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過去の記録
過去の記録 ～10/31｜本日 11/01 | 今後の予定 11/02～
2025年10月31日(金)
代数幾何学セミナー
13:00-14:30 数理科学研究科棟(駒場) 118号室
いつもと開始時間が異なります。
Miguel Angel Barja 氏 (UPC-Barcelona)
Asymptotic and continuous constructions in the geography of fibred varieties
いつもと開始時間が異なります。
Miguel Angel Barja 氏 (UPC-Barcelona)
Asymptotic and continuous constructions in the geography of fibred varieties
[ 講演概要 ]
Given a fibred variety $X$ onto a smooth variety $T$ it is possible to consider different types of inequalities between birational invariants associated to a line bundle $L$, such as Noether, Slope or Severi inequalities. Most of these inequalities are closely related through asymptotic constructions and/or continuous functions that suggest the use of some new invariants. We will survey different constructions both in characteristic 0 and positive characteristic, and will focus in the case of varieties of maximal Albanese dimension, fibred over curves. If time permits, we will also give some ideas on fibrations over surfaces.
Given a fibred variety $X$ onto a smooth variety $T$ it is possible to consider different types of inequalities between birational invariants associated to a line bundle $L$, such as Noether, Slope or Severi inequalities. Most of these inequalities are closely related through asymptotic constructions and/or continuous functions that suggest the use of some new invariants. We will survey different constructions both in characteristic 0 and positive characteristic, and will focus in the case of varieties of maximal Albanese dimension, fibred over curves. If time permits, we will also give some ideas on fibrations over surfaces.
代数幾何学セミナー
15:00-16:30 数理科学研究科棟(駒場) 118号室
いつもと開始時間が異なります。
服部真史 氏 (ノッティンガム大学)
Normal stable degeneration of Noether-Horikawa surfaces: Deformation Part
いつもと開始時間が異なります。
服部真史 氏 (ノッティンガム大学)
Normal stable degeneration of Noether-Horikawa surfaces: Deformation Part
[ 講演概要 ]
Koll’ar and Shepherd-Barron constructed a general theory for a canonical geometric compactification of moduli of smooth surfaces with ample canonical class by adding degenerations with only semi log canonical singularities. Their moduli is now called the KSBA moduli and degenerations are called stable degenerations. It has been a long standing question to classify all stable degenerations for smooth canonically polarized surfaces. In this talk, we focus on Q-Gorenstein deformation theory on Horikawa surfaces, which are minimal surfaces of general type in the case where the Noether inequality $K^2\geq 2p_g-4$ is an equality. This talk is based on the joint work (arXiv:2507:17633) with Hiroto Akaike, Makoto Enokizono, and Yuki Koto.
Koll’ar and Shepherd-Barron constructed a general theory for a canonical geometric compactification of moduli of smooth surfaces with ample canonical class by adding degenerations with only semi log canonical singularities. Their moduli is now called the KSBA moduli and degenerations are called stable degenerations. It has been a long standing question to classify all stable degenerations for smooth canonically polarized surfaces. In this talk, we focus on Q-Gorenstein deformation theory on Horikawa surfaces, which are minimal surfaces of general type in the case where the Noether inequality $K^2\geq 2p_g-4$ is an equality. This talk is based on the joint work (arXiv:2507:17633) with Hiroto Akaike, Makoto Enokizono, and Yuki Koto.
2025年10月29日(水)
幾何解析セミナー
13:30-14:30 数理科学研究科棟(駒場) 126号室
Tommaso Rossi 氏 (Scuola Internazionale Superiore di Studi Avanzati)
On the rectifiability of metric measure spaces with lower Ricci curvature bounds (英語)
https://sites.google.com/view/tommasorossi/home-page
Tommaso Rossi 氏 (Scuola Internazionale Superiore di Studi Avanzati)
On the rectifiability of metric measure spaces with lower Ricci curvature bounds (英語)
[ 講演概要 ]
Given a metric measure space (X,d,m), the curvature-dimension condition CD(K,N), and the measure contraction property MCP(K,N), are synthetic notions of having Ricci curvature bounded below by K (and dimension bounded above by N). We prove some rectifiability results for CD(K,N) and MCP(K,N) metric measure spaces (X,d,m) with pointwise Ahlfors regular reference measure m and with m-almost everywhere unique metric tangents. Our strategy is based on the failure of the CD condition in sub-Finsler Carnot groups, on a new result on the failure of the non-collapsed MCP on sub-Finsler Carnot groups, and on a recent breakthrough by D. Bate. This is a joint work with M. Magnabosco and A. Mondino.
