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過去の記録 ～04/30｜本日 05/01 | 今後の予定 05/02～
2026年04月28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/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。
佐野 岳人 氏 (理化学研究所)
A y-ification of Khovanov homology (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。
佐野 岳人 氏 (理化学研究所)
A y-ification of Khovanov homology (JAPANESE)
[ 講演概要 ]
In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
[ 参考URL ]In this talk, I will explain the main results of my recent paper (arXiv:2602.17435).
Khovanov homology is a categorification of the Jones polynomial, introduced by M. Khovanov. A persistent theme in the subject is that adding extra structures on Khovanov homology strengthens the invariant, and often detects phenomena invisible at the level of polynomials or bigraded vector spaces.
Motivated by the y-ification of HOMFLY--PT homology by Gorsky and Hogancamp, and the sl2-action constructed by Gorsky, Hogancamp and Mellit, we construct a y-ification of Khovanov homology and define an action of the element e in sl2 on these y-ifications. Our construction is compatible with the previous ones via Rasmussen's spectral sequence from HOMFLY--PT homology to Khovanov homology; yet our approach is more elementary and suited to diagrammatic and algorithmic computations. As an application, we show that the additional structure can distinguish knots with identical Khovanov homology and identical HOMFLY--PT homology, in particular the Conway knot and the Kinoshita--Terasaka knot.
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
Roozbeh Hazrat 氏 (Western Sydney University)
An attempt to classify combinatorial algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Roozbeh Hazrat 氏 (Western Sydney University)
An attempt to classify combinatorial algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
Khalid Koufany 氏 (University of Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(English)
[ 講演概要 ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
日仏数学拠点FJ-LMIセミナー
16:00-17:00 数理科学研究科棟(駒場) 128号室
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
https://fj-lmi.cnrs.fr/seminars/
Khalid Koufany 氏 (Université de Lorraine)
Geometric Means that preserve sparsity on homogeneous cones
(英語)
[ 講演概要 ]
This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
[ 参考URL ]This talk starts from a simple question: how can one define a geometric mean for sparse positive definite matrices without destroying their zero pattern?
For the arrowhead pattern, this leads naturally to the five-dimensional Vinberg cone, a basic non-symmetric homogeneous cone.
I will present two intrinsic means on this cone: a Cholesky-Vinberg mean built from triangular Cholesky factors, and a logarithmic Vinberg mean built from global clan (Vinberg algebra) coordinates.
The first is tied to a flat affine geometry with torsion, while the second belongs to a torsion-free flat geometry.
I will also explain why these means differ from the classical Riemannian midpoint and why this difference is a genuinely non-symmetric phenomenon.
If time permits, I will give an application to quantum information theory.
https://fj-lmi.cnrs.fr/seminars/
2026年04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) 126号室
大野 高志 氏 (京大数理研)
Manton’s Exotic Vortex Equations (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
大野 高志 氏 (京大数理研)
Manton’s Exotic Vortex Equations (Japanese)
[ 講演概要 ]
The vortex equation is a second-order PDE on a Riemann surface, defined in terms of a triple consisting of a holomorphic line bundle, a section, and a Hermitian metric. Its solutions are closely related to Hermitian–Einstein metrics and to geometric structures such as metrics with conical singularities. In https://arxiv.org/abs/1612.06710, Manton introduced several generalizations of the vortex equation, leading to five distinct types of vortex equations, which we refer to as Manton’s exotic vortex equations. In this talk, I will introduce these equations and discuss the existence of their solutions. I will also explain how these solutions can be obtained via dimensional reduction of a solution of Hermitian–Einstein equation.
[ 参考URL ]The vortex equation is a second-order PDE on a Riemann surface, defined in terms of a triple consisting of a holomorphic line bundle, a section, and a Hermitian metric. Its solutions are closely related to Hermitian–Einstein metrics and to geometric structures such as metrics with conical singularities. In https://arxiv.org/abs/1612.06710, Manton introduced several generalizations of the vortex equation, leading to five distinct types of vortex equations, which we refer to as Manton’s exotic vortex equations. In this talk, I will introduce these equations and discuss the existence of their solutions. I will also explain how these solutions can be obtained via dimensional reduction of a solution of Hermitian–Einstein equation.
https://forms.gle/8ERsVDLuKHwbVzm57
東京確率論セミナー
14:00-17:30 数理科学研究科棟(駒場) 126号室
講演の開始が早くなっています。15:30~ 教室126でTea timeを行います。ぜひこちらにもご参加ください。
Clément Cosco 氏 (Université Paris Dauphine) 14:00-15:30
The maximum of 2d directed polymers. (Joint work with Shuta Nakajima and Ofer Zeitouni.)
