
Eamon Quinlan 氏 (University of Utah)
Introduction to the Bernstein-Sato polynomial in positive characteristic
[ 講演概要 ]
The Bernstein-Sato polynomial of a holomorphic function is an invariant that originated in complex analysis, and with now strong applications to birational geometry and singularity theory over the complex numbers. For example, it detects the log-canonical threshold as well as the eigenvalues of the monodromy action on nearby cycles. In this talk I will define a characteristic-p analogue of this invariant, I will survey some of its basic properties, and I will illustrate how its behavior reflects arithmetic phenomena. This will serve as an introduction to the talk by Hiroki Kato.
[ 参考URL ]The Bernstein-Sato polynomial of a holomorphic function is an invariant that originated in complex analysis, and with now strong applications to birational geometry and singularity theory over the complex numbers. For example, it detects the log-canonical threshold as well as the eigenvalues of the monodromy action on nearby cycles. In this talk I will define a characteristic-p analogue of this invariant, I will survey some of its basic properties, and I will illustrate how its behavior reflects arithmetic phenomena. This will serve as an introduction to the talk by Hiroki Kato.
https://eamonqg.github.io/
代数学コロキウム
18:10-19:10 数理科学研究科棟(駒場) 117号室
加藤大輝 氏 (IHES)
Bernstein--Sato theory in positive characteristic and unit root nearby cycles.
加藤大輝 氏 (IHES)
Bernstein--Sato theory in positive characteristic and unit root nearby cycles.
[ 講演概要 ]
I will talk about how to formulate (and outline an idea of a proof of) a positive characteristic analogue of the theorem of Kashiwara and Malgrange about the relationship, in characteristic zero, between the Bernstein-Sato polynomial and the eigenvalues of the monodromy action on nearby cycles. It will/is expected to give a cohomological explanation for some of the arithmetic phenomena that will be presented in the talk by Eamon Quinlan. This is a joint work in progress with him and Daichi Takeuchi.
I will talk about how to formulate (and outline an idea of a proof of) a positive characteristic analogue of the theorem of Kashiwara and Malgrange about the relationship, in characteristic zero, between the Bernstein-Sato polynomial and the eigenvalues of the monodromy action on nearby cycles. It will/is expected to give a cohomological explanation for some of the arithmetic phenomena that will be presented in the talk by Eamon Quinlan. This is a joint work in progress with him and Daichi Takeuchi.
2025年05月13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
崔瀷瀚 氏 (東大数理)
Haagerup's problems on normal weights
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
崔瀷瀚 氏 (東大数理)
Haagerup's problems on normal weights
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
15:45-16:45 数理科学研究科棟(駒場) 128号室
上田衛 氏 (東大数理)
アファインヤンギアンと非長方形型W代数 (Japanese)
上田衛 氏 (東大数理)
アファインヤンギアンと非長方形型W代数 (Japanese)
[ 講演概要 ]
ヤンギアンはDrinfeldにより導入された量子群であり、有限型の場合にはカレントリー代数の変形となる。近年、ヤンギアンは頂点代数の一種であるW代数の研究で重要な役割を果たしている。
その代表的な成果の一つとして、BrundanとKleshchevがA型有限W代数をシフト型ヤンギアンの商代数として書き下したことで挙げられる。シフト型ヤンギアンはA型有限型ヤンギアンを部分代数として含んでいる。De Sole-Kac-ValeriはLax作用素を用いてこの部分代数からA型有限W代数への写像を構成した。
本講演では、De Sole-Kac-Valeriの結果のアファイン版に相当する、A型アファインヤンギアンからA型非長方形型W代数への写像を構成する方法について解説する。この写像は、AGT予想の一般化に繋がると期待されている。
ヤンギアンはDrinfeldにより導入された量子群であり、有限型の場合にはカレントリー代数の変形となる。近年、ヤンギアンは頂点代数の一種であるW代数の研究で重要な役割を果たしている。
その代表的な成果の一つとして、BrundanとKleshchevがA型有限W代数をシフト型ヤンギアンの商代数として書き下したことで挙げられる。シフト型ヤンギアンはA型有限型ヤンギアンを部分代数として含んでいる。De Sole-Kac-ValeriはLax作用素を用いてこの部分代数からA型有限W代数への写像を構成した。
本講演では、De Sole-Kac-Valeriの結果のアファイン版に相当する、A型アファインヤンギアンからA型非長方形型W代数への写像を構成する方法について解説する。この写像は、AGT予想の一般化に繋がると期待されている。
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。
池 祐一 氏 (東京大学大学院数理科学研究科)
Interleaving distance for sheaves and its application to symplectic geometry (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。
池 祐一 氏 (東京大学大学院数理科学研究科)
Interleaving distance for sheaves and its application to symplectic geometry (JAPANESE)
[ 講演概要 ]
The Interleaving distance was first introduced in the context of the stability of persistent homology and is now used in various fields. It was adapted to sheaves by the pioneering work of Curry, and later in the derived setting by Kashiwara and Schapira. In this talk, I will explain that the interleaving distance for sheaves is related to the energy of Hamiltonian actions on cotangent bundles. Moreover, I will show that the derived interleaving distance is complete, which enables us to treat non-smooth objects in symplectic geometry using sheaf-theoretic methods. This is based on joint work with Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, and Claude Viterbo.
