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過去の記録 ～11/11｜本日 11/12 | 今後の予定 11/13～
2011年06月16日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
磯野優介 氏 (東大数理)
Introduction to rigidity theory of von Neumann algebras (JAPANESE)
磯野優介 氏 (東大数理)
Introduction to rigidity theory of von Neumann algebras (JAPANESE)
2011年06月15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
阿部知行 氏 (東大IPMU)
Product formula for $p$-adic epsilon factors (ENGLISH)
阿部知行 氏 (東大IPMU)
Product formula for $p$-adic epsilon factors (ENGLISH)
[ 講演概要 ]
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
(本講演は「東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とIHESとの双方向同時中継で行います。)
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
(本講演は「東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とIHESとの双方向同時中継で行います。)
2011年06月14日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
満渕 俊樹 氏 (大阪大学大学院理学研究科)
Donaldson-Tian-Yau's Conjecture (JAPANESE)
Tea: 16:40 - 17:00 コモンルーム
満渕 俊樹 氏 (大阪大学大学院理学研究科)
Donaldson-Tian-Yau's Conjecture (JAPANESE)
[ 講演概要 ]
For polarized algebraic manifolds, the concept of K-stability
introduced by Tian and Donaldson is conjecturally strongly correlated
to the existence of constant scalar curvature metrics (or more
generally extremal K\\"ahler metrics) in the polarization class. This is
known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable
progress has been made by many authors toward its solution. In this
talk, I'll discuss the topic mainly with emphasis on the existence
part of the conjecture.
For polarized algebraic manifolds, the concept of K-stability
introduced by Tian and Donaldson is conjecturally strongly correlated
to the existence of constant scalar curvature metrics (or more
generally extremal K\\"ahler metrics) in the polarization class. This is
known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable
progress has been made by many authors toward its solution. In this
talk, I'll discuss the topic mainly with emphasis on the existence
part of the conjecture.
2011年06月13日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
大沢 健夫 氏 (名古屋大学)
On the complement of effective divisors with semipositive normal bundle (JAPANESE)
大沢 健夫 氏 (名古屋大学)
On the complement of effective divisors with semipositive normal bundle (JAPANESE)
講演会
16:00-17:30 数理科学研究科棟(駒場) 128号室
CHEN Hua 氏 (Wuhan University)
Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)
CHEN Hua 氏 (Wuhan University)
Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)
[ 講演概要 ]
In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including
(1) generalized Kolmogorov equations,
(2) Fokker-Planck equations,
(3) Landau equations and
(4) sub-elliptic Monge-Ampere equations.
In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including
(1) generalized Kolmogorov equations,
(2) Fokker-Planck equations,
(3) Landau equations and
(4) sub-elliptic Monge-Ampere equations.
2011年06月09日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
吉田裕亮 氏 (お茶の水女子大)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
吉田裕亮 氏 (お茶の水女子大)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
応用解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
時間が普段と異なりますのでご注意ください
望月清 氏 (東京都立大学 名誉教授)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
時間が普段と異なりますのでご注意ください
望月清 氏 (東京都立大学 名誉教授)
Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)
[ 講演概要 ]
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
2011年06月08日(水)
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 056号室
平野雄一 氏 (東京大学数理科学研究科)
保型形式の合同式と岩澤λ不変量について (JAPANESE)
