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過去の記録 ～12/08｜本日 12/09 | 今後の予定 12/10～
2016年10月24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
清水 悟 氏 (東北大学)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
清水 悟 氏 (東北大学)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
[ 講演概要 ]
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
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
磯野優介 氏 (京大数理研)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
磯野優介 氏 (京大数理研)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
2016年10月18日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
橋本 義武 氏 (東京都市大学)
拡大W代数に対する共形場理論 (JAPANESE)
Tea: Common Room 17:00-17:30
橋本 義武 氏 (東京都市大学)
拡大W代数に対する共形場理論 (JAPANESE)
[ 講演概要 ]
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.
In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.
In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".
2016年10月17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
野村 隆昭 氏 (九州大学)
等質開凸錐の実現 (JAPANESE)
野村 隆昭 氏 (九州大学)
等質開凸錐の実現 (JAPANESE)
[ 講演概要 ]
等質開凸錐は等質ジーゲル領域の構成要素の一つである．その観点で，等質開凸錐の研究を，伊師英之，中島秀斗，山崎貴史等，若い研究者達と一緒にここ10年ほど続けてきて得られた成果のいくつかを紹介したい．中心となる話題は等質開凸錐の実現であり，これは山崎との共著論文として昨年の Kyushu J. Math.に出版されたもので，向き付けグラフを援用しながら，5次元の非対称等質開凸錐の記述にVinbergが用いたアイデア（露語オリジナルは1960年）が，そのままの形で一般の等質開凸錐の実現に通用することを示すものである．基本相対不変式における伊師等による成果を用いる証明を完全にブラックボックス化し，結果としては単に手続きを述べる形になっているので，非専門家にもアクセスが容易で，統計学等への応用も可能であると考えている．また，一般の非対称等質開凸錐に付随する管状領域の正則同型群やその構造の研究への応用も十分に見込める．さらに，Graczyk-Ishi による等質開凸錐の presentation (2014)の内で最小サイズのものも，上述の実現からやはり単なる手続き論で得られる．呈示される行列のサイズ等や零行列となるブロック・小ブロック等も，付随する向き付けグラフから読み取れる．
等質開凸錐は等質ジーゲル領域の構成要素の一つである．その観点で，等質開凸錐の研究を，伊師英之，中島秀斗，山崎貴史等，若い研究者達と一緒にここ10年ほど続けてきて得られた成果のいくつかを紹介したい．中心となる話題は等質開凸錐の実現であり，これは山崎との共著論文として昨年の Kyushu J. Math.に出版されたもので，向き付けグラフを援用しながら，5次元の非対称等質開凸錐の記述にVinbergが用いたアイデア（露語オリジナルは1960年）が，そのままの形で一般の等質開凸錐の実現に通用することを示すものである．基本相対不変式における伊師等による成果を用いる証明を完全にブラックボックス化し，結果としては単に手続きを述べる形になっているので，非専門家にもアクセスが容易で，統計学等への応用も可能であると考えている．また，一般の非対称等質開凸錐に付随する管状領域の正則同型群やその構造の研究への応用も十分に見込める．さらに，Graczyk-Ishi による等質開凸錐の presentation (2014)の内で最小サイズのものも，上述の実現からやはり単なる手続き論で得られる．呈示される行列のサイズ等や零行列となるブロック・小ブロック等も，付随する向き付けグラフから読み取れる．
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)
Unitarizability, Maurey-Nikishin factorization and Polish groups of finite type (English)
安藤浩志 氏 (千葉大)
Unitarizability, Maurey-Nikishin factorization and Polish groups of finite type (English)
2016年10月12日(水)
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
Uwe Jannsen 氏 (Universität Regensburg, 東京大学数理科学研究科)
Filtered de Rham Witt complexes and wildly ramified higher class field theory over finite fields (joint work with Shuji Saito and Yigeng Zhao) (English)
Uwe Jannsen 氏 (Universität Regensburg, 東京大学数理科学研究科)
Filtered de Rham Witt complexes and wildly ramified higher class field theory over finite fields (joint work with Shuji Saito and Yigeng Zhao) (English)
[ 講演概要 ]
We will consider abelian coverings of smooth projective varieties over finite fields which are wildly ramified along a divisor D with normal crossings, and will describe the corresponding abelianized fundamental group via modified logarithmic de Rham-Witt sheaves.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
We will consider abelian coverings of smooth projective varieties over finite fields which are wildly ramified along a divisor D with normal crossings, and will describe the corresponding abelianized fundamental group via modified logarithmic de Rham-Witt sheaves.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
2016年10月11日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Nam Quang Le 氏 (Indiana University)
Global solutions to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations (English)
Nam Quang Le 氏 (Indiana University)
Global solutions to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations (English)
[ 講演概要 ]
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-Weinkove and the author solved this global problem under some restrictions on the sign or integrability of the affine mean curvature. In this talk, we explain how to remove these restrictions and obtain global solutions under optimal integrability conditions on the affine mean curvature. Our analysis also covers the case of Abreu's equation arising in complex geometry.
