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過去の記録
過去の記録 ～11/17｜本日 11/18 | 今後の予定 11/19～
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
小木曾 啓示 氏 (東京大学大学院数理科学研究科)
On K3 surfaces with non-elementary hyperbolic automorphism group (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
小木曾 啓示 氏 (東京大学大学院数理科学研究科)
On K3 surfaces with non-elementary hyperbolic automorphism group (JAPANESE)
[ 講演概要 ]
This talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).
Main result of this talk is the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic, under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling basic facts and some special nice properties of K3 surfaces, the notion of hyperbolicity of group due to Gromov, and their importance and interest (in our view), I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Néron-Severi lattices and then how one can deduce the above-mentioned finiteness, via a recent important observation by Professors Kikuta and Takatsu (independently) on geometrically finiteness, with a new algebro-geometric study of genus one fibrations on K3 surfaces by us.
[ 参考URL ]This talk is based on my joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjin University).
Main result of this talk is the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic, under the assumption that the Picard number greater than or equal to 6 (which is optimal to ensure the finiteness). In this talk, after recalling basic facts and some special nice properties of K3 surfaces, the notion of hyperbolicity of group due to Gromov, and their importance and interest (in our view), I would like to explain first why the non-elementary hyperbolicity of K3 surface automorphism group is the problem of the Néron-Severi lattices and then how one can deduce the above-mentioned finiteness, via a recent important observation by Professors Kikuta and Takatsu (independently) on geometrically finiteness, with a new algebro-geometric study of genus one fibrations on K3 surfaces by us.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
可香谷 隆 氏 (室蘭工業大学)
Inverse curvature flow of Legendre curves (Japanese)
可香谷 隆 氏 (室蘭工業大学)
Inverse curvature flow of Legendre curves (Japanese)
[ 講演概要 ]
逆曲率流方程式はある種の放物型方程式に分類される微分方程式である．本講演では，逆曲率流に対し，初期曲線がある程度のカスプを持つ場合に，カスプ型の特異性が保たれることを示すため，滑らかなはめ込みとしてカスプ型の特異性を持つ曲線を記述できるルジャンドル曲線を導入し，ルジャンドル曲線の枠組みでの初期値問題の時間大域解の一意存在性と時間無限大での漸近挙動解析について考察する．なお，本講演は高橋雅朋氏(室蘭工業大学)との共同研究に基づく．
逆曲率流方程式はある種の放物型方程式に分類される微分方程式である．本講演では，逆曲率流に対し，初期曲線がある程度のカスプを持つ場合に，カスプ型の特異性が保たれることを示すため，滑らかなはめ込みとしてカスプ型の特異性を持つ曲線を記述できるルジャンドル曲線を導入し，ルジャンドル曲線の枠組みでの初期値問題の時間大域解の一意存在性と時間無限大での漸近挙動解析について考察する．なお，本講演は高橋雅朋氏(室蘭工業大学)との共同研究に基づく．
2025年10月10日(金)
代数幾何学セミナー
10:00-11:30 数理科学研究科棟(駒場) 122号室
いつもと時間・部屋が異なります。
Yuri Tschinkel 氏 (New York University)
Equivariant birational geometry
いつもと時間・部屋が異なります。
Yuri Tschinkel 氏 (New York University)
Equivariant birational geometry
[ 講演概要 ]
I will report on new results and constructions in higher-dimensional birational geometry in presence of actions of finite groups.
I will report on new results and constructions in higher-dimensional birational geometry in presence of actions of finite groups.
