本文印刷
全画面プリント
過去の記録
過去の記録 ～07/23｜本日 07/24 | 今後の予定 07/25～
2026年07月23日(木)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 122号室
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
2026年07月21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
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年07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号室
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
[ 講演概要 ]
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
2026年07月15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
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
[ 講演概要 ]
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
2026年07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
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
[ 講演概要 ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
トポロジー火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) hybrid/056号室
Lie群論・表現論セミナーと合同開催。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Lie群論・表現論セミナーと合同開催。 参加を希望される場合は、セミナーのウェブページをご覧下さい。
田中 雄一郎 氏 (東京大学大学院数理科学研究科)
Visible actions of real reductive groups on complex algebraic varieties (JAPANESE)
[ 講演概要 ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
[ 参考URL ]A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition. To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds. This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi's propagation theorem of multiplicity-freeness property for visible actions. In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties. We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
榊原航也 氏 (金沢大学理工研究域)
制約付き平面閉曲線流に対する安定化 dual-SAV パラメトリック有限要素法 (Japanese)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
榊原航也 氏 (金沢大学理工研究域)
制約付き平面閉曲線流に対する安定化 dual-SAV パラメトリック有限要素法 (Japanese)
[ 講演概要 ]
曲率に駆動される平面閉曲線の時間発展をパラメトリック有限要素法で計算する際には，高階の幾何学的剛性に加え，節点の集中・疎化によるメッシュの劣化，さらに面積や酋長などの大域的制約に由来する非線型性を同時に扱う必要がある．本講演では，物理的な幾何エネルギーと人工的なメッシュ正則化エネルギーに対して，独立な2つの scalar auxiliary variable (SAV) を導入する安定化 dual-SAV パラメトリック有限要素法を紹介する．メッシュ正則化に対応する力を接線方向にのみ作用させることで，曲線の法線方向の幾何学的運動を変えることなく，節点の再配置を実現する．また，既知時刻の計量を凍結した半陰的離散化と，速度そのものに作用する零次安定化を組み合わせることにより，各時間ステップに現れる空間方向の問題を正定値対称な線型応答問題へと帰着させ，幾何 SAV エネルギーおよびメッシュ修正 SAV エネルギーに対する離散散逸則を導く．さらに，K 個の大域的制約を課す場合，ブロック消去によって残る非線型問題が，メッシュ節点数によらない K+1 次元の代数系に縮約されることを示す．曲線短縮流，面積保存曲線短縮流，曲線拡散流，ならびに面積・周長制約付き Helfrich 型流の数値例を通じて，時間精度，修正エネルギー散逸，制約を高精度に満たすこと，メッシュ品質および計算効率を検証する．
[ 参考URL ]曲率に駆動される平面閉曲線の時間発展をパラメトリック有限要素法で計算する際には，高階の幾何学的剛性に加え，節点の集中・疎化によるメッシュの劣化，さらに面積や酋長などの大域的制約に由来する非線型性を同時に扱う必要がある．本講演では，物理的な幾何エネルギーと人工的なメッシュ正則化エネルギーに対して，独立な2つの scalar auxiliary variable (SAV) を導入する安定化 dual-SAV パラメトリック有限要素法を紹介する．メッシュ正則化に対応する力を接線方向にのみ作用させることで，曲線の法線方向の幾何学的運動を変えることなく，節点の再配置を実現する．また，既知時刻の計量を凍結した半陰的離散化と，速度そのものに作用する零次安定化を組み合わせることにより，各時間ステップに現れる空間方向の問題を正定値対称な線型応答問題へと帰着させ，幾何 SAV エネルギーおよびメッシュ修正 SAV エネルギーに対する離散散逸則を導く．さらに，K 個の大域的制約を課す場合，ブロック消去によって残る非線型問題が，メッシュ節点数によらない K+1 次元の代数系に縮約されることを示す．曲線短縮流，面積保存曲線短縮流，曲線拡散流，ならびに面積・周長制約付き Helfrich 型流の数値例を通じて，時間精度，修正エネルギー散逸，制約を高精度に満たすこと，メッシュ品質および計算効率を検証する．
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2026年07月13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) 126号室
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
[ 講演概要 ]
It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
[ 参考URL ]It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
https://forms.gle/8ERsVDLuKHwbVzm57
2026年07月08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
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
https://vova-sosnilo.com/
Vova Sosnilo 氏 (理化学研究所 数理創造研究センター)
Descent for algebraic K-theory of algebraic stacks
[ 講演概要 ]
Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
[ 参考URL ]Algebraic K-theory satisfies descent with respect to Nisnevich covers, which allows one to deduce global computations for schemes to the affine case. For algebraic stacks this is insufficient, since algebraic stacks with nontrivial stabilizers do not admit Nisnevich covers by affine schemes. However, a theorem of Deshmukh shows that any algebraic stack with separated diagonal admits a Nisnevich surjection from an affine scheme. The Atiyah—Segal completion theorem measures precisely the failure of algebraic K-theory to satisfy descent with respect to Nisnevich surjections. We show that it holds for ANS algebraic stacks of finite type over a field of characteristic 0 using trace methods and equivariant resolution of singularities. Time permitting, we discuss an ongoing work attempting to extend this result in characteristic p.