[ 参考URL ]Given a metric measure space (X,d,m), the curvature-dimension condition CD(K,N), and the measure contraction property MCP(K,N), are synthetic notions of having Ricci curvature bounded below by K (and dimension bounded above by N). We prove some rectifiability results for CD(K,N) and MCP(K,N) metric measure spaces (X,d,m) with pointwise Ahlfors regular reference measure m and with m-almost everywhere unique metric tangents. Our strategy is based on the failure of the CD condition in sub-Finsler Carnot groups, on a new result on the failure of the non-collapsed MCP on sub-Finsler Carnot groups, and on a recent breakthrough by D. Bate. This is a joint work with M. Magnabosco and A. Mondino.
https://sites.google.com/view/tommasorossi/home-page
2025年10月28日(火)
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) 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。
井上 歩 氏 (津田塾大学)
On a relationship between quandle homology and relative group homology, from the view point of Seifert surfaces (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。
井上 歩 氏 (津田塾大学)
On a relationship between quandle homology and relative group homology, from the view point of Seifert surfaces (JAPANESE)
[ 講演概要 ]
Quandles and their homology are known to have good chemistry with knot theory. Associated with a triple of a group G, its automorphism, and its subgroup H satisfying a certain condition, we have a quandle. In this talk, we see that we have a chain map from the quandle chain complex of the quandle to the (Adamson/Hochschild) relative group chain complex of (G, H). We also see that this chain map has good chemistry with a triangulation of Seifert surface of a knot.
[ 参考URL ]Quandles and their homology are known to have good chemistry with knot theory. Associated with a triple of a group G, its automorphism, and its subgroup H satisfying a certain condition, we have a quandle. In this talk, we see that we have a chain map from the quandle chain complex of the quandle to the (Adamson/Hochschild) relative group chain complex of (G, H). We also see that this chain map has good chemistry with a triangulation of Seifert surface of a knot.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
解析学火曜セミナー
15:00-17:30 数理科学研究科棟(駒場) 002号室
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
今回は講演が2件あります。日時・場所にご注意ください。
Lauri Särkiö 氏 (Aalto University) 15:00-16:00
Gradient higher integrability of parabolic double-phase equations (English)
[ 講演概要 ]
Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
木下 真也 氏 (名古屋大学) 16:30-17:30Elliptic double-phase problems have been studied extensively in the last decade since a series of results by Mingione and others. Recently several regularity results have been obtained also for parabolic double-phase equations, yet many questions remain unsolved. In this talk, we focus on gradient higher integrability, showing that solutions to parabolic double-phase equations belong to a slightly higher Sobolev class than assumed a priori. The talk is based on joint work with Wontae Kim, Juha Kinnunen and Kristian Moring.
Global well-posedness for 3D quadratic nonlinear Schrödinger equations (Japanese)
[ 講演概要 ]
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
In this talk, we consider the Cauchy problem of the 3D nonlinear Schrödinger equations. It is known that if the nonlinearity is homogeneous of degree $p >2$, the general theory would provide the small data global existence of 3D NLS. In the quadratic case, which can be seen as a threshold of the small data global existence, the structure of nonlinearity plays a role and more sophisticated analysis is required. The aim in this talk is to show the global well-posedness in the scaling critical space with an additional angular regularity. The proof is based on the Fourier restriction norm method combined with several linear and bilinear estimates for the linear solutions.