Gaussian fluctuations for spin systems and point processes: near-optimal rates via quantitative Marcinkiewicz's theorem
講演の開始が早くなっています。15:30~ 教室126でTea timeを行います。ぜひこちらにもご参加ください。
Clément Cosco 氏 (Université Paris Dauphine) 14:00-15:30
The maximum of 2d directed polymers. (Joint work with Shuta Nakajima and Ofer Zeitouni.)
[ 講演概要 ]
Directed polymers can be described as a tilting of the simple random walk, where some local random noise can attract or repel the trajectory of the walk. In the subcritical regime of the two-dimensional model, the partition function is known to be asymptotically approximated by a Gaussian log-correlated field. In a work in collaboration with Shuta Nakajima and Ofer Zeitouni, we could refine this result by proving that the maximum of the partition function field converges to that of a branching Brownian motion, which is the source of the log-correlation. In this talk, I will introduce the model as well as the objects related to it and present our result.
Subhro Ghosh 氏 (National University of Singapore) 16:00-17:30Directed polymers can be described as a tilting of the simple random walk, where some local random noise can attract or repel the trajectory of the walk. In the subcritical regime of the two-dimensional model, the partition function is known to be asymptotically approximated by a Gaussian log-correlated field. In a work in collaboration with Shuta Nakajima and Ofer Zeitouni, we could refine this result by proving that the maximum of the partition function field converges to that of a branching Brownian motion, which is the source of the log-correlation. In this talk, I will introduce the model as well as the objects related to it and present our result.
Gaussian fluctuations for spin systems and point processes: near-optimal rates via quantitative Marcinkiewicz's theorem
[ 講演概要 ]
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates.
For spin models, we demonstrate Gaussian asymptotics for the magnetization (i.e., the total spin) for a wide class of ferromagnetic spin systems on Euclidean lattices, in particular those with continuous spins. Specific applications include, in particular, the celebrated XY and Heisenberg models under ferromagnetic conditions, and more broadly, systems with very general rotationally invariant spins in arbitrary dimensions. We address both the setting of free boundary conditions and a large class of ferromagnetic boundary conditions, and our CLTs are endowed with near-optimal rate of O(log |Λ| · |Λ|−1/2) in the Kolmogorov-Smirnov distance, where the system size is |Λ|. Our approach leverages the classical Lee-Yang theory for the zeros of partition functions, and subsumes as a special case results of Lebowitz, Ruelle, Pittel and Speer on CLTs in discrete statistical mechanical models for which we obtain sharper convergence rates.
In a different direction, we obtain CLTs for linear statistics of a wide class of point processes known as α-determinantal point processes which interpolate between negatively and positively associated random point fields (including the usual determinantal, permanental and Poisson point processes).
We contribute a unified approach to CLTs in such models (agnostic to the parameter α that modulates the nature of association). Our methods are able to address a broad class of kernels including in particular those with slow spatial decay (such as the Bessel kernel in general dimensions). Significantly, our approach is able to analyse such processes in dimensions ≥ 3, where structural alternatives such as connections to random matrix theory are not available, and obtain explicit rates for fast convergence in a wide spectrum of models.
A key ingredient of our approach is a broad, quantitative extension of the classical Marcinkiewicz Theorem that holds under the limited condition that the characteristic function is non-vanishing only on a bounded disk. This technique complements classical work of Ostrovskii, Linnik, Zimogljad and others, as well as recent work of Michelen and Sahasrabudhe, and Eremenko and Fryntov. In spite of the general applicability of the results, including to heavy-tailed setups, our rates for the CLT match the classic Berry- Esseen bounds for independent sums up to a log factor.
Based on joint work with T.C. Dinh, H.S. Tran and M.H. Tran. Under revision at Annals of Applied Probability.