The second boundary value problem of the prescribed affine mean curvature equation is a nonlinear, fourth order, geometric partial differential equation. It was introduced by Trudinger and Wang in 2005 in their investigation of the affine Plateau problem in affine geometry. The previous works of Trudinger-Wang, Chau-Weinkove and the author solved this global problem under some restrictions on the sign or integrability of the affine mean curvature. In this talk, we explain how to remove these restrictions and obtain global solutions under optimal integrability conditions on the affine mean curvature. Our analysis also covers the case of Abreu's equation arising in complex geometry.
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
江尻 祥 氏 (東大数理)
On varieties with splittings of relative Frobenius morphisms of Albanese maps
江尻 祥 氏 (東大数理)
On varieties with splittings of relative Frobenius morphisms of Albanese maps
[ 講演概要 ]
Varieties with splittings of Frobenius morphisms are called F-split varieties, which satisfy strong properties such as Kodaira vanishing. However, some important varieties are not F-split. For example, an abelian variety is F-split if and only if its p-rank is maximum. In this talk, we discuss the class of varieties with splittings of relative Frobenius morphisms of Albanese maps, which includes abelian varieties. As a consequence of Sannai and Tanaka's characterization of ordinary abelian varieties, we see that this class also includes F-split varieties. Furthermore, for varieties in this class, we show that the Kodaira vanishing theorem holds, and that Albanese maps are algebraic fiber spaces.
Varieties with splittings of Frobenius morphisms are called F-split varieties, which satisfy strong properties such as Kodaira vanishing. However, some important varieties are not F-split. For example, an abelian variety is F-split if and only if its p-rank is maximum. In this talk, we discuss the class of varieties with splittings of relative Frobenius morphisms of Albanese maps, which includes abelian varieties. As a consequence of Sannai and Tanaka's characterization of ordinary abelian varieties, we see that this class also includes F-split varieties. Furthermore, for varieties in this class, we show that the Kodaira vanishing theorem holds, and that Albanese maps are algebraic fiber spaces.
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
Tea: Common Room 16:30-17:00
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero (JAPANESE)
Tea: Common Room 16:30-17:00
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The Kashiwara-Vergne problem and the Goldman-Turaev Lie bialgebra in genus zero (JAPANESE)
[ 講演概要 ]
In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.
In view of results of Goldman and Turaev, the free vector space over the free loops on an oriented surface has a natural Lie bialgebra structure. The Goldman bracket has a formal description by using a special (or symplectic) expansion of the fundamental group of the surface. It is natural to ask for a formal description of the Turaev cobracket. We will show how to obtain a formal description of the Goldman-Turaev Lie bialgebra for genus 0 using a solution of the Kashiwara-Vergne problem. A similar description was recently obtained by Massuyeau using the Kontsevich integral. Moreover we propose a generalization of the Kashiwara-Vergne problem in the context of the Goldman-Turaev Lie bialgebra. This talk is based on a joint work with A. Alekseev, Y. Kuno and F. Naef.