2025年10月08日(水)
幾何解析セミナー
10:30-11:30 数理科学研究科棟(駒場) 126号室
Jinpeng Lu 氏 (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
https://www.mv.helsinki.fi/home/jinpeng/
Jinpeng Lu 氏 (University of Helsinki)
Quantitative stability of Gel'fand's inverse problem (英語)
[ 講演概要 ]
Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
[ 参考URL ]Inverse problems study the determination of the global structure of a space or coefficients of a system from local measurements of solutions to the system. The problems are originally motivated from imaging sciences, where the goal is to deduce the structure of the inaccessible interior of a body from measurements at the exterior. A fundamental inverse problem, Gel'fand's inverse problem, asks to determine the geometry of a Riemannian manifold from local measurements of the heat kernel. In this talk, I will explain how the unique solvability of the classical Gel'fand's inverse problem can be established on manifolds via Tataru's optimal unique continuation theorem for the wave operator. Next, I will discuss our recent works on the uniqueness and stability of the inverse problem for the Gromov-Hausdorff limits of Riemannian manifolds with bounded sectional curvature. This talk is based on joint works with Y. Kurylev, M. Lassas, and T. Yamaguchi.
https://www.mv.helsinki.fi/home/jinpeng/
日仏数学拠点FJ-LMIセミナー
15:00-16:00 数理科学研究科棟(駒場) 056号室
Sourav Ghosh 氏 (Ashoka University)
Proper actions on group manifolds (英語)
Sourav Ghosh 氏 (Ashoka University)
Proper actions on group manifolds (英語)
[ 講演概要 ]
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
In this talk, I will show how to use known examples of flat affine manifolds to obtain new examples of proper actions of discrete groups on group manifolds. This is a joint work with Toshiyuki Kobayashi.
2025年10月07日(火)
トポロジー火曜セミナー
17:00-18:00 オンライン開催
セミナーのホームページから参加登録を行って下さい。
菅原 朔見 氏 (北海道大学)
Topology of hyperplane arrangements and related 3-manifolds (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
セミナーのホームページから参加登録を行って下さい。
菅原 朔見 氏 (北海道大学)
Topology of hyperplane arrangements and related 3-manifolds (JAPANESE)
[ 講演概要 ]
One of the central questions in the topology of hyperplane arrangements is whether several topological invariants are combinatorially determined. While the cohomology ring of the complement has a combinatorial description, it remains open whether even the first Betti number of the Milnor fiber is. In contrast, the homeomorphism types of 3-manifolds appearing as the boundary manifold of projective line arrangements and the Milnor fiber boundary of arrangements in a 3-dimensional space are combinatorially determined. In this talk, we focus on these 3-manifolds. In particular, we will present the cohomology ring structure for the boundary manifold, originally due to Cohen-Suciu, and an explicit formula for the homology group of the Milnor fiber boundary of generic arrangements.
[ 参考URL ]One of the central questions in the topology of hyperplane arrangements is whether several topological invariants are combinatorially determined. While the cohomology ring of the complement has a combinatorial description, it remains open whether even the first Betti number of the Milnor fiber is. In contrast, the homeomorphism types of 3-manifolds appearing as the boundary manifold of projective line arrangements and the Milnor fiber boundary of arrangements in a 3-dimensional space are combinatorially determined. In this talk, we focus on these 3-manifolds. In particular, we will present the cohomology ring structure for the boundary manifold, originally due to Cohen-Suciu, and an explicit formula for the homology group of the Milnor fiber boundary of generic arrangements.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年10月06日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
竹内 有哉 氏 (筑波大学)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
竹内 有哉 氏 (筑波大学)
CR Paneitz operator on non-embeddable CR manifolds (Japanese)
[ 講演概要 ]
The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
[ 参考URL ]The CR Paneitz operator, a CR invariant fourth-order linear differential operator, plays a crucial role in three-dimensional CR geometry. It is closely related to global embeddability, the CR positive mass theorem, and the logarithmic singularity of the Szegő kernel. In this talk, I will discuss the spectrum of the CR Paneitz operator on non-embeddable CR manifolds, with particular emphasis on how it differs from the embeddable case.