We establish asymptotically Gaussian fluctuations for functionals of a large class of spin models and strongly correlated random point fields, achieving near-optimal rates.
For spin models, we demonstrate Gaussian asymptotics for the magnetization (i.e., the total spin) for a wide class of ferromagnetic spin systems on Euclidean lattices, in particular those with continuous spins. Specific applications include, in particular, the celebrated XY and Heisenberg models under ferromagnetic conditions, and more broadly, systems with very general rotationally invariant spins in arbitrary dimensions. We address both the setting of free boundary conditions and a large class of ferromagnetic boundary conditions, and our CLTs are endowed with near-optimal rate of O(log |Λ| · |Λ|−1/2) in the Kolmogorov-Smirnov distance, where the system size is |Λ|. Our approach leverages the classical Lee-Yang theory for the zeros of partition functions, and subsumes as a special case results of Lebowitz, Ruelle, Pittel and Speer on CLTs in discrete statistical mechanical models for which we obtain sharper convergence rates.
In a different direction, we obtain CLTs for linear statistics of a wide class of point processes known as α-determinantal point processes which interpolate between negatively and positively associated random point fields (including the usual determinantal, permanental and Poisson point processes).
We contribute a unified approach to CLTs in such models (agnostic to the parameter α that modulates the nature of association). Our methods are able to address a broad class of kernels including in particular those with slow spatial decay (such as the Bessel kernel in general dimensions). Significantly, our approach is able to analyse such processes in dimensions ≥ 3, where structural alternatives such as connections to random matrix theory are not available, and obtain explicit rates for fast convergence in a wide spectrum of models.
A key ingredient of our approach is a broad, quantitative extension of the classical Marcinkiewicz Theorem that holds under the limited condition that the characteristic function is non-vanishing only on a bounded disk. This technique complements classical work of Ostrovskii, Linnik, Zimogljad and others, as well as recent work of Michelen and Sahasrabudhe, and Eremenko and Fryntov. In spite of the general applicability of the results, including to heavy-tailed setups, our rates for the CLT match the classic Berry- Esseen bounds for independent sums up to a log factor.
Based on joint work with T.C. Dinh, H.S. Tran and M.H. Tran. Under revision at Annals of Applied Probability.
2026年04月24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
毛塚由佳子 氏 (東京大学大学院数理科学研究科)
Birch–Swinnerton-Dyer予想のdichotomy (日本語)
毛塚由佳子 氏 (東京大学大学院数理科学研究科)
Birch–Swinnerton-Dyer予想のdichotomy (日本語)
[ 講演概要 ]
本講演では, Birch–Swinnerton-Dyer予想を一つの「dichotomy」として捉える視点を紹介し, その枠組みのもとでBSD予想の内容をどのように捉え直せるかを考察する. この枠組みにおいては, 楕円曲線の解析的階数とMordell–Weil群の階数の一致や, Tate–Shafarevich群の有限性といった性質を個別に仮定しない. むしろ, これらの性質が互いに強く結びついており, 一方が成り立たないときには他方もまた特定の形で成り立たなくなる, という相関に着目する. 講演では, この考えに至る動機として, (1) 岩澤理論との類似, (2) 楕円曲線に関する既知の結果との関連, (3) 函数体の場合との対比, という三つの観点から説明する.
本講演の内容はDon Zagier氏(MPIM Bonn)との共同研究に基づく.
本講演では, Birch–Swinnerton-Dyer予想を一つの「dichotomy」として捉える視点を紹介し, その枠組みのもとでBSD予想の内容をどのように捉え直せるかを考察する. この枠組みにおいては, 楕円曲線の解析的階数とMordell–Weil群の階数の一致や, Tate–Shafarevich群の有限性といった性質を個別に仮定しない. むしろ, これらの性質が互いに強く結びついており, 一方が成り立たないときには他方もまた特定の形で成り立たなくなる, という相関に着目する. 講演では, この考えに至る動機として, (1) 岩澤理論との類似, (2) 楕円曲線に関する既知の結果との関連, (3) 函数体の場合との対比, という三つの観点から説明する.
本講演の内容はDon Zagier氏(MPIM Bonn)との共同研究に基づく.