平野雄一 氏 (東京大学数理科学研究科)
保型形式の合同式と岩澤λ不変量について (JAPANESE)
[ 講演概要 ]
カスプ形式とEisenstein級数のFourier係数の間の合同式からそれらに付随する L 関数の特殊値の間の合同式を導くという問題を考える。
これは保型形式の重さが 2 の場合はVatsal氏によって証明された。本講演では,重さが 2 以上の場合に一般化できた結果を紹介する。
さらに、この結果を保型形式に付随する p 進Galois表現が剰余して可約という特別な場合の岩澤主予想に応用する。これは、重さが 2 の場合のGreenberg氏及びVatsal氏の結果を部分的に一般化したものである。
カスプ形式とEisenstein級数のFourier係数の間の合同式からそれらに付随する L 関数の特殊値の間の合同式を導くという問題を考える。
これは保型形式の重さが 2 の場合はVatsal氏によって証明された。本講演では,重さが 2 以上の場合に一般化できた結果を紹介する。
さらに、この結果を保型形式に付随する p 進Galois表現が剰余して可約という特別な場合の岩澤主予想に応用する。これは、重さが 2 の場合のGreenberg氏及びVatsal氏の結果を部分的に一般化したものである。
2011年06月07日(火)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Chenyang Xu 氏 (MIT)
Log canonical closure (ENGLISH)
Chenyang Xu 氏 (MIT)
Log canonical closure (ENGLISH)
[ 講演概要 ]
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
中澤嵩 氏 (岡山大学大学院環境学研究科
)
水質改善を目的として水面に設置されたプロペラが誘起する流れ場の線形安定性解析
(JAPANESE)
http://www.infsup.jp/utnas/
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
中澤嵩 氏 (岡山大学大学院環境学研究科
)
水質改善を目的として水面に設置されたプロペラが誘起する流れ場の線形安定性解析
(JAPANESE)
[ 講演概要 ]
閉鎖性水域における水質改善を目的として、水面上に置かれた小型プロペラによって誘起された流れ場について考察する。このような小型プロペラは、水質改善に有効である鉛直方向循環流を誘起すると考えられている。しかし、当該機器は水質改善に有効でない水平方向回転流も誘起すると実験等から観測されており、効率的に水質改善を行うためには当該機器が誘起する流れ場のメカニズムを解明する必要がある。
本講演では、当該機器が誘起する流れ場の擾乱に対する線形安定性解析結果を紹介する。線形安定性解析の結果、レイノルズ数が臨界レイノルズ数を超えた際に、水質改善を促進すると考えられる擾乱の発達を確認した。
[ 講演参考URL ]閉鎖性水域における水質改善を目的として、水面上に置かれた小型プロペラによって誘起された流れ場について考察する。このような小型プロペラは、水質改善に有効である鉛直方向循環流を誘起すると考えられている。しかし、当該機器は水質改善に有効でない水平方向回転流も誘起すると実験等から観測されており、効率的に水質改善を行うためには当該機器が誘起する流れ場のメカニズムを解明する必要がある。
本講演では、当該機器が誘起する流れ場の擾乱に対する線形安定性解析結果を紹介する。線形安定性解析の結果、レイノルズ数が臨界レイノルズ数を超えた際に、水質改善を促進すると考えられる擾乱の発達を確認した。
http://www.infsup.jp/utnas/
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同で行います
金井雅彦 氏 (東京大学)
Rigidity of group actions via invariant geometric structures
(JAPANESE)
トポロジー火曜セミナーと合同で行います
金井雅彦 氏 (東京大学)
Rigidity of group actions via invariant geometric structures
(JAPANESE)
[ 講演概要 ]
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Lie群論・表現論セミナーと合同 Tea: 16:00 - 16:30 コモンルーム
金井 雅彦 氏 (東京大学大学院数理科学研究科)
Rigidity of group actions via invariant geometric structures (JAPANESE)
Lie群論・表現論セミナーと合同 Tea: 16:00 - 16:30 コモンルーム
金井 雅彦 氏 (東京大学大学院数理科学研究科)
Rigidity of group actions via invariant geometric structures (JAPANESE)
[ 講演概要 ]
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
2011年06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
篠原知子 氏 (都立産業技術高専)
An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)
篠原知子 氏 (都立産業技術高専)
An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
石井 志保子 氏 (東京大学数理科学研究科)
Multiplier ideals via Mather discrepancies (JAPANESE)
石井 志保子 氏 (東京大学数理科学研究科)
Multiplier ideals via Mather discrepancies (JAPANESE)
[ 講演概要 ]
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
2011年06月02日(木)
東京無限可積分系セミナー
16:30-17:30 数理科学研究科棟(駒場) 056号室
斎藤義久 氏 (東大数理)
On the module category of $¥overline{U}_q(¥mathfrak{sl}_2)$ (JAPANESE)
斎藤義久 氏 (東大数理)
On the module category of $¥overline{U}_q(¥mathfrak{sl}_2)$ (JAPANESE)
[ 講演概要 ]
In the representation theory of quantum groups at roots of unity, it is
often assumed that the parameter $q$ is a primitive $n$-th root of unity
where $n$ is a odd prime number. However, there has recently been
increasing interest in the the cases where $n$ is an even integer ---
for example, in the study of logarithmic conformal field theories, or in
knot invariants. In this talk,
we work out a fairly detailed study on the category of finite
dimensional
modules of the restricted quantum $¥overline{U}_q(¥mathfrak{sl}_2)$
where
$q$ is a $2p$-th root of unity, $p¥ge2$.