https://forms.gle/gTP8qNZwPyQyxjTj8
東京確率論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
講演の開始が遅くなっています。今日はTea Time はありません。
河備 浩司 氏 (慶應義塾大学)
Riemann多様体上の排他過程に対する流体力学極限
講演の開始が遅くなっています。今日はTea Time はありません。
河備 浩司 氏 (慶應義塾大学)
Riemann多様体上の排他過程に対する流体力学極限
[ 講演概要 ]
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
(コンパクトとは限らない)完備なRiemann多様体をグラフで離散化し, その上の排他過程に対するスケール極限を考察する。
本講演では, 石渡 聡 氏 (山形大学), 角田 謙吉 氏 (九州大学)と現在進行中の共同研究に基づき, 流体力学極限について得られた成果を報告する。
2025年10月03日(金)
統計数学セミナー
16:00-17:10 数理科学研究科棟(駒場) 123号室
ハイブリッド開催
Freddy Delbaen 氏 (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
ハイブリッド開催
Freddy Delbaen 氏 (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
[ 講演概要 ]
With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
[ 参考URL ]With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
2025年09月25日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
尾上文彦 氏 (ミュンヘン工科大学)
On the shape of fractional minimal surfaces (Japanese)
尾上文彦 氏 (ミュンヘン工科大学)
On the shape of fractional minimal surfaces (Japanese)
[ 講演概要 ]
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
Fractional perimeter (or fractional area) has been studied for more than a decade since Caffarelli, Roquejofffre, and Savin introduced its notion in 2010; however, there are still a lot of things unknown. In this talk, we discuss the shape of the boundary of sets minimizing their fractional perimeter under several boundary conditions, reviewing several interesting examples distinct from sets minimizing their classical perimeter. Moreover, if time permits, we present another notion of fractional area for smooth hypersurfaces with boundary, which was introduced by Paroni, Podio-Guidugli, and Seguin in 2018. Then we discuss the shape of critical points of their fractional area in several simple situations. This talk is partially based on a joint work with S. Dipierro and E. Valdinoci.
2025年09月09日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Kang Li 氏 (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
Kang Li 氏 (FAU Erlangen-Nürnberg)
Dimension theories from groupoids to classifiable $C^*$-algebras, and back again
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/seminar/operalge/future.html
2025年08月22日(金)
博士論文発表会
16:00-17:15 数理科学研究科棟(駒場) 128号室
星野 真生 氏 (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
星野 真生 氏 (東京大学大学院数理科学研究科)
A tensor categorical aspect of quantum group actions
(量子群作用のテンソル圏的様相)
2025年08月19日(火)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 117号室
いつもと曜日・部屋が異なります。
Trung Tuyen Truong 氏 (University of Oslo)
Some new results concerning Tate's questions and generalisations
いつもと曜日・部屋が異なります。
Trung Tuyen Truong 氏 (University of Oslo)
Some new results concerning Tate's questions and generalisations
[ 講演概要 ]
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
In the 1960s, Tate formulated (inspired by Weil's conjectures and a result of Serre on compact Kahler manifolds) a couple of questions concerning eigenvalues for pullback on cohomology of polarized endomorphisms. Grothendieck and Bombieri proposed Standard conjectures to solve these questions by Tate. The speaker, inspired by complex dynamics, proposed a generalisation of one of Tate's questions to rational maps and dynamical correspondences. This talk presents some new results and approaches (which are less demanding than the Standard conjectures, in that Standard Conjecture of Hodge type is not required) concerning these Tate's questions and generalisation. The talk includes joint works with Fei Hu and Junyi Xie.