2026年04月22日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
通常の曜日と異なります。
吉岡 秀和 氏 (北陸先端科学技術大学院大学)
水圏環境を深く理解するための非標準的な数理モデル (日本語)
通常の曜日と異なります。
吉岡 秀和 氏 (北陸先端科学技術大学院大学)
水圏環境を深く理解するための非標準的な数理モデル (日本語)
[ 講演概要 ]
水に関わる環境や生物を対象とした研究では，教科書的な数理モデルでは記述できないかもしれない現象が数多く存在する．この講演では，まず，講演者が対象としてきた理論・フィールド研究事例を概観する．つぎに，以下の２研究の成果を紹介する：① (Musielak-)Orlicz空間を用いた長記憶的な河川流況の不確実性のモデル化，② 係数が爆発する確率微分方程式に基づく回遊魚の遡上現象の理論構築．この講演を通して，私たちに身近な環境には数理的によくわからない対象がたくさん存在することを知って頂ければ幸いである．
水に関わる環境や生物を対象とした研究では，教科書的な数理モデルでは記述できないかもしれない現象が数多く存在する．この講演では，まず，講演者が対象としてきた理論・フィールド研究事例を概観する．つぎに，以下の２研究の成果を紹介する：① (Musielak-)Orlicz空間を用いた長記憶的な河川流況の不確実性のモデル化，② 係数が爆発する確率微分方程式に基づく回遊魚の遡上現象の理論構築．この講演を通して，私たちに身近な環境には数理的によくわからない対象がたくさん存在することを知って頂ければ幸いである．
2026年04月21日(火)
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。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (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。
谷口 正樹 氏 (京都大学)
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilization (JAPANESE)
[ 講演概要 ]
Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
[ 参考URL ]Wall's stabilization principle suggests that exotic phenomena in dimension four in the orientable category disappear after taking connected sums with sufficiently many S2xS2. Since most known exotic pairs of closed 4-manifolds become diffeomorphic after one stabilization, a natural question was: is a single S2xS2 enough? Recently, Jianfeng Lin constructed an exotic diffeomorphism on a closed 4-manifold-a diffeomorphism topologically isotopic to the identity but not smoothly isotopic-that survives one stabilization. In this talk, we provide a relative exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations. This gives the first exotic phenomenon in the orientable category that survives two stabilizations. This is joint work with Sungkyung Kang and Junghwan Park.
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
Ayoub Hafid 氏 (東大数理)
量子距離空間上の疎幾何について
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ayoub Hafid 氏 (東大数理)
量子距離空間上の疎幾何について
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年04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) 126号室
千葉 優作 氏 (お茶の水女子大学)
正値直線束の高次テンソルにおける $\overline{\partial}$ 方程式の $C^{\ell}$ 評価 (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
千葉 優作 氏 (お茶の水女子大学)
正値直線束の高次テンソルにおける $\overline{\partial}$ 方程式の $C^{\ell}$ 評価 (Japanese)
[ 講演概要 ]
$M$ をコンパクト複素多様体，$L$ を $M$ 上の正値正則直線束，$E$ を $M$ 上の正則ベクトル束とする. このとき，$k$ が十分大きいときにはコホモロジー群 $H^i(M, L^k \otimes E)$ は $i>0$ に対して消滅することが知られている．この消滅定理は通常，Hörmander の $L^2$ 評価を用いて $\overline{\partial}$ 方程式を解くことで証明される．本講演では，Hörmander の方法を使わず，Andersson–Berndtsson（1982）の重み付き積分公式を用いることで，$\overline{\partial}$ 方程式の解に対する漸近的な $C^{\ell}$ ノルム評価を得る．
[ 参考URL ]$M$ をコンパクト複素多様体，$L$ を $M$ 上の正値正則直線束，$E$ を $M$ 上の正則ベクトル束とする. このとき，$k$ が十分大きいときにはコホモロジー群 $H^i(M, L^k \otimes E)$ は $i>0$ に対して消滅することが知られている．この消滅定理は通常，Hörmander の $L^2$ 評価を用いて $\overline{\partial}$ 方程式を解くことで証明される．本講演では，Hörmander の方法を使わず，Andersson–Berndtsson（1982）の重み付き積分公式を用いることで，$\overline{\partial}$ 方程式の解に対する漸近的な $C^{\ell}$ ノルム評価を得る．
https://forms.gle/8ERsVDLuKHwbVzm57
2026年04月14日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Nicola Fusco 氏 (University of Naples Federico II)
Consistency for the surface diffusion flow in three dimensions (English)
Nicola Fusco 氏 (University of Naples Federico II)
Consistency for the surface diffusion flow in three dimensions (English)
[ 講演概要 ]
We will discuss the flat flow solution for the surface diffusion equation via a discrete minimizing movements scheme proposed in 1994 in a celebrated paper by J.W. Cahn and J.E. Taylor. We will show that in dimension three the scheme converges to the unique smooth solution of the equation, provided the initial set is sufficiently regular. Joint paper with Marco Cicalese, Vesa Julin and Andrea Kubin.