統計数学セミナー
16:50-18:00 数理科学研究科棟(駒場) 052号室
磯貝 孝 氏 (首都大学東京)
ネットワーク理論を応用した相関クラスタリングによる株価の自動分類
磯貝 孝 氏 (首都大学東京)
ネットワーク理論を応用した相関クラスタリングによる株価の自動分類
[ 講演概要 ]
本研究では、東証１部上場の株価の日次収益率データを用いて、株価の銘柄間の
相関行列を推定し、銘柄をノードとする相関ネットワークを構築した。この相関
ネットワークに対して複雑ネットワーク理論で用いられているクラスタリング手
法を適用し、業種分類とは別の銘柄グループを構成し、それらの銘柄グループが
どのような特徴を持つのか、業種分類とどのような関係があるのか、などについ
て明らかとなった点について紹介する。
本研究では、東証１部上場の株価の日次収益率データを用いて、株価の銘柄間の
相関行列を推定し、銘柄をノードとする相関ネットワークを構築した。この相関
ネットワークに対して複雑ネットワーク理論で用いられているクラスタリング手
法を適用し、業種分類とは別の銘柄グループを構成し、それらの銘柄グループが
どのような特徴を持つのか、業種分類とどのような関係があるのか、などについ
て明らかとなった点について紹介する。
2016年10月04日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
鈴木拓 氏 (早稲田大学)
Higher order minimal families of rational curves and Fano manifolds with nef Chern characters (Japanese. Writing in English. )
鈴木拓 氏 (早稲田大学)
Higher order minimal families of rational curves and Fano manifolds with nef Chern characters (Japanese. Writing in English. )
[ 講演概要 ]
In this talk, we introduce higher order minimal families $H_i$ of rational curves
associated to Fano manifolds $X$. We prove that $H_i$ is also a Fano manifold
if the Chern characters of $X$ satisfy some positivity conditions. We also provide
a sufficient condition for Fano manifolds to be covered by higher rational manifolds.
In this talk, we introduce higher order minimal families $H_i$ of rational curves
associated to Fano manifolds $X$. We prove that $H_i$ is also a Fano manifold
if the Chern characters of $X$ satisfy some positivity conditions. We also provide
a sufficient condition for Fano manifolds to be covered by higher rational manifolds.
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 002号室
Odo Diekmann 氏 (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
http://www.uu.nl/staff/ODiekmann
Odo Diekmann 氏 (Utrecht University)
Waning and boosting : on the dynamics of immune status (ENGLISH)
[ 講演概要 ]
A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.
[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis
of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388
[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259
[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7
[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47
[ 参考URL ]A first aim is to briefly review various mathematical models of infectious disease dynamics that incorporate waning and boosting of immunity. The focus will be on models that are described by delay equations, in particular renewal equations [1]. Concerning within-host dynamics, we limit ourselves to the rather caricatural models of Aron [2] and de Graaf e.a. [3].From a biomedical point of view the main conclusion is that a higher force of infection may lead to less disease,see [4] and the references given there.
[1] O.Diekmann, M.Gyllenberg, J.A.J.Metz, H.R.Thieme, On the formulation and analysis
of general deterministic structured population models. I. Linear theory, J. Math. Biol. (1998) 36 : 349 - 388
[2] J.L. Aron, Dynamics of acquired immunity boosted by exposure to infection, Math. Biosc. (1983) 64 : 249-259
[3] W.F. de Graaf, M.E.E. Kretzschmar, P.M.F. Teunis, O. Diekmann, A two-phase within host model for immune response and its application to seriological profiles of pertussis, Epidemics (2014) 9 : 1-7
[4] A.N. Swart, M. Tomasi, M. Kretzschmar, A.H. Havelaar, O. Diekmann, The protective effect of temporary immunity under imposed infection pressure, Epidemics (2012) 4 : 43-47
http://www.uu.nl/staff/ODiekmann
2016年10月03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
島内 宏和 氏 (山梨英和大学)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
島内 宏和 氏 (山梨英和大学)
Visualizing the radial Loewner flow and the evolution family (JAPANESE)
[ 講演概要 ]
Herglotz 関数が１つ与えられたとき，対応する radial Loewner 方程式は単位円板から拡張する単連結領域族への等角写像族を定め，それは evolution family と呼ばれる単位円板の自己正則写像族と密接に関係する．本講演では， 与えられた Herglotz 関数に対する radial Loewner flow と evolution family を可視化するアルゴリズムを提示し，近似解の収束性と数値実験結果について紹介する．本研究は，堀田一敬氏（山口大学）との共同研究である．
Herglotz 関数が１つ与えられたとき，対応する radial Loewner 方程式は単位円板から拡張する単連結領域族への等角写像族を定め，それは evolution family と呼ばれる単位円板の自己正則写像族と密接に関係する．本講演では， 与えられた Herglotz 関数に対する radial Loewner flow と evolution family を可視化するアルゴリズムを提示し，近似解の収束性と数値実験結果について紹介する．本研究は，堀田一敬氏（山口大学）との共同研究である．
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
荒野悠輝 氏 (東大数理)
$C^*$-tensor categories and subfactors for totally disconnected groups
(English)
荒野悠輝 氏 (東大数理)