https://vova-sosnilo.com/
東京名古屋代数セミナー
13:00-14:30 オンライン開催
髙谷 悠太 氏 (東京大学)
Characteristic-free approaches around Yu's construction (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
髙谷 悠太 氏 (東京大学)
Characteristic-free approaches around Yu's construction (Japanese)
[ 講演概要 ]
Yu's construction is one of the most wide-ranging constructions of supercuspidal representations. Recently, Fintzen, Kaletha, and Spice introduced a quadratic twist of this construction to build stable L-packets, which also appears in the geometric realization via positive-depth Deligne-Lusztig induction. In this talk, I will present a direct approach to twisted Yu's construction and explain how to remove technical conditions on small primes in the theory of Yu's construction and positive-depth Deligne-Lusztig induction.
Zoom ID 882 6509 3568 Password 616173
[ 参考URL ]Yu's construction is one of the most wide-ranging constructions of supercuspidal representations. Recently, Fintzen, Kaletha, and Spice introduced a quadratic twist of this construction to build stable L-packets, which also appears in the geometric realization via positive-depth Deligne-Lusztig induction. In this talk, I will present a direct approach to twisted Yu's construction and explain how to remove technical conditions on small primes in the theory of Yu's construction and positive-depth Deligne-Lusztig induction.
Zoom ID 882 6509 3568 Password 616173
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026年07月07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
橋本七海 氏 (慶応大)
Equivalence of categories of KK-theory or E-theory for $C^*$-algebras over topological spaces by reflection functors
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
橋本七海 氏 (慶応大)
Equivalence of categories of KK-theory or E-theory for $C^*$-algebras over topological spaces by reflection functors
[ 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
16:00-17:00 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。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (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。
矢ヶ崎 達彦 氏 ( 京都工芸繊維大学)
Topological properties of groups of volume-preserving diffeomorphisms and groups of uniform homeomorphisms (JAPANESE)
[ 講演概要 ]
This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
[ 参考URL ]This talk is a continuation of survey on topological properties of groups of homeomorphisms/diffeomorphisms on noncompact manifolds. As a subject related to ends of noncompact manifolds, we discuss volume transfer towards ends, which leads to the existence of continuous sections under the compact-open topology for the actions of diffeomorphism groups on the spaces of volume forms on noncompact manifolds (a noncompact version of Moser's theorem) and for the end charge homomorphisms introduced by Alpern and Prasad. We also give a brief survey on the local and end deformation properties in groups of uniform homeomorphisms on noncompact metric manifolds with the sup-metric.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年07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) 126号室
Xiaojun Wu 氏 (筑波大学)
Generalised Ueda Obstruction Classes and Non-Semipositive Line Bundles (English)
https://forms.gle/8ERsVDLuKHwbVzm57
Xiaojun Wu 氏 (筑波大学)
Generalised Ueda Obstruction Classes and Non-Semipositive Line Bundles (English)
[ 講演概要 ]
Serre’s classical example provides a fundamental instance of a nef but non-semipositive line bundle and motivated the analytic definition of nefness introduced by Demailly–Peternell–Schneider. Building on subsequent developments by Koike, the classical Ueda obstruction classes provide a natural criterion for non-semipositivity. In this talk, we introduce a natural generalisation of the Ueda obstruction classes that is always well defined and for which the Chern curvature naturally determines representatives. As an application, we obtain an elementary and systematic method for constructing nef but non-semipositive line bundles.