We will discuss the flat flow solution for the surface diffusion equation via a discrete minimizing movements scheme proposed in 1994 in a celebrated paper by J.W. Cahn and J.E. Taylor. We will show that in dimension three the scheme converges to the unique smooth solution of the equation, provided the initial set is sufficiently regular. Joint paper with Marco Cicalese, Vesa Julin and Andrea Kubin.
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
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。
岡本 幸大 氏 (東京都立大学)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
岡本 幸大 氏 (東京都立大学)
Non-contractible loops of Legendrian tori from families of knots (JAPANESE)
[ 講演概要 ]
The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
[ 参考URL ]The unit cotangent bundle of the Euclidean space R3 has a canonical contact structure. In this talk, we discuss loops of Legendrian tori in this 5-dimensional contact manifold. In particular, we focus on loops arising as families of the unit conormal bundles of knots in R3, and I will explain a topological method to compute the monodromy on the Legendrian contact homology in degree 0 induced by those loops. As an application, we get examples of non-contractible loops of Legendrian tori which are contractible in the space of smoothly embedded tori. This is joint work with Marián Poppr.
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
新居聡彦 氏 (千葉大学)
On the isomorphism problem for ultraproducts of $C^*$-algebras in continuous model theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
新居聡彦 氏 (千葉大学)
On the isomorphism problem for ultraproducts of $C^*$-algebras in continuous model theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年04月13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
15:20〜 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。
白石 大典 氏 (京都大学)
4次元単純ランダムウォークの交叉と長距離パーコレーションの関係
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。
白石 大典 氏 (京都大学)
4次元単純ランダムウォークの交叉と長距離パーコレーションの関係
[ 講演概要 ]
よく知られているように、4次元ブラウン運動の軌跡は単純曲線になる。一方で4次元単純ランダムウォークの軌跡は、ループ除去ランダムウォークの長さに非自明な対数項が現れる程度のループを持つ。本講演では、4次元単純ランダムウォークの軌跡の交叉とある長距離パーコレーションモデルとの関係性について解説する。
よく知られているように、4次元ブラウン運動の軌跡は単純曲線になる。一方で4次元単純ランダムウォークの軌跡は、ループ除去ランダムウォークの長さに非自明な対数項が現れる程度のループを持つ。本講演では、4次元単純ランダムウォークの軌跡の交叉とある長距離パーコレーションモデルとの関係性について解説する。
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
下地 泰斗 氏 (大阪大学)
On the nilpotent quasi-projective groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
下地 泰斗 氏 (大阪大学)