東京名古屋代数セミナー
15:00-16:30 オンライン開催
平前 直也 氏 (京都大学)
自己入射的代数のCartan行列の正定値性と$\tau$-傾有限性 (Japanese)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
平前 直也 氏 (京都大学)
自己入射的代数のCartan行列の正定値性と$\tau$-傾有限性 (Japanese)
[ 講演概要 ]
有限次元代数の$\tau$-傾有限性は，ねじれ対の関手的有限性やbrickの有限性，さらには$g$-扇の完備性や準傾複体の連結性などといった表現論において重要な性質と密接に関係しており，昨今さかんに研究されている．有限群のモジュラー表現論（＝正標数体上の群環の加群論）の文脈では，正標数$p$の代数閉体$k$と有限群$G$に対して，群環$kG$の$\tau$-傾有限性は$G$の$p$-超焦点部分群によって決まるのではないかと予想されており（[Hiramae-Kozakai, 2025]），これは群環$kG$の表現型が$G$の$p$-Sylow部分群によって決定されるという古典的な結果の類似である．本講演ではまず自己入射的代数の$\tau$-傾有限性とCartan行列の正定値性の関係について説明し，その応用例としてある半直積群の群環に対して上の予想が成り立つことを示す．
ミーティング ID: 825 9241 0495
パスコード: 699837
[ 参考URL ]有限次元代数の$\tau$-傾有限性は，ねじれ対の関手的有限性やbrickの有限性，さらには$g$-扇の完備性や準傾複体の連結性などといった表現論において重要な性質と密接に関係しており，昨今さかんに研究されている．有限群のモジュラー表現論（＝正標数体上の群環の加群論）の文脈では，正標数$p$の代数閉体$k$と有限群$G$に対して，群環$kG$の$\tau$-傾有限性は$G$の$p$-超焦点部分群によって決まるのではないかと予想されており（[Hiramae-Kozakai, 2025]），これは群環$kG$の表現型が$G$の$p$-Sylow部分群によって決定されるという古典的な結果の類似である．本講演ではまず自己入射的代数の$\tau$-傾有限性とCartan行列の正定値性の関係について説明し，その応用例としてある半直積群の群環に対して上の予想が成り立つことを示す．
ミーティング ID: 825 9241 0495
パスコード: 699837
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
幾何解析セミナー
16:00-17:00 数理科学研究科棟(駒場) 123号室
Hiro Lee Tanaka 氏 (Texas State University)
For Liouville sectors, Floer theory in families without Floer theory in families
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
Hiro Lee Tanaka 氏 (Texas State University)
For Liouville sectors, Floer theory in families without Floer theory in families
[ 講演概要 ]
Numbers do not have automorphisms, but most other mathematical objects do.
So when Floer theory yields non-numerical invariants, one can hope for symmetries to act on such invariants. Typically, one realizes these actions by carefully setting up an analytical framework for Floer theory to vary over the fibers of some bundle. In the setting of Floer theory for a class of symplectic manifolds called Liouville sectors, we show that a completely different technique -- localization of infinity-categories -- achieves the same goals, and more! This talk is based on some old joint work with Oleg Lazarev and Zachary Sylvan.
[ 参考URL ]Numbers do not have automorphisms, but most other mathematical objects do.
So when Floer theory yields non-numerical invariants, one can hope for symmetries to act on such invariants. Typically, one realizes these actions by carefully setting up an analytical framework for Floer theory to vary over the fibers of some bundle. In the setting of Floer theory for a class of symplectic manifolds called Liouville sectors, we show that a completely different technique -- localization of infinity-categories -- achieves the same goals, and more! This talk is based on some old joint work with Oleg Lazarev and Zachary Sylvan.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/geometricanalysisseminar/
2025年07月31日(木)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
講演は木曜日です。教室は１２８です。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。
Xinyi Li 氏 (北京大学)
Analyticity of 3D Brownian intersection exponents
講演は木曜日です。教室は１２８です。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。
Xinyi Li 氏 (北京大学)
Analyticity of 3D Brownian intersection exponents
[ 講演概要 ]
In this talk, we will discuss the boundary Harnack principle (BHP) of the domain in \mathbb{R}^3 with the trace of a 3D Brownian motion removed and how it implies the analyticity of the intersection exponents for 3D Brownian motion. Based on a joint work (available at arXiv:2411.14921) with Yifan Gao (CityU HK), Yifan Li, Runsheng Liu and Xiangyi Liu (PKU).