[ 参考URL ]Serre’s classical example provides a fundamental instance of a nef but non-semipositive line bundle and motivated the analytic definition of nefness introduced by Demailly–Peternell–Schneider. Building on subsequent developments by Koike, the classical Ueda obstruction classes provide a natural criterion for non-semipositivity. In this talk, we introduce a natural generalisation of the Ueda obstruction classes that is always well defined and for which the Chern curvature naturally determines representatives. As an application, we obtain an elementary and systematic method for constructing nef but non-semipositive line bundles.
https://forms.gle/8ERsVDLuKHwbVzm57
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
15:20〜 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。
舟木直久 氏 (北京雁栖湖応用数学研究院)
Interface motion from non-gradient Glauber-Kawasaki dynamics
15:20〜 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。
舟木直久 氏 (北京雁栖湖応用数学研究院)
Interface motion from non-gradient Glauber-Kawasaki dynamics
[ 講演概要 ]
Motivated by the problem of dynamic phase transitions, we study the derivation of interface motion from non-gradient Glauber-Kawasaki dynamics. In the balanced case, the limiting interface evolves according to the anisotropic curvature flow, while in the unbalanced case it is governed by a geometric Hamilton-Jacobi equation. We establish this result as a quantitative hydrodynamic limit and, by applying the method of quantitative homogenization, obtain convergence rates. We also investigate fluctuations of the interface and derive a linear stochastic partial differential equation. This talk is partially based on several joint works with Chenlin Gu (Tsinghua U), Han Wang (Tsinghua U), Shuhan Zhou (Peking U), Hyunjoon Park (Meiji U), Claudio Landim (IMPA), Sunder Sethuraman (U Arizona).
Motivated by the problem of dynamic phase transitions, we study the derivation of interface motion from non-gradient Glauber-Kawasaki dynamics. In the balanced case, the limiting interface evolves according to the anisotropic curvature flow, while in the unbalanced case it is governed by a geometric Hamilton-Jacobi equation. We establish this result as a quantitative hydrodynamic limit and, by applying the method of quantitative homogenization, obtain convergence rates. We also investigate fluctuations of the interface and derive a linear stochastic partial differential equation. This talk is partially based on several joint works with Chenlin Gu (Tsinghua U), Han Wang (Tsinghua U), Shuhan Zhou (Peking U), Hyunjoon Park (Meiji U), Claudio Landim (IMPA), Sunder Sethuraman (U Arizona).
2026年07月03日(金)
代数幾何学セミナー
13:15-14:45 数理科学研究科棟(駒場) 117号室
吉川 翔 氏 (東京科学大学)
Hodge–Tate splitting and Akizuki–Nakano vanishing
吉川 翔 氏 (東京科学大学)
Hodge–Tate splitting and Akizuki–Nakano vanishing
[ 講演概要 ]
Akizuki–Nakano vanishing theorem は、Kodaira vanishing theorem を微分形式係数のコホモロジーへ拡張する基本的な消滅定理であり、複素代数幾何においてコホモロジーの制御や変形理論に重要な役割を果たす。一方、正標数ではこの定理は一般には成立せず、どのような幾何学的条件の下で同様の消滅定理が成り立つかは、自然かつ重要な問題である。
この方向の出発点として、Deligne–Illusie は、滑らかな固有多様体がW_2-lift をもち、かつその次元が標数より小さい場合に、de Rham complex の分解を用いて Akizuki–Nakano vanishing を証明した。近年、Petrov は quasi-F-split 多様体に対して、次元に関する制限なしに Akizuki–Nakano vanishing が従うことを証明した。
本講演では、これらの結果を統一的に捉える枠組みとして Hodge–Tate splitting という条件を考察し、この条件から Akizuki–Nakano vanishing が導かれることを説明する。また、この結果の混標数における類似についても紹介したい。
本講演は石塚彾氏との共同研究に基づく。
Akizuki–Nakano vanishing theorem は、Kodaira vanishing theorem を微分形式係数のコホモロジーへ拡張する基本的な消滅定理であり、複素代数幾何においてコホモロジーの制御や変形理論に重要な役割を果たす。一方、正標数ではこの定理は一般には成立せず、どのような幾何学的条件の下で同様の消滅定理が成り立つかは、自然かつ重要な問題である。
この方向の出発点として、Deligne–Illusie は、滑らかな固有多様体がW_2-lift をもち、かつその次元が標数より小さい場合に、de Rham complex の分解を用いて Akizuki–Nakano vanishing を証明した。近年、Petrov は quasi-F-split 多様体に対して、次元に関する制限なしに Akizuki–Nakano vanishing が従うことを証明した。
本講演では、これらの結果を統一的に捉える枠組みとして Hodge–Tate splitting という条件を考察し、この条件から Akizuki–Nakano vanishing が導かれることを説明する。また、この結果の混標数における類似についても紹介したい。
本講演は石塚彾氏との共同研究に基づく。