On the nilpotent quasi-projective groups (Japanese)
[ 講演概要 ]
準射影群とは、非特異準射影複素代数多様体の基本群のことである。Aguilar と Campana は、ねじれのない冪零準射影群に関する問題を提起した。この問題は、そのような群が 2 ステップ冪零群またはアーベル群であるかどうかを問うものである（arXiv:2301.11232, Question 26）。本講演では、ねじれのない冪零準射影群と上の問題に関する講演者のいくつかの結果を紹介する。特に、最新の結果は、3 ステップ以上のねじれのない冪零準射影群が存在する可能性を示唆している。
[ 参考URL ]準射影群とは、非特異準射影複素代数多様体の基本群のことである。Aguilar と Campana は、ねじれのない冪零準射影群に関する問題を提起した。この問題は、そのような群が 2 ステップ冪零群またはアーベル群であるかどうかを問うものである（arXiv:2301.11232, Question 26）。本講演では、ねじれのない冪零準射影群と上の問題に関する講演者のいくつかの結果を紹介する。特に、最新の結果は、3 ステップ以上のねじれのない冪零準射影群が存在する可能性を示唆している。
https://forms.gle/8ERsVDLuKHwbVzm57
2026年04月10日(金)
幾何解析セミナー
16:00-17:00 数理科学研究科棟(駒場) 056号室
松尾信一郎 氏 (名古屋大学)
Dirac作用素の指数の離散化と格子ゲージ理論 (日本語)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
松尾信一郎 氏 (名古屋大学)
Dirac作用素の指数の離散化と格子ゲージ理論 (日本語)
[ 講演概要 ]
講演者の真の目的はSeiberg-Witten理論の離散化であり，四次元におけるPL=DIFFを念頭にPL的SW理論の構築を目論んでいる．
その第一歩として，Dirac作用素の指数を離散化した．
ただし，Fredholm指数とは無限次元的なものであり，Dirac作用素を単純に離散化してもその指数は自明になってしまう．
そこで，格子ゲージ理論のアイデアを活用する．
本講演は，物理学者四人と数学者三人の共同研究である次の二本の論文に基づく．
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
[ 参考URL ]講演者の真の目的はSeiberg-Witten理論の離散化であり，四次元におけるPL=DIFFを念頭にPL的SW理論の構築を目論んでいる．
その第一歩として，Dirac作用素の指数を離散化した．
ただし，Fredholm指数とは無限次元的なものであり，Dirac作用素を単純に離散化してもその指数は自明になってしまう．
そこで，格子ゲージ理論のアイデアを活用する．
本講演は，物理学者四人と数学者三人の共同研究である次の二本の論文に基づく．
https://arxiv.org/abs/2602.12576
https://arxiv.org/abs/2407.17708
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
2026年04月08日(水)
東京名古屋代数セミナー
13:00-14:30 オンライン開催
朝永 龍 氏 (東京大学)
d-無限表現型代数と射影多様体の導来同値について (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
朝永 龍 氏 (東京大学)
d-無限表現型代数と射影多様体の導来同値について (Japanese)
[ 講演概要 ]
d-無限表現型代数とは、高次元Auslander-Reiten理論の観点からの、non-Dynkin型の道代数の大域次元dへの一般化である[Herschend-Iyama-Oppermann]。d-無限表現型代数は、non-Dynkin型の道代数と同様の表現論をもつが、特にtame型の場合は、d-regular componentがあるd次元射影多様体の閉点により添字付けられる。一方、d次元の滑らかな射影多様体がd-傾束(=自己準同型環の大域次元がd以下である傾束)をもてば、その自己準同型環は自動的にd-無限表現型代数となる[Buchweitz-Hille]。このようにd-無限表現型代数は、d次元の射影幾何と密接な関わりを持つ。
本講演では、d-無限表現型代数の基本事項から始め、d-傾束を持つようなd次元の射影多様体(もしくはスタック)に関する講演者の結果を紹介する。
ミーティングID：867 3982 9708
パスコード：163904
[ 参考URL ]d-無限表現型代数とは、高次元Auslander-Reiten理論の観点からの、non-Dynkin型の道代数の大域次元dへの一般化である[Herschend-Iyama-Oppermann]。d-無限表現型代数は、non-Dynkin型の道代数と同様の表現論をもつが、特にtame型の場合は、d-regular componentがあるd次元射影多様体の閉点により添字付けられる。一方、d次元の滑らかな射影多様体がd-傾束(=自己準同型環の大域次元がd以下である傾束)をもてば、その自己準同型環は自動的にd-無限表現型代数となる[Buchweitz-Hille]。このようにd-無限表現型代数は、d次元の射影幾何と密接な関わりを持つ。
本講演では、d-無限表現型代数の基本事項から始め、d-傾束を持つようなd次元の射影多様体(もしくはスタック)に関する講演者の結果を紹介する。
ミーティングID：867 3982 9708
パスコード：163904