2025年10月27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
馬 昭平 氏 (東京科学大学)
高次チャウサイクルから生ずるジーゲルモジュラー形式 (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
馬 昭平 氏 (東京科学大学)
高次チャウサイクルから生ずるジーゲルモジュラー形式 (Japanese)
[ 講演概要 ]
種数３以下のgenericなアーベル多様体上のある種の高次チャウサイクルからベクトル値ジーゲルモジュラー形式が得られること、そしてこの構成がアーベル多様体のランク１の退化に関して関手的であること（すなわちK理論エレベーターがジーゲル作用素と対応すること）をお話ししたいと思います。モジュラー形式の理論と代数サイクルの理論は楕円積分論という共通の起源を持っています。この200年の間の発展の代償として二つの分野は徐々に分化してきましたが、21世紀の今でもまだつながりがあることを伝えられたらと思います。
[ 参考URL ]種数３以下のgenericなアーベル多様体上のある種の高次チャウサイクルからベクトル値ジーゲルモジュラー形式が得られること、そしてこの構成がアーベル多様体のランク１の退化に関して関手的であること（すなわちK理論エレベーターがジーゲル作用素と対応すること）をお話ししたいと思います。モジュラー形式の理論と代数サイクルの理論は楕円積分論という共通の起源を持っています。この200年の間の発展の代償として二つの分野は徐々に分化してきましたが、21世紀の今でもまだつながりがあることを伝えられたらと思います。
https://forms.gle/gTP8qNZwPyQyxjTj8
2025年10月21日(火)
日仏数学拠点FJ-LMIセミナー
16:00-16:40 数理科学研究科棟(駒場) 128号室
Ramla ABDELLATIF 氏 (Université de Picardie)
Studying $p$-modular representations of $p$-adic groups in the setting of the Langlands programme (英語)
Ramla ABDELLATIF 氏 (Université de Picardie)
Studying $p$-modular representations of $p$-adic groups in the setting of the Langlands programme (英語)
[ 講演概要 ]
This talk aims to introduce the context of my primary research topic, namely $p$-modular representations of $p$-adic groups, as well as a current state of the art in the field, including some related questions I am currently exploring. After motivating the study of classical and modular Langlands correspondences for $p$-adic groups, I will explain why the $p$-modular setting (i.e. when representations of $p$-adic groups have coefficients in a field of positive characteristic equal to $p$) differs significantly from other settings (namely the complex and $\ell$-modular ones, with $\ell$ a prime distinct from $p$), then I will present the main results known so far about $p$-modular irreducible smooth representations of $p$-adic groups, with a particular focus on the special linear group $\mathrm{SL}_{2}$.
This talk aims to introduce the context of my primary research topic, namely $p$-modular representations of $p$-adic groups, as well as a current state of the art in the field, including some related questions I am currently exploring. After motivating the study of classical and modular Langlands correspondences for $p$-adic groups, I will explain why the $p$-modular setting (i.e. when representations of $p$-adic groups have coefficients in a field of positive characteristic equal to $p$) differs significantly from other settings (namely the complex and $\ell$-modular ones, with $\ell$ a prime distinct from $p$), then I will present the main results known so far about $p$-modular irreducible smooth representations of $p$-adic groups, with a particular focus on the special linear group $\mathrm{SL}_{2}$.
2025年10月20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
伊師 英之 氏 (大阪公立大学)
A CR-Laplacian type operator for the Silov boundary of a homogeneous Siegel domain (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
伊師 英之 氏 (大阪公立大学)
A CR-Laplacian type operator for the Silov boundary of a homogeneous Siegel domain (Japanese)
[ 講演概要 ]
Let $\Sigma$ be the Silov boundary of a homogeneous Siegel domain $D$ on which a Lie group $G$ acts transitively as affine transformations. The CR-structure on $\Sigma$ naturally induced from the ambient complex vector space is non-trivial if and only if $D$ is of non-tube type. In this case, $\Sigma$ is naturally identified with a two-step nilpotent Lie subgroup $N$ of $G$, called a generalized Heisenberg Lie group. Since the CR-structure is invariant under the action of $G$, the CR-cohomology space over $\Sigma$ can be regarded as a $G$-module. We consider unitarization of this presentation of $G$. The kernel of the CR-Laplacian does not give the solution because the natural Riemannian metric on $\Sigma$ is not $G$-invariant, so that the $G$-action does not preserve the space of CR-harmonic forms. Nevertheless, Nomura defined a unitary $G$-action on the space indirectly when $G$ is split solvable. In this talk, we introduce a space of CR-cochains with $G$-invariant inner product defined via the Fourier transform. Then the associated CR-operator is no longer a differential operator, while the kernel of the operator gives a unitarization of the representation of $G$ over the cohomology space.
[ 参考URL ]Let $\Sigma$ be the Silov boundary of a homogeneous Siegel domain $D$ on which a Lie group $G$ acts transitively as affine transformations. The CR-structure on $\Sigma$ naturally induced from the ambient complex vector space is non-trivial if and only if $D$ is of non-tube type. In this case, $\Sigma$ is naturally identified with a two-step nilpotent Lie subgroup $N$ of $G$, called a generalized Heisenberg Lie group. Since the CR-structure is invariant under the action of $G$, the CR-cohomology space over $\Sigma$ can be regarded as a $G$-module. We consider unitarization of this presentation of $G$. The kernel of the CR-Laplacian does not give the solution because the natural Riemannian metric on $\Sigma$ is not $G$-invariant, so that the $G$-action does not preserve the space of CR-harmonic forms. Nevertheless, Nomura defined a unitary $G$-action on the space indirectly when $G$ is split solvable. In this talk, we introduce a space of CR-cochains with $G$-invariant inner product defined via the Fourier transform. Then the associated CR-operator is no longer a differential operator, while the kernel of the operator gives a unitarization of the representation of $G$ over the cohomology space.