2026年07月01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
石倉麟太郎 氏 (東京大学大学院数理科学研究科)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
石倉麟太郎 氏 (東京大学大学院数理科学研究科)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
[ 講演概要 ]
The notion of ordinary modular forms, introduced and developed in Hida theory, has played a central role in the study of p-adic families of automorphic forms. It is therefore natural to ask how this notion extends to automorphic representations of covering groups. This talk is concerned with p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions for a representation to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
The notion of ordinary modular forms, introduced and developed in Hida theory, has played a central role in the study of p-adic families of automorphic forms. It is therefore natural to ask how this notion extends to automorphic representations of covering groups. This talk is concerned with p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions for a representation to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
2026年06月30日(火)
トポロジー火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) hybrid/123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。
Sang-hyun Kim 氏 (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Sang-hyun Kim 氏 (Korea Institute For Advanced Study)
Structure and rigidity of manifold diffeomorphism groups (ENGLISH)
[ 講演概要 ]
Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
[ 参考URL ]Given a manifold M and a structure S, we denote by Homeo(M;S) the group of S-preserving homeomorphisms of M. We will be particularly concerned with the case tha S is the C^r structure in the sense of Hölder continuity. In such a case, the group is written as Diff^r(M). The goal of this lecture series is to survey recent results and open questions on the rigidity of the group structures involving these groups. When M is a compact one-manifold, namely an interval or a circle, each real number r≥1 admits a finitely generated subgroup G_r of Diff^r(M) such that G_r never embeds into Diff^s(M) for any s>r. This generalizes observations by earlier foliation theorists on the case r=0 or r=1. In the second talk, I will propose a rigidity phenomenon regarding higher dimensional manifolds. Namely, we consider the question exactly when two manifold diffeomorphism groups Diff^r(M) and Diff^s(N) have the same logical structure. Modern findings regarding this question gives a generalization of classical results of Whittaker (1963), and of Takens-Filipkiewicz (1982). This talk is based on joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年06月29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) 126号室
Chin-Yu Hsiao 氏 (国立台湾大学)
Heat kernel asymptotics for the $\bar{\partial}$-Neumann Laplacian on manifolds with boundary (English)
https://forms.gle/8ERsVDLuKHwbVzm57
Chin-Yu Hsiao 氏 (国立台湾大学)
Heat kernel asymptotics for the $\bar{\partial}$-Neumann Laplacian on manifolds with boundary (English)
[ 講演概要 ]
We study the heat kernel asymptotics of the $\bar{\partial}$-Neumann Laplacian associated with high tensor powers of a holomorphic line bundle. Specifically, for a relatively compact complex submanifold with smooth boundary in a complex manifold, we consider the $\bar{\partial}$-Neumann Laplacian acting on holomorphic sections of a holomorphic bundle over the submanifold. As the tensor power of the line bundle approaches infinity, we obtain explicit asymptotic expansions of the heat kernel in the submanifold's interior, on its boundary, and near the boundary. This is achieved by explicitly solving the heat equation for the weighted $\bar{\partial}$-Neumann Laplacian in domains that are not necessarily strongly pseudoconvex and showing uniform convergence of the associated scaled Laplacian's heat kernel to this solution. As an application, we establish analogue holomorphic Morse inequalities of Demailly on complex manifolds with boundary.