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2026年04月07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/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。
鈴木 龍正 氏 (東京大学大学院数理科学研究科)
非単連結な4次元閉多様体を構成する Price ツイストとポシェット手術 (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。
鈴木 龍正 氏 (東京大学大学院数理科学研究科)
非単連結な4次元閉多様体を構成する Price ツイストとポシェット手術 (JAPANESE)
[ 講演概要 ]
4次元多様体に埋め込まれた実射影平面に沿った切り貼り操作はPriceツイストと呼ばれる。4次元球面に対するPriceツイストは、微分同相の差を除いて高々3つの4次元多様体、すなわち4次元球面、ある4次元ホモトピー球面、および非単連結な4次元閉多様体を生成する。一般に、非単連結な4次元閉多様体の微分同相類の分類はまだ十分に理解されていない。本講演では、4次元球面に対するPriceツイストのうち、樹下型の実射影平面の埋め込みに対する非単連結な4次元閉多様体を生成する場合に着目する。これらの多様体のいくつかの性質および微分同相類の分類についての結果を紹介する。さらに、本研究と密接に関連する手術として、岩瀬 順一氏と松本 幸夫氏により導入されたポシェット手術についても解説する。本講演は磯島 司氏（慶應義塾大学）との共同研究に基づく。
[ 参考URL ]4次元多様体に埋め込まれた実射影平面に沿った切り貼り操作はPriceツイストと呼ばれる。4次元球面に対するPriceツイストは、微分同相の差を除いて高々3つの4次元多様体、すなわち4次元球面、ある4次元ホモトピー球面、および非単連結な4次元閉多様体を生成する。一般に、非単連結な4次元閉多様体の微分同相類の分類はまだ十分に理解されていない。本講演では、4次元球面に対するPriceツイストのうち、樹下型の実射影平面の埋め込みに対する非単連結な4次元閉多様体を生成する場合に着目する。これらの多様体のいくつかの性質および微分同相類の分類についての結果を紹介する。さらに、本研究と密接に関連する手術として、岩瀬 順一氏と松本 幸夫氏により導入されたポシェット手術についても解説する。本講演は磯島 司氏（慶應義塾大学）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
阪本皓貴 氏 (東大数理)
On the spectral gap conjecture for pairs in SU(2)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
阪本皓貴 氏 (東大数理)
On the spectral gap conjecture for pairs in SU(2)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年03月27日(金)
談話会・数理科学講演会
16:00-17:00 数理科学研究科棟(駒場) NISSAY Lecture Hall(大講義室)号室
吉田朋広 氏 (東京大学大学院数理科学研究科)
偶然と無作為の研究：選択バイアスがある私的小史 (日本語)
吉田朋広 氏 (東京大学大学院数理科学研究科)
偶然と無作為の研究：選択バイアスがある私的小史 (日本語)
[ 講演概要 ]
確率統計学を学んできましたが、方針が半ば無作為ながらも多くの偶然に導かれてまいりました。
話題の選択と成り行きの評価にバイアスがあることを承知の上で、今に至った経緯を振り返りたいと思います。
確率統計学を学んできましたが、方針が半ば無作為ながらも多くの偶然に導かれてまいりました。
話題の選択と成り行きの評価にバイアスがあることを承知の上で、今に至った経緯を振り返りたいと思います。
2026年03月19日(木)
日仏数学拠点FJ-LMIセミナー
13:30-14:15 数理科学研究科棟(駒場) 056号室
Amaury HAYAT 氏 (ENPC, Paris)
How can AI Help Mathematicians? (英語)
https://fj-lmi.cnrs.fr/seminars/
Amaury HAYAT 氏 (ENPC, Paris)
How can AI Help Mathematicians? (英語)
[ 講演概要 ]
The advent of artificial intelligence raises an important question: can AI assist mathematicians in solving open problems in mathematics? This talk explores this question from multiple perspectives. We will explore how different types of AI models can be trained to provide valuable insights into mathematical questions from different areas of mathematics and applied mathematics. We will also present recent works on AI models specifically designed for automated theorem proving.