In this talk, we will discuss the boundary Harnack principle (BHP) of the domain in \mathbb{R}^3 with the trace of a 3D Brownian motion removed and how it implies the analyticity of the intersection exponents for 3D Brownian motion. Based on a joint work (available at arXiv:2411.14921) with Yifan Gao (CityU HK), Yifan Li, Runsheng Liu and Xiangyi Liu (PKU).
2025年07月30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
Bruno Chiarellotto 氏 (Dipartimento di Matematica "Tullio Levi-Civita", Universita' degli Studi di Padova)
The tempered tube and the tempered cohomology
https://www.math.unipd.it/~chiarbru/
Bruno Chiarellotto 氏 (Dipartimento di Matematica "Tullio Levi-Civita", Universita' degli Studi di Padova)
The tempered tube and the tempered cohomology
[ 講演概要 ]
We will discuss a recent joint work with F. Bambozzi and P. Vanni (https://arxiv.org/abs/2410.09473). In the derived analytic spaces in the non arch. setting there are opens where the sections not only converge but they have also some arithmetic properties (log-growth). We will discuss how to construct such a spaces and we will give some applications: to the classical log-growth transfer theorem and on a new interpretation of convergent cohomology where one can replace the classical tube of the rigid cohomology with a "tempered one".
[ 参考URL ]We will discuss a recent joint work with F. Bambozzi and P. Vanni (https://arxiv.org/abs/2410.09473). In the derived analytic spaces in the non arch. setting there are opens where the sections not only converge but they have also some arithmetic properties (log-growth). We will discuss how to construct such a spaces and we will give some applications: to the classical log-growth transfer theorem and on a new interpretation of convergent cohomology where one can replace the classical tube of the rigid cohomology with a "tempered one".
https://www.math.unipd.it/~chiarbru/
2025年07月29日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 123号室
鈴木貴 氏 (大阪大学)
有界領域上のHodge分解の解析的証明とその応用 (Japanese)
鈴木貴 氏 (大阪大学)
有界領域上のHodge分解の解析的証明とその応用 (Japanese)
[ 講演概要 ]
有界領域上での微分形式についてそのHodge分解の解析的証明を与えていくつかの応用を紹介する。これは3次元のベクトル場に関する最近の結果の自然な拡張になっている。境界のある多様体の場合やBrezzi-Kikuchi不等式との関連性を述べ、Helmholtz分解の数値解法について新しいスキームを提案する。
有界領域上での微分形式についてそのHodge分解の解析的証明を与えていくつかの応用を紹介する。これは3次元のベクトル場に関する最近の結果の自然な拡張になっている。境界のある多様体の場合やBrezzi-Kikuchi不等式との関連性を述べ、Helmholtz分解の数値解法について新しいスキームを提案する。
2025年07月28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。
江崎 翔太 氏 (大分大学)
Difference between n-dimensional Cauchy distribution and n-times product of Cauchy distribution from perspective of measure concentration
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。
江崎 翔太 氏 (大分大学)
Difference between n-dimensional Cauchy distribution and n-times product of Cauchy distribution from perspective of measure concentration
[ 講演概要 ]
確率解析と測度距離幾何学はそれぞれにおいて広く研究されているが，お互いの関わりはまだ深いとは言えない．ところが，両者ともに，極限定理，特に測度集中現象を通して深く関わりあうと考えることができる．本講演では確率論的な模型である多次元コーシー分布, または, 1次元コーシー分布の直積に基づく測度集中現象について述べ、それらの測度距離幾何的な相違点について述べる. 時間が許した場合には, これらに対応する安定分布の結果についても紹介する. この講演は東京都立大学の数川大輔氏と福岡大学の三石史人氏との共同研究に基づく．
確率解析と測度距離幾何学はそれぞれにおいて広く研究されているが，お互いの関わりはまだ深いとは言えない．ところが，両者ともに，極限定理，特に測度集中現象を通して深く関わりあうと考えることができる．本講演では確率論的な模型である多次元コーシー分布, または, 1次元コーシー分布の直積に基づく測度集中現象について述べ、それらの測度距離幾何的な相違点について述べる. 時間が許した場合には, これらに対応する安定分布の結果についても紹介する. この講演は東京都立大学の数川大輔氏と福岡大学の三石史人氏との共同研究に基づく．
2025年07月25日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室(auditorium)号室
岡田いず海 氏 (東京大学大学院数理科学研究科)
単純ランダムウォークに関する新たな進展 (日本語)
岡田いず海 氏 (東京大学大学院数理科学研究科)