$C^*$-tensor categories and subfactors for totally disconnected groups
(English)
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
星野壮登 氏 (東京大学大学院数理科学研究科)
Coupled KPZ equations and complex-valued stochastic Ginzburg-Landau equation (日本語)
星野壮登 氏 (東京大学大学院数理科学研究科)
Coupled KPZ equations and complex-valued stochastic Ginzburg-Landau equation (日本語)
[ 講演概要 ]
Gubinelli-Imkeller-PerkowskiのParacontrolled calculusによりある種の特異な非線形確率偏微分方程式について解の理論が構築されたが、一般論からは時間局所解の一意存在しか分からない。本講演では、タイトルの２つの方程式について時間大域解の存在について述べる。
Gubinelli-Imkeller-PerkowskiのParacontrolled calculusによりある種の特異な非線形確率偏微分方程式について解の理論が構築されたが、一般論からは時間局所解の一意存在しか分からない。本講演では、タイトルの２つの方程式について時間大域解の存在について述べる。
2016年09月27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
Tea: Common Room 16:30-17:00
藤内 翔太 氏 (東京大学大学院数理科学研究科)
CAT(0) properties for orthoscheme complexes (JAPANESE)
Tea: Common Room 16:30-17:00
藤内 翔太 氏 (東京大学大学院数理科学研究科)
CAT(0) properties for orthoscheme complexes (JAPANESE)
[ 講演概要 ]
Gromov showed that a cubical complex is locally CAT(0) if and only if the link of every vertex is a flag complex. Brady and MacCammond introduced an orthoscheme complex as a generalization of cubical complexes. It is, however, difficult to tell whether an orthoscheme complex is (locally) CAT(0) or not. In this talk, I will discuss a translation of Gromov's characterization for orthoscheme complexes. As a generalization of Gromov's characterization, I will show that the orthoscheme complex of locally distributive semilattice is CAT(0) if and only if it is a flag semilattice.
Gromov showed that a cubical complex is locally CAT(0) if and only if the link of every vertex is a flag complex. Brady and MacCammond introduced an orthoscheme complex as a generalization of cubical complexes. It is, however, difficult to tell whether an orthoscheme complex is (locally) CAT(0) or not. In this talk, I will discuss a translation of Gromov's characterization for orthoscheme complexes. As a generalization of Gromov's characterization, I will show that the orthoscheme complex of locally distributive semilattice is CAT(0) if and only if it is a flag semilattice.
2016年09月26日(月)
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
Sorin Popa 氏 (UCLA)
未定 (English)
Sorin Popa 氏 (UCLA)
未定 (English)
FMSPレクチャーズ
16:00-17:30 数理科学研究科棟(駒場) 056号室
Murray Muraskin 氏 (University of North Dakota, Grand Forks)
Mathematical Aesthetic Principles and Nonintegrable Systems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Muraskin.pdf
Murray Muraskin 氏 (University of North Dakota, Grand Forks)
Mathematical Aesthetic Principles and Nonintegrable Systems (ENGLISH)
[ 講演概要 ]
The discussion presents a study of a set of mathematical principles that can be classified as "aesthetic”and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations causes the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.
[ 参考URL ]The discussion presents a study of a set of mathematical principles that can be classified as "aesthetic”and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three dimensional lattices, as well as multi wave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations causes the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Muraskin.pdf
2016年08月29日(月)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 268号室
通常の開催曜日、会場と異なります。
Nguyen Cong Phuc 氏 (Louisiana State University)
The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (English)
https://www.math.lsu.edu/~pcnguyen/
通常の開催曜日、会場と異なります。
Nguyen Cong Phuc 氏 (Louisiana State University)
The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (English)
[ 講演概要 ]
In this talk, both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. We obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. This result can be viewed as the stationary counterpart of an existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with small initial data in $BMO^{-1}$. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations which imply the regularity condition $L_{t}^{\infty}(X)$, where $X$ is a non-endpoint borderline Lorentz space $X=L_{x}^{3, q}, q\not=\infty$. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier–Stokes equations with profiles in $L^{12/5}(\mathbb{R}^3)$ or in the Marcinkiewicz space $L^{q, \infty}(\mathbb{R}^{3})$ for any $q \in (12/5, 6)$.
This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.