[ 参考URL ]The advent of artificial intelligence raises an important question: can AI assist mathematicians in solving open problems in mathematics? This talk explores this question from multiple perspectives. We will explore how different types of AI models can be trained to provide valuable insights into mathematical questions from different areas of mathematics and applied mathematics. We will also present recent works on AI models specifically designed for automated theorem proving.
https://fj-lmi.cnrs.fr/seminars/
2026年03月18日(水)
日仏数学拠点FJ-LMIセミナー
13:30-14:15 数理科学研究科棟(駒場) 056号室
Amaury HAYAT 氏 (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
https://fj-lmi.cnrs.fr/seminars/
Amaury HAYAT 氏 (ENPC, Paris)
Stabilization of PDEs and AI for mathematics (英語)
[ 講演概要 ]
Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
[ 参考URL ]Control theory consists in asking: if we can act on a system, what can we make it do? One of the main problems is the stabilization problem: how can we act on a system to guarantee the long-term behavior of its solutions? In this presentation, we will examine this problem from several angles. First, we will look at the problem of stabilizing PDEs from an abstract perspective and present a recent approach called F-equivalence (or sometimes Fredholm backstepping). The principle is simple: instead of trying to find a control that makes the system stable, we look at another problem: we try find a control that renders the PDE system dynamically equivalent to a simpler system for which stability is already known. Besides being interesting in itself, this approach has also resulted in new results in control theory, and we will review the progress that has been made in the last three years. In a second part, we will focus on a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We will show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-world scenarios, and we will discuss their application to traffic regulation and the reduction of traffic jams.
https://fj-lmi.cnrs.fr/seminars/
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
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
A phasefield approach to two-scale topology optimization (English)
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
A phasefield approach to two-scale topology optimization (English)
[ 講演概要 ]
Subject of my presentation is a novel approach for optimizing both the macroscopic shape and the porous mesoscopic structure of components. In the first part of my presentation I will introduce the concept of phasefield based topology optimization. The second part of my presentation is devoted to two-scale topology optimization. The key feature here is the introduction of an additional local volume control (LVC), which allows to adjust the desired spatial scales. The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. I will present some analytical results for the resulting optimal control problem and conclude with numerical results showing the versatility of our approach for creating optimal macroscopic designs with tailored mesostructures.
Subject of my presentation is a novel approach for optimizing both the macroscopic shape and the porous mesoscopic structure of components. In the first part of my presentation I will introduce the concept of phasefield based topology optimization. The second part of my presentation is devoted to two-scale topology optimization. The key feature here is the introduction of an additional local volume control (LVC), which allows to adjust the desired spatial scales. The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. I will present some analytical results for the resulting optimal control problem and conclude with numerical results showing the versatility of our approach for creating optimal macroscopic designs with tailored mesostructures.
2026年03月11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
Kam Fai Tam 氏 (Xiamen Malaysia University)
A conjectural construction of Arthur Packets in Fargues-Scholze's categorical local Langlands correspondence
Kam Fai Tam 氏 (Xiamen Malaysia University)
A conjectural construction of Arthur Packets in Fargues-Scholze's categorical local Langlands correspondence
[ 講演概要 ]
The presentation consists of two parts. In the first part, we review -- from a novice point of view -- the categorical local Langlands correspondence due to Fargues and Scholze. Topics include: the structure of Bun_G and LocSys_{\hat G}, spectral action via Hecke operators, geometric Satake transform, and some conjectural consequences proposed by Fargues. (Apologies: the p-adic geometry underlying the relative Fargues-Fontaine curve is not included.)
In the second part, I will present a conjectural construction of Arthur packets in Fargues-Scholze's framework. This construction is based on the vanishing cycle functor introduced by Cunningham-Fiori-Moussaoui-Mracek-Xu, which is in turn inspired by Adams-Barbasch-Vogan for real groups. (A confession for curious audiences: this presentation offers essentially no new results. My goal is to illustrate how the legacy of James Arthur may influence other theories.)
The presentation consists of two parts. In the first part, we review -- from a novice point of view -- the categorical local Langlands correspondence due to Fargues and Scholze. Topics include: the structure of Bun_G and LocSys_{\hat G}, spectral action via Hecke operators, geometric Satake transform, and some conjectural consequences proposed by Fargues. (Apologies: the p-adic geometry underlying the relative Fargues-Fontaine curve is not included.)
In the second part, I will present a conjectural construction of Arthur packets in Fargues-Scholze's framework. This construction is based on the vanishing cycle functor introduced by Cunningham-Fiori-Moussaoui-Mracek-Xu, which is in turn inspired by Adams-Barbasch-Vogan for real groups. (A confession for curious audiences: this presentation offers essentially no new results. My goal is to illustrate how the legacy of James Arthur may influence other theories.)
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