単純ランダムウォークに関する新たな進展 (日本語)
[ 講演概要 ]
整数格子上の単純ランダムウォークは、たとえば2次元の場合、各時刻に上下左右へそれぞれ1/4の確率で動く確率過程である。古典的な題材でありながら、単純な設定においても未解決の問題が数多く残されている。本講演では、最近の研究動向や新たに得られた結果について紹介する。
整数格子上の単純ランダムウォークは、たとえば2次元の場合、各時刻に上下左右へそれぞれ1/4の確率で動く確率過程である。古典的な題材でありながら、単純な設定においても未解決の問題が数多く残されている。本講演では、最近の研究動向や新たに得られた結果について紹介する。
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
金光秋博 氏 (東京都立大学)
Quintic del Pezzo threefolds in positive and mixed characteristic
金光秋博 氏 (東京都立大学)
Quintic del Pezzo threefolds in positive and mixed characteristic
[ 講演概要 ]
We will show that, over any base scheme, (families of) quintic del Pezzo threefolds V5 are classified by non-degenerate ternary symmetric bilinear forms.
As applications, we will discuss (1) the geometry of quintic del Pezzo threefolds in positive characteristic, especially in characteristic two, and (2) finiteness results of V5 over number fields/rings of integers.
(Based on joint work with Tetsushi Ito, Teppei Takamatsu, Yuuji Tanaka)
We will show that, over any base scheme, (families of) quintic del Pezzo threefolds V5 are classified by non-degenerate ternary symmetric bilinear forms.
As applications, we will discuss (1) the geometry of quintic del Pezzo threefolds in positive characteristic, especially in characteristic two, and (2) finiteness results of V5 over number fields/rings of integers.
(Based on joint work with Tetsushi Ito, Teppei Takamatsu, Yuuji Tanaka)
2025年07月22日(火)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 117号室
Giovanni Ferrer 氏 (Ohio State University)
Higher quantum symmetries
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Giovanni Ferrer 氏 (Ohio State University)
Higher quantum symmetries
[ 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) 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。
Alexis Marchand 氏 (京都大学)
Sharp spectral gaps for scl from negative curvature (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。
Alexis Marchand 氏 (京都大学)
Sharp spectral gaps for scl from negative curvature (ENGLISH)
[ 講演概要 ]
Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
[ 参考URL ]Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
片山 翔 氏 (東京大学大学院数理科学研究科)
On positive solutions to inhomogeneous elliptic problems
on unbounded domains
(非有界傾域上の非斉次楕円型問題の正値解について)
片山 翔 氏 (東京大学大学院数理科学研究科)
On positive solutions to inhomogeneous elliptic problems
on unbounded domains
(非有界傾域上の非斉次楕円型問題の正値解について)
2025年07月15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。
Anastasiia Tsvietkova 氏 (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (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。
Anastasiia Tsvietkova 氏 (Rutgers University)
Polynomially many genus g surfaces in a hyperbolic 3-manifold (ENGLISH)
[ 講演概要 ]
For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
[ 参考URL ]For a low-dimensional manifold, one often tries to understand its intrinsic topology through its submanifolds, in particular of co-dimension 1. For example,
it was noticed before that presence of embedded essential surfaces in a 3-manifold can give information about that manifold. However to construct, classify or count such surfaces is a non-trivial task. We will discuss a universal upper bound for the number of non-isotopic genus g surfaces embedded in a hyperbolic 3-manifold, polynomial in hyperbolic volume. The surfaces are all closed essential surfaces, oriented and connected. This is joint work with Marc Lackenby.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
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