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
大泉 嶺 氏 (国立社会保障・人口問題研究所 (厚生労働省))
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
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。
大泉 嶺 氏 (国立社会保障・人口問題研究所 (厚生労働省))
Fredholm Integral Equations and Eigenstructure: Genealogical Expansions via Non–Hilbert–Schmidt Solutions
[ 講演概要 ]
Fredholm integral equations play a central role in describing the long-term behavior of structured population models. In this talk, I present a determinant-free approach that constructs eigenfunctions through genealogical expansions, valid even beyond the Hilbert–Schmidt setting. The expansion is closely related to taboo probabilities in Markov chains, allowing eigenfunctions to be interpreted as cumulative ancestral contributions. As an application, I discuss age-structured branching processes and show how quantities such as expected generation counts and reproduction numbers naturally arise from the eigenvalue problem. This perspective highlights how eigenstructure encodes genealogical memory and opens connections between population dynamics, probability theory, and evolutionary processes.
Fredholm integral equations play a central role in describing the long-term behavior of structured population models. In this talk, I present a determinant-free approach that constructs eigenfunctions through genealogical expansions, valid even beyond the Hilbert–Schmidt setting. The expansion is closely related to taboo probabilities in Markov chains, allowing eigenfunctions to be interpreted as cumulative ancestral contributions. As an application, I discuss age-structured branching processes and show how quantities such as expected generation counts and reproduction numbers naturally arise from the eigenvalue problem. This perspective highlights how eigenstructure encodes genealogical memory and opens connections between population dynamics, probability theory, and evolutionary processes.
東京名古屋代数セミナー
16:30-18:00 オンライン開催
百合草 寿哉 氏 (大阪公立大学)
Finiteness and tameness of Jacobian algebras (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
百合草 寿哉 氏 (大阪公立大学)
Finiteness and tameness of Jacobian algebras (Japanese)
[ 講演概要 ]
本講演では、有限次元ヤコビ代数をその表現型の観点から研究し、$E$不変量によって定義される$E$有限性および$E$-tame性と、$g$有限性、$\tau$傾有限性、表現有限性などの他の有限性・tame性の概念との対応について述べる。
まず、これらの性質がクイバーとポテンシャルの変異の下で不変であることを示す。その結果として、有限次元ヤコビ代数$\mathcal{J}(Q,W)$が$E$有限であることは、$g$有限、$\tau$傾有限、表現有限であることと同値であり、この場合には $Q$がDynkin型であることが分かる。この結果は、Demonetの「$E$有限なら$g$有限である」という予想を含む形で成立している。
また、$E$-tame性に関しては、例外的な3つの型を除いて、$g$-tame性および表現tame性と対応することが分かる。本講演は、Mohamad Haerizadeh氏との共同研究に基づくものである。
Zoom ID 829 2845 2592
Password 265160
[ 参考URL ]本講演では、有限次元ヤコビ代数をその表現型の観点から研究し、$E$不変量によって定義される$E$有限性および$E$-tame性と、$g$有限性、$\tau$傾有限性、表現有限性などの他の有限性・tame性の概念との対応について述べる。
まず、これらの性質がクイバーとポテンシャルの変異の下で不変であることを示す。その結果として、有限次元ヤコビ代数$\mathcal{J}(Q,W)$が$E$有限であることは、$g$有限、$\tau$傾有限、表現有限であることと同値であり、この場合には $Q$がDynkin型であることが分かる。この結果は、Demonetの「$E$有限なら$g$有限である」という予想を含む形で成立している。
また、$E$-tame性に関しては、例外的な3つの型を除いて、$g$-tame性および表現tame性と対応することが分かる。本講演は、Mohamad Haerizadeh氏との共同研究に基づくものである。
Zoom ID 829 2845 2592
Password 265160
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2025年10月17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) NISSAY Lecture Hall (大講義室)号室
坂内健一 氏 (慶應義塾大学/理化学研究所)
包摂的な教育研究環境の構築と人材育成に向けて
〜個々の現状と責任〜 (日本語)
坂内健一 氏 (慶應義塾大学/理化学研究所)
包摂的な教育研究環境の構築と人材育成に向けて
〜個々の現状と責任〜 (日本語)
[ 講演概要 ]
講演者は約10年前より理化学研究所革新知能統合研究センターにおいて人工知能・機械学習の研究に携わり、多様な分野の研究者と交流してきました。また、2020年から2024年の5年間、日本数学会男女共同参画社会推進委員会の委員・委員長を務めた経験を通じ、学術分野における社会的課題をより深く意識するようになりました。