[ 参考URL ]We study the heat kernel asymptotics of the $\bar{\partial}$-Neumann Laplacian associated with high tensor powers of a holomorphic line bundle. Specifically, for a relatively compact complex submanifold with smooth boundary in a complex manifold, we consider the $\bar{\partial}$-Neumann Laplacian acting on holomorphic sections of a holomorphic bundle over the submanifold. As the tensor power of the line bundle approaches infinity, we obtain explicit asymptotic expansions of the heat kernel in the submanifold's interior, on its boundary, and near the boundary. This is achieved by explicitly solving the heat equation for the weighted $\bar{\partial}$-Neumann Laplacian in domains that are not necessarily strongly pseudoconvex and showing uniform convergence of the associated scaled Laplacian's heat kernel to this solution. As an application, we establish analogue holomorphic Morse inequalities of Demailly on complex manifolds with boundary.
https://forms.gle/8ERsVDLuKHwbVzm57
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
15:20〜 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。
野田 涼一郎 氏 (早稲田大学)
Fine geometry of collision measures
15:20〜 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。
野田 涼一郎 氏 (早稲田大学)
Fine geometry of collision measures
[ 講演概要 ]
Given several independent stochastic processes, their collision measure is a random measure that records when and where they collide. In this talk, I will discuss fine geometric properties of collision measures for independent Markov processes on metric measure spaces. Under standard heat kernel estimates, we identify the local dimensions of the temporal and spatial marginals of the collision measure. We also determine the Hausdorff dimensions of their supports, as well as those of the corresponding sets of collision times and collision sites. Finally, we study logarithmic limsup gauges describing typical and thick collision times and sites.
Given several independent stochastic processes, their collision measure is a random measure that records when and where they collide. In this talk, I will discuss fine geometric properties of collision measures for independent Markov processes on metric measure spaces. Under standard heat kernel estimates, we identify the local dimensions of the temporal and spatial marginals of the collision measure. We also determine the Hausdorff dimensions of their supports, as well as those of the corresponding sets of collision times and collision sites. Finally, we study logarithmic limsup gauges describing typical and thick collision times and sites.
2026年06月26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号室
ベズ ニール 氏 (東京大学大学院数理科学研究科)
掛谷予想とBrascamp-Lieb不等式 (日本語)
ベズ ニール 氏 (東京大学大学院数理科学研究科)
掛谷予想とBrascamp-Lieb不等式 (日本語)
[ 講演概要 ]
掛谷予想は、表向きは幾何学的測度論の問題であるにもかかわらず、
現代のフーリエ解析において極めて重要な役割を果たしています。
本講演では、このつながりについて議論した後、
この文脈におけるBrascamp-Lieb不等式の重要性を説明し、
同不等式の理論における最近の進展について紹介します。
掛谷予想は、表向きは幾何学的測度論の問題であるにもかかわらず、
現代のフーリエ解析において極めて重要な役割を果たしています。
本講演では、このつながりについて議論した後、
この文脈におけるBrascamp-Lieb不等式の重要性を説明し、
同不等式の理論における最近の進展について紹介します。
幾何解析セミナー
13:30-14;30 数理科学研究科棟(駒場) 002号室
Federica Dragoni 氏 (Cardiff University)
Convexity: from the Euclidean space to Riemannian and sub-Riemannian manifolds (英語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Federica Dragoni 氏 (Cardiff University)
Convexity: from the Euclidean space to Riemannian and sub-Riemannian manifolds (英語)
[ 講演概要 ]
In this talk I will give an overview on different notions of convexity introduced in the last decades to generalise the standard (Euclidean) convexity to different geometries such as Riemannian manifolds, Carnot groups and the geometry of vector fields. Later I will show some more recent developments and how this new geometrical approach can connect most of the previous notions.