[ 参考URL ]In this talk, both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. We obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. This result can be viewed as the stationary counterpart of an existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with small initial data in $BMO^{-1}$. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations which imply the regularity condition $L_{t}^{\infty}(X)$, where $X$ is a non-endpoint borderline Lorentz space $X=L_{x}^{3, q}, q\not=\infty$. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier–Stokes equations with profiles in $L^{12/5}(\mathbb{R}^3)$ or in the Marcinkiewicz space $L^{q, \infty}(\mathbb{R}^{3})$ for any $q \in (12/5, 6)$.
This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.
https://www.math.lsu.edu/~pcnguyen/
2016年08月12日(金)
FMSPレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 128号室
Eric Chung 氏 (Chinese Univ. of Hong Kong)
Multiscale simulations of waves and applications (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Chung.pdf
Eric Chung 氏 (Chinese Univ. of Hong Kong)
Multiscale simulations of waves and applications (ENGLISH)
[ 講演概要 ]
Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.
In this talk, we will present a new multiscale approach for seismic wave propagation.
The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.
The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.
We will also present applications to inverse problems.
[ 参考URL ]Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.
In this talk, we will present a new multiscale approach for seismic wave propagation.
The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.
The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.
We will also present applications to inverse problems.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Chung.pdf
FMSPレクチャーズ
16:00-17:00 数理科学研究科棟(駒場) 128号室
Christian Clason 氏 (University Duisburg-Essen)
Discrete regularization of parameter identification problems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Clason.pdf
Christian Clason 氏 (University Duisburg-Essen)
Discrete regularization of parameter identification problems (ENGLISH)
[ 講演概要 ]
This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.
[ 参考URL ]This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Clason.pdf
2016年08月10日(水)
FMSPレクチャーズ
10:00-11:00 数理科学研究科棟(駒場) 370号室
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)
[ 講演概要 ]
We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.
[ 参考URL ]We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf
統計数学セミナー
13:00-14:30 数理科学研究科棟(駒場) 117号室
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations
2016年08月09日(火)
統計数学セミナー
13:00-16:30 数理科学研究科棟(駒場) 117号室
本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています.
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations
http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=180
本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています.
David Nualart 氏 (Kansas University)
Malliavin calculus and normal approximations
[ 講演概要 ]
The purpose of these lectures is to introduce some recent results on the application of Malliavin calculus combined with Stein's method to normal approximation. The Malliavin calculus is a differential calculus on the Wiener space. First, we will present some elements of Malliavin calculus, defining the basic differential operators: the derivative, its adjoint called the divergence operator and the generator of the Ornstein-Uhlenbeck semigroup. The behavior of these operators on the Wiener chaos expansion will be discussed. Then, we will introduce the Stein's method for normal approximation, which leads to general bounds for the Kolmogorov and total variation distances between the law of a Brownian functional and the standard normal distribution. In this context, the integration by parts formula of Malliavin calculus will allow us to express these bounds in terms of the Malliavin operators. We will present the application of this methodology to derive the Fourth Moment Theorem for a sequence of multiple stochastic integrals, and we will discuss some results on the uniform convergence of densities obtained using Malliavin calculus techniques. Finally, examples of functionals of Gaussian processes, such as the fractional Brownian motion, will be discussed.
[ 参考URL ]The purpose of these lectures is to introduce some recent results on the application of Malliavin calculus combined with Stein's method to normal approximation. The Malliavin calculus is a differential calculus on the Wiener space. First, we will present some elements of Malliavin calculus, defining the basic differential operators: the derivative, its adjoint called the divergence operator and the generator of the Ornstein-Uhlenbeck semigroup. The behavior of these operators on the Wiener chaos expansion will be discussed. Then, we will introduce the Stein's method for normal approximation, which leads to general bounds for the Kolmogorov and total variation distances between the law of a Brownian functional and the standard normal distribution. In this context, the integration by parts formula of Malliavin calculus will allow us to express these bounds in terms of the Malliavin operators. We will present the application of this methodology to derive the Fourth Moment Theorem for a sequence of multiple stochastic integrals, and we will discuss some results on the uniform convergence of densities obtained using Malliavin calculus techniques. Finally, examples of functionals of Gaussian processes, such as the fractional Brownian motion, will be discussed.
http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=180
2016年08月08日(月)
FMSPレクチャーズ
16:30-17:30 数理科学研究科棟(駒場) 128号室
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon.pdf
Benny Y C Hon 氏 (City Univ. of Hong Kong)
Global-local-integration-based kernel approximation methods (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon.pdf
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