多様な背景を持つ構成員が安心して活躍できる包摂的な教育研究環境を整えることは、活発で持続可能な教育研究活動の基盤となります。本講演およびパネルディスカッションでは、現状の課題や個々が果たすべき責任について参加者とともに考え、よりよい環境づくりのための具体的な方向性を議論する機会としたいと思います。
講演者は約10年前より理化学研究所革新知能統合研究センターにおいて人工知能・機械学習の研究に携わり、多様な分野の研究者と交流してきました。また、2020年から2024年の5年間、日本数学会男女共同参画社会推進委員会の委員・委員長を務めた経験を通じ、学術分野における社会的課題をより深く意識するようになりました。
多様な背景を持つ構成員が安心して活躍できる包摂的な教育研究環境を整えることは、活発で持続可能な教育研究活動の基盤となります。本講演およびパネルディスカッションでは、現状の課題や個々が果たすべき責任について参加者とともに考え、よりよい環境づくりのための具体的な方向性を議論する機会としたいと思います。
2025年10月14日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Frank Taipe 氏 (IMCA)
Compact quantum ergodic systems arising from planar algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Frank Taipe 氏 (IMCA)
Compact quantum ergodic systems arising from planar 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) 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。
小木曾 啓示 氏 (東京大学大学院数理科学研究科)
On K3 surfaces with non-elementary hyperbolic automorphism group (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。
小木曾 啓示 氏 (東京大学大学院数理科学研究科)
On K3 surfaces with non-elementary hyperbolic automorphism group (JAPANESE)
[ 講演概要 ]
This talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).
Main result of this talk is the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic, under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling basic facts and some special nice properties of K3 surfaces, the notion of hyperbolicity of group due to Gromov, and their importance and interest (in our view), I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Néron-Severi lattices and then how one can deduce the above-mentioned finiteness, via a recent important observation by Professors Kikuta and Takatsu (independently) on geometrically finiteness, with a new algebro-geometric study of genus one fibrations on K3 surfaces by us.
[ 参考URL ]This talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).
Main result of this talk is the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic, under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling basic facts and some special nice properties of K3 surfaces, the notion of hyperbolicity of group due to Gromov, and their importance and interest (in our view), I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Néron-Severi lattices and then how one can deduce the above-mentioned finiteness, via a recent important observation by Professors Kikuta and Takatsu (independently) on geometrically finiteness, with a new algebro-geometric study of genus one fibrations on K3 surfaces by us.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
可香谷 隆 氏 (室蘭工業大学)
Inverse curvature flow of Legendre curves (Japanese)
可香谷 隆 氏 (室蘭工業大学)
Inverse curvature flow of Legendre curves (Japanese)
[ 講演概要 ]
逆曲率流方程式はある種の放物型方程式に分類される微分方程式である．本講演では，逆曲率流に対し，初期曲線がある程度のカスプを持つ場合に，カスプ型の特異性が保たれることを示すため，滑らかなはめ込みとしてカスプ型の特異性を持つ曲線を記述できるルジャンドル曲線を導入し，ルジャンドル曲線の枠組みでの初期値問題の時間大域解の一意存在性と時間無限大での漸近挙動解析について考察する．なお，本講演は高橋雅朋氏(室蘭工業大学)との共同研究に基づく．
逆曲率流方程式はある種の放物型方程式に分類される微分方程式である．本講演では，逆曲率流に対し，初期曲線がある程度のカスプを持つ場合に，カスプ型の特異性が保たれることを示すため，滑らかなはめ込みとしてカスプ型の特異性を持つ曲線を記述できるルジャンドル曲線を導入し，ルジャンドル曲線の枠組みでの初期値問題の時間大域解の一意存在性と時間無限大での漸近挙動解析について考察する．なお，本講演は高橋雅朋氏(室蘭工業大学)との共同研究に基づく．
2025年10月10日(金)
代数幾何学セミナー
10:00-11:30 数理科学研究科棟(駒場) 122号室
いつもと時間・部屋が異なります。
Yuri Tschinkel 氏 (New York University)
Equivariant birational geometry
いつもと時間・部屋が異なります。
Yuri Tschinkel 氏 (New York University)
Equivariant birational geometry
[ 講演概要 ]
I will report on new results and constructions in higher-dimensional birational geometry in presence of actions of finite groups.
