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過去の記録
過去の記録 ～01/14｜本日 01/15 | 今後の予定 01/16～
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。
Serban Matei Mihalache 氏 (東京大学大学院数理科学研究科)
Polygon 方程式と Simplex 方程式の解の構成 (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。
Serban Matei Mihalache 氏 (東京大学大学院数理科学研究科)
Polygon 方程式と Simplex 方程式の解の構成 (JAPANESE)
[ 講演概要 ]
Polygon 方程式は Dimakis--Müller-Hoissen により定式化された. これは, n次元PL多様体の三角形分割に対する Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-変形に対応する代数的な方程式であると解釈でき, n 次元 PL 多様体の不変量の構成に用いることができるのではないかと期待される. この講演では, 低次元の"可換"な Polygon 方程式の解の組を用いることで, 高次元の Polygon 方程式の解が構成できることを示し, Polygon方程式の解の具体例を与える. また, Polygon 方程式の解の組で mixed 関係式と呼ばれるものを満たすものが与えられたとき, Yang-Baxter 方程式の高次元版である Simplex 方程式の解が構成できることを示す. この講演は持田知朗との共同研究に基づく．
[ 参考URL ]Polygon 方程式は Dimakis--Müller-Hoissen により定式化された. これは, n次元PL多様体の三角形分割に対する Pachner (⌊(n+1)/2⌋+1, ⌈(n+1)/2⌉)-変形に対応する代数的な方程式であると解釈でき, n 次元 PL 多様体の不変量の構成に用いることができるのではないかと期待される. この講演では, 低次元の"可換"な Polygon 方程式の解の組を用いることで, 高次元の Polygon 方程式の解が構成できることを示し, Polygon方程式の解の具体例を与える. また, Polygon 方程式の解の組で mixed 関係式と呼ばれるものを満たすものが与えられたとき, Yang-Baxter 方程式の高次元版である Simplex 方程式の解が構成できることを示す. この講演は持田知朗との共同研究に基づく．
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
Valerio Proietti 氏 (Univ. Oslo)
Base change, groupoid homology, and hyperbolic dynamics
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Valerio Proietti 氏 (Univ. Oslo)
Base change, groupoid homology, and hyperbolic dynamics
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025年11月10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。
濱口 雄史 氏 (京都大学)
確率ヴォルテラ方程式のマルコフリフトの弱エルゴード性
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。
濱口 雄史 氏 (京都大学)
確率ヴォルテラ方程式のマルコフリフトの弱エルゴード性
[ 講演概要 ]
確率ヴォルテラ方程式の解は一般に非マルコフかつ非セミマルチンゲールであるような(有限次元)確率過程であるが、無限次元空間への持ち上げを考えることで、あるヒルベルト空間上のマルコフ過程(マルコフリフト)が得られる。
また、元の確率ヴォルテラ方程式の解は、このマルコフリフトのある種の射影として復元できる。
本研究の目的は、マルコフリフトの長時間漸近挙動を調べ、元の確率ヴォルテラ方程式の解に関する極限定理を得ることである。
そのうえで解決すべき難点は、マルコフリフトが満たす確率発展方程式が退化型であること、すなわち状態空間は無限次元であるが、ノイズを駆動するブラウン運動は有限次元であるという点である。
前回の東京確率論セミナー(2023年6月19日)では、マルコフリフトの漸近的対数ハルナック不等式、特に不変確率測度の一意性に関する結果を報告した。
本講演では、マルコフリフトの不変確率測度の存在性と指数型弱エルゴ―ド評価について、現在までに得られた研究成果を報告する。
確率ヴォルテラ方程式の解は一般に非マルコフかつ非セミマルチンゲールであるような(有限次元)確率過程であるが、無限次元空間への持ち上げを考えることで、あるヒルベルト空間上のマルコフ過程(マルコフリフト)が得られる。
また、元の確率ヴォルテラ方程式の解は、このマルコフリフトのある種の射影として復元できる。
本研究の目的は、マルコフリフトの長時間漸近挙動を調べ、元の確率ヴォルテラ方程式の解に関する極限定理を得ることである。
そのうえで解決すべき難点は、マルコフリフトが満たす確率発展方程式が退化型であること、すなわち状態空間は無限次元であるが、ノイズを駆動するブラウン運動は有限次元であるという点である。
前回の東京確率論セミナー(2023年6月19日)では、マルコフリフトの漸近的対数ハルナック不等式、特に不変確率測度の一意性に関する結果を報告した。
本講演では、マルコフリフトの不変確率測度の存在性と指数型弱エルゴ―ド評価について、現在までに得られた研究成果を報告する。
2025年11月06日(木)
東京確率論セミナー
14:00-17:30 数理科学研究科棟(駒場) 128号室
講演は木曜日で開始時間が早まっています。教室は１２８です。今日はTea Time はありません。
Mo Dick Wong 氏 (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
de Finetti Random Walks on a Hypercube and Gaussian Fields
講演は木曜日で開始時間が早まっています。教室は１２８です。今日はTea Time はありません。
Mo Dick Wong 氏 (Durham University) 14:00-15:30
On the limiting distribution of partial sums of random multiplicative functions
[ 講演概要 ]
Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
Robert Griffiths 氏 (Monash University) 16:00-17:30Consider a random walk associated with a Steinhaus multiplicative function (i.e. the increments are completely multiplicative and uniformly distributed on the complex unit circle): what can we say about its asymptotic behaviour? In his seminal work, Harper resolved a conjecture of Helson by showing that low fractional moments exhibit better-than-square-root cancellation, but the asymptotic distribution remained a mystery and was left as an open problem. In this talk, I will first explain some history and the number-theoretic motivations behind this model, and then present a central limit theorem that features a nonstandard renormalisation as well as a random variance described by the Riemann Zeta function on the critical line. I will highlight the probabilistic aspects of our proof, and in particular discuss a universality result for critical non-Gaussian multiplicative chaos. This is based on joint work with Ofir Gorodetsky.