[ 参考URL ]In this talk I will give an overview on different notions of convexity introduced in the last decades to generalise the standard (Euclidean) convexity to different geometries such as Riemannian manifolds, Carnot groups and the geometry of vector fields. Later I will show some more recent developments and how this new geometrical approach can connect most of the previous notions.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
統計数学セミナー
13:30-14:30 数理科学研究科棟(駒場) 122号室
ハイブリッド開催
Prof. Hsin-Hsiung 'Bill’ Huang 氏 (School of Data, Mathematical, and Statistical Sciences, University of Central Florida)
Scalable Bayesian Conformal Inference for High-Dimensional Spatiotemporal Zero-Inflated Count Data (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/UmviZSskR766wD4QoUvP2g
ハイブリッド開催
Prof. Hsin-Hsiung 'Bill’ Huang 氏 (School of Data, Mathematical, and Statistical Sciences, University of Central Florida)
Scalable Bayesian Conformal Inference for High-Dimensional Spatiotemporal Zero-Inflated Count Data (English)
[ 講演概要 ]
I will present a Bayesian framework for spatiotemporal count data with excess zeros, overdispersion, and ultrahigh-dimensional covariates. The model combines zero-inflated negative binomial regression, TPBN shrinkage priors for sparse fixed effects, graph-Laplacian or SPDE-type spatial random effects, smooth global time effects, and unit-specific Ornstein--Uhlenbeck SDE random effects. Pólya--Gamma augmentation yields a conditionally Gaussian structure, supporting both blocked Gibbs sampling and scalable structured variational inference. I will also discuss split conformal calibration for discrete predictive sets and an auxiliary LAQ/QMLE perspective for the OU component. Simulation studies and a measles surveillance analysis illustrate calibrated prediction and recovery of latent spatiotemporal structure.
[ 参考URL ]I will present a Bayesian framework for spatiotemporal count data with excess zeros, overdispersion, and ultrahigh-dimensional covariates. The model combines zero-inflated negative binomial regression, TPBN shrinkage priors for sparse fixed effects, graph-Laplacian or SPDE-type spatial random effects, smooth global time effects, and unit-specific Ornstein--Uhlenbeck SDE random effects. Pólya--Gamma augmentation yields a conditionally Gaussian structure, supporting both blocked Gibbs sampling and scalable structured variational inference. I will also discuss split conformal calibration for discrete predictive sets and an auxiliary LAQ/QMLE perspective for the OU component. Simulation studies and a measles surveillance analysis illustrate calibrated prediction and recovery of latent spatiotemporal structure.
https://u-tokyo-ac-jp.zoom.us/meeting/register/UmviZSskR766wD4QoUvP2g
2026年06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) 002号室
Xiao Dongyuan 氏 (東北大学)
Complete classification of traveling wave solutions to monotone dynamical systems (Japanese)
Xiao Dongyuan 氏 (東北大学)
Complete classification of traveling wave solutions to monotone dynamical systems (Japanese)
[ 講演概要 ]
To study the propagation phenomena of solutions to the reaction-diffusion equation the asymptotic behavior of traveling wave solutions plays a crucial role. When the nonlinear reaction term satisfies the monostable condition, it is known that there exists a minimal traveling wave speed, and that traveling wave solutions exist for any speed c larger than or equal to the minimal speed. It has been shown, through simple phase plane analysis, that these traveling waves can be classified into three cases based on their decay rates.
It Is expected that a similar classification should hold for more general order-preserving systems, such as nonlocal diffusion equations, Lotka–Volterra systems, and reaction–diffusion equations with time delay. However, a complete classification remains unavailable because direct phase plane analysis is no longer applicable in these settings. In this talk, I will introduce a method based on comparison argument and sliding method to classify traveling waves. This research is based on joint work with Maolin Zhou (Nankai University) and Chang-hong Wu (National Yang Ming Chiao Tung University).
To study the propagation phenomena of solutions to the reaction-diffusion equation the asymptotic behavior of traveling wave solutions plays a crucial role. When the nonlinear reaction term satisfies the monostable condition, it is known that there exists a minimal traveling wave speed, and that traveling wave solutions exist for any speed c larger than or equal to the minimal speed. It has been shown, through simple phase plane analysis, that these traveling waves can be classified into three cases based on their decay rates.
It Is expected that a similar classification should hold for more general order-preserving systems, such as nonlocal diffusion equations, Lotka–Volterra systems, and reaction–diffusion equations with time delay. However, a complete classification remains unavailable because direct phase plane analysis is no longer applicable in these settings. In this talk, I will introduce a method based on comparison argument and sliding method to classify traveling waves. This research is based on joint work with Maolin Zhou (Nankai University) and Chang-hong Wu (National Yang Ming Chiao Tung University).
2026年06月23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
Ravi Mistry 氏 (東大数理)
Knots, Invariants, QFT, and Beyond
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ravi Mistry 氏 (東大数理)
Knots, Invariants, QFT, and Beyond
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207 次へ >