I will report on new results and constructions in higher-dimensional birational geometry in presence of actions of finite groups.
2025年10月08日(水)
幾何解析セミナー
10:30-11:30 数理科学研究科棟(駒場) 126号室
Jinpeng Lu 氏 (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
https://www.mv.helsinki.fi/home/jinpeng/
Jinpeng Lu 氏 (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
[ 講演概要 ]
Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
[ 参考URL ]Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
https://www.mv.helsinki.fi/home/jinpeng/
日仏数学拠点FJ-LMIセミナー
15:00-16:00 数理科学研究科棟(駒場) 056号室
Sourav Ghosh 氏 (Ashoka University)
Proper actions on group manifolds (英語)
Sourav Ghosh 氏 (Ashoka University)
Proper actions on group manifolds (英語)
[ 講演概要 ]
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
2025年10月07日(火)
トポロジー火曜セミナー
17:00-18:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
菅原 朔見 氏 (北海道大学)
Topology of hyperplane arrangements and related 3-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
菅原 朔見 氏 (北海道大学)
Topology of hyperplane arrangements and related 3-manifolds (JAPANESE)
[ 講演概要 ]
One of the central questions in the topology of hyperplane arrangements is whether several topological invariants are combinatorially determined. While the cohomology ring of the complement has a combinatorial description, it remains open whether even the first Betti number of the Milnor fiber is. In contrast, the homeomorphism types of 3-manifolds appearing as the boundary manifold of projective line arrangements and the Milnor fiber boundary of arrangements in a 3-dimensional space are combinatorially determined. In this talk, we focus on these 3-manifolds. In particular, we will present the cohomology ring structure for the boundary manifold, originally due to Cohen-Suciu, and an explicit formula for the homology group of the Milnor fiber boundary of generic arrangements.
[ 参考URL ]One of the central questions in the topology of hyperplane arrangements is whether several topological invariants are combinatorially determined. While the cohomology ring of the complement has a combinatorial description, it remains open whether even the first Betti number of the Milnor fiber is. In contrast, the homeomorphism types of 3-manifolds appearing as the boundary manifold of projective line arrangements and the Milnor fiber boundary of arrangements in a 3-dimensional space are combinatorially determined. In this talk, we focus on these 3-manifolds. In particular, we will present the cohomology ring structure for the boundary manifold, originally due to Cohen-Suciu, and an explicit formula for the homology group of the Milnor fiber boundary of generic arrangements.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年10月06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
竹内 有哉 氏 (筑波大学)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
竹内 有哉 氏 (筑波大学)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
[ 講演概要 ]
The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
[ 参考URL ]The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:30-18:00 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。
河備 浩司 氏 (慶應義塾大学)
Riemann多様体上の排他過程に対する流体力学極限
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。
河備 浩司 氏 (慶應義塾大学)
Riemann多様体上の排他過程に対する流体力学極限
[ 講演概要 ]
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
2025年10月03日(金)
統計数学セミナー
16:00-17:10 数理科学研究科棟(駒場) 123号室
ハイブリッド開催
Freddy Delbaen 氏 (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
ハイブリッド開催
Freddy Delbaen 氏 (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
[ 講演概要 ]
With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
[ 参考URL ]With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
2025年09月25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
尾上文彦 氏 (ミュンヘン工科大学)
On the shape of fractional minimal surfaces (Japanese)
尾上文彦 氏 (ミュンヘン工科大学)
On the shape of fractional minimal surfaces (Japanese)
[ 講演概要 ]
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
2025年09月09日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Kang Li 氏 (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
Kang Li 氏 (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
2025年08月22日(金)
博士論文発表会
16:00-17:15 数理科学研究科棟(駒場) 128号室
星野 真生 氏 (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
星野 真生 氏 (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
2025年08月19日(火)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 117号室
いつもと曜日・部屋が異なります。
Trung Tuyen Truong 氏 (University of Oslo)
Some new results concerning Tate's questions and generalisations
いつもと曜日・部屋が異なります。
Trung Tuyen Truong 氏 (University of Oslo)
Some new results concerning Tate's questions and generalisations
[ 講演概要 ]
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
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