de Finetti Random Walks on a Hypercube and Gaussian Fields
[ 講演概要 ]
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
This talk will discuss a random walk on the infinite hypercube,
Xt+1 = Xt + Zt mod 2.
The increments (Zt) are i.i.d. with entries that form an infinite exchange- able {0,1} sequence, a de Finetti sequence. There is geometric killing in the random walk. A Gaussian free field (gx)x∈{0,1}∞ is associated with the random walk by taking the covariance function to be proportional to the Green function of the random walk. The Green function and a strong rep- resentation for (gx) are characterized by a negative binomial point process which involves the de Finetti measure of the increments of the random walk.
2025年11月04日(火)
トポロジー火曜セミナー
17:00-18:00 オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
高尾 和人 氏 (東北大学)
Heegaard分解の強既約性とGoeritz群の有限性の判定条件 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
高尾 和人 氏 (東北大学)
Heegaard分解の強既約性とGoeritz群の有限性の判定条件 (JAPANESE)
[ 講演概要 ]
３次元多様体のHeegaard分解に対して，Casson-Gordonは，その強既約性を保証する判定条件を導入した．Lustig-Moriahによって，その強化版も定義され，Heegaard分解のGoeritz群の有限性をも保証する判定条件となっている．それらに用いる情報源はHeegaard図式，ただし，各ハンドル体の最大の円盤系から構成されるHeegaard図式だった．本講演では，最小の場合も含む任意の円盤系に対して，上記の判定条件を一般化する．また，その応用により，最小ではない種数を持ちながらGoeritz群は有限となるHeegaard分解の具体例も与える．れらは古宇田悠哉氏との共同研究に基づく．
[ 参考URL ]３次元多様体のHeegaard分解に対して，Casson-Gordonは，その強既約性を保証する判定条件を導入した．Lustig-Moriahによって，その強化版も定義され，Heegaard分解のGoeritz群の有限性をも保証する判定条件となっている．それらに用いる情報源はHeegaard図式，ただし，各ハンドル体の最大の円盤系から構成されるHeegaard図式だった．本講演では，最小の場合も含む任意の円盤系に対して，上記の判定条件を一般化する．また，その応用により，最小ではない種数を持ちながらGoeritz群は有限となるHeegaard分解の具体例も与える．れらは古宇田悠哉氏との共同研究に基づく．
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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
岩佐亮明 氏 (University of Copenhagen)
Descent and pro-excision
岩佐亮明 氏 (University of Copenhagen)
Descent and pro-excision
[ 講演概要 ]
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
The theme of this talk is descent and excision of cohomology theories of schemes. We will start with a discussion of the canonical topology on spectral schemes. Unlike on classical schemes, this topology includes many other types of covers, such as h-covers. Then I will explain that THH and TC satisfy descent with respect to the canonical topology, which generalizes the flat descent by Bhatt—Morrow—Scholze. This in turn implies the cdh descent of K-theory on spectral schemes, despite its failure on classical schemes. Furthermore, this implies the cdh pro-excision of K-theory on spectral schemes, which generalizes the derived case by Kelly—Saito—Tamme (the original noetherian case is due to Kerz—Strunk—Tamme). Our proof of the cdh pro-excision is quite different from the previous ones and is more algebraic in nature. The results presented here are based on discussions with Antieau, Burklund, and Krause.
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
Jesse Reimann 氏 (TU Delft)
Split exact sequences and KK-equivalences of quantum flag manifolds
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Jesse Reimann 氏 (TU Delft)
Split exact sequences and KK-equivalences of quantum flag manifolds
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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
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