[ 参考URL ]The Interleaving distance was first introduced in the context of the stability of persistent homology and is now used in various fields. It was adapted to sheaves by the pioneering work of Curry, and later in the derived setting by Kashiwara and Schapira. In this talk, I will explain that the interleaving distance for sheaves is related to the energy of Hamiltonian actions on cotangent bundles. Moreover, I will show that the derived interleaving distance is complete, which enables us to treat non-smooth objects in symplectic geometry using sheaf-theoretic methods. This is based on joint work with Tomohiro Asano, Stéphane Guillermou, Vincent Humilière, and Claude Viterbo.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
統計数学セミナー
13:30-14:30 数理科学研究科棟(駒場) 126号室
ハイブリッド開催
江村 剛志 氏 (広島大学 大学院先進理工系科学研究科)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
ハイブリッド開催
江村 剛志 氏 (広島大学 大学院先進理工系科学研究科)
Change point estimation for Gaussian and binomial time series data with copula-based Markov chain models (Japanese)
[ 講演概要 ]
Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
[ 参考URL ]Estimation of a change point is a classical statistical problem in sequential analysis and process control.
The classical maximum likelihood estimators (MLEs) for a change point are limited to independent observations or linearly dependent observations. If these conditions are violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator is proposed under a copula-based Markov chain model for serially dependent observations, where the marginal distribution is binomial or Gaussian. The main novelty is the adaptation of a three-state copula model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood.
A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data and the financial crisis data. This is joint work with Prof. Li‑Hsien Sun from National Central University, Taiwan. The presentation is based on two papers:
Emura T, Lai CC, Sun LH (2023) Change point estimation under a copula-based Markov chain model for binomial time series, Econ Stat 28:120-37
Sun LH, Wang YK, Liu LH, Emura T, Chiu CY (2025) Change point estimation for Gaussian time series data with copula-based Markov chain models, Comp Stat, 40:1541–81
https://u-tokyo-ac-jp.zoom.us/meeting/register/5OvWlB-9SMu4HiB6Zzy5Fw
日仏数学拠点FJ-LMIセミナー
14:30-15:15 数理科学研究科棟(駒場) 002号室
Matthew CELLOT 氏 (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
https://fj-lmi.cnrs.fr/seminars/
Matthew CELLOT 氏 (University of Lille (France))
Homotopy quantum field theories and 3-types (英語)
[ 講演概要 ]
Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
[ 参考URL ]Quantum topology is a field that came about in the 1980s following remarkable discoveries by Jones, Drinfeld and Witten, whose work dramatically renewed topology, in particular in low dimension. A fundamental notion in quantum topology is that of topological quantum field theory (TQFT) formulated by Witten and Atiyah. This notion originates in ideas from quantum physics and constitutes a framework that organizes certain topological invariants of manifolds, called quantum invariants, which are defined by means of quantum groups. Homotopy quantum field theories (HQFTs) are a generalization of TQFTs. The idea is to use TQFT techniques to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a (fixed) topological space called the target.
Turaev and Virelizier have recently constructed 3-dimensional HQFTs (by state-sum) when the target space is aspherical (i.e. its n-th homotopy groups are trivial for n>1) and Sözer and Virelizier have constructed 3-dimensional HQFTs when the target space is a 2-type (i.e. its n-th homotopy groups are trivial for n>2). Using state sum techniques, Douglas and Reutter have constructed 4-dimensional TQFTs from spherical fusion 2-categories. In this talk, we combine both these approaches: we construct state sum 4-dimensional HQFTs with a 3-type target from fusion 2-categories graded by a 2-crossed module.
https://fj-lmi.cnrs.fr/seminars/
2025年05月12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
神田 秀峰 氏 (東京大学)
LCK幾何学におけるOeljeklaus-Toma多様体の特徴づけ (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
神田 秀峰 氏 (東京大学)
LCK幾何学におけるOeljeklaus-Toma多様体の特徴づけ (Japanese)
[ 講演概要 ]
Oeljeklaus–Toma（OT）多様体はKähler計量を持たない複素多様体の例として知られ, 井上曲面の高次元への一般化とみなされている. OT多様体は数論的データを用いて構成される可解多様体であり, いくつかのOT多様体は局所共形Kähler（LCK）計量を持つ. これによりLCK計量を持つ可解多様体が大量に構成されたことになり, OT多様体はLCK幾何における重要な例として盛んに研究されてきた. その構成は技巧的に見えるが, LCK計量をもつ可解多様体はこれまでOT多様体を除いて簡単なものしか知られていない.
本講演では, ある種の可解多様体がLCK計量を持つならば, それは本質的にOT多様体と一致することを示す. 幾何学的な制約から数論が現れることから, 本結果はある種の可解多様体の構成において, 数論的議論を用いることの必然性を示唆していると言える.
本講演はプレプリントarXiv:2502.12500の内容に基づく.
[ 参考URL ]Oeljeklaus–Toma（OT）多様体はKähler計量を持たない複素多様体の例として知られ, 井上曲面の高次元への一般化とみなされている. OT多様体は数論的データを用いて構成される可解多様体であり, いくつかのOT多様体は局所共形Kähler（LCK）計量を持つ. これによりLCK計量を持つ可解多様体が大量に構成されたことになり, OT多様体はLCK幾何における重要な例として盛んに研究されてきた. その構成は技巧的に見えるが, LCK計量をもつ可解多様体はこれまでOT多様体を除いて簡単なものしか知られていない.
本講演では, ある種の可解多様体がLCK計量を持つならば, それは本質的にOT多様体と一致することを示す. 幾何学的な制約から数論が現れることから, 本結果はある種の可解多様体の構成において, 数論的議論を用いることの必然性を示唆していると言える.
本講演はプレプリントarXiv:2502.12500の内容に基づく.
https://forms.gle/gTP8qNZwPyQyxjTj8
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