In the representation theory of quantum groups at roots of unity, it is
often assumed that the parameter $q$ is a primitive $n$-th root of unity
where $n$ is a odd prime number. However, there has recently been
increasing interest in the the cases where $n$ is an even integer ---
for example, in the study of logarithmic conformal field theories, or in
knot invariants. In this talk,
we work out a fairly detailed study on the category of finite
dimensional
modules of the restricted quantum $¥overline{U}_q(¥mathfrak{sl}_2)$
where
$q$ is a $2p$-th root of unity, $p¥ge2$.
2011年05月31日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
盛田 健彦 氏 (大阪大学大学院理学研究科)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
Tea: 16:40 - 17:00 コモンルーム
盛田 健彦 氏 (大阪大学大学院理学研究科)
Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps (JAPANESE)
[ 講演概要 ]
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\\mathcal{E}
^{1}(M,M)$ is generic.
\\begin{itemize}
\\item[(1)] $T$ has a unique measure with maximum total exponent.
\\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\\end{itemize}
On the contrary, we show that for $r\\ge 2$, a generic element
in $\\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
Lie群論・表現論セミナー
16:30-17:30 数理科学研究科棟(駒場) 126号室
栗原 大武 氏 (東北大学大学院理学研究科)
On character tables of association schemes based on attenuated
spaces (JAPANESE)
栗原 大武 氏 (東北大学大学院理学研究科)
On character tables of association schemes based on attenuated
spaces (JAPANESE)
[ 講演概要 ]
An association scheme is a pair of a finite set $X$
and a set of relations $\\{R_i\\}_{0\\le i\\le d}$
on $X$ which satisfies several axioms of regularity.
The notion of association schemes is viewed as some axiomatized
properties of transitive permutation groups in terms of combinatorics, and also the notion of association schemes is regarded as a generalization of the subring of the group ring spanned by the conjugacy classes of finite groups.
Thus, the theory of association schemes had been developed in the
study of finite permutation groups and representation theory.
To determine the character tables of association schemes is an
important first step to a systematic study of association schemes, and is helpful toward the classification of those schemes.
In this talk, we determine the character tables of association schemes based on attenuated spaces.
These association schemes are obtained from subspaces of a given
dimension in attenuated spaces.
An association scheme is a pair of a finite set $X$
and a set of relations $\\{R_i\\}_{0\\le i\\le d}$
on $X$ which satisfies several axioms of regularity.
The notion of association schemes is viewed as some axiomatized
properties of transitive permutation groups in terms of combinatorics, and also the notion of association schemes is regarded as a generalization of the subring of the group ring spanned by the conjugacy classes of finite groups.
Thus, the theory of association schemes had been developed in the
study of finite permutation groups and representation theory.
To determine the character tables of association schemes is an
important first step to a systematic study of association schemes, and is helpful toward the classification of those schemes.
In this talk, we determine the character tables of association schemes based on attenuated spaces.
These association schemes are obtained from subspaces of a given
dimension in attenuated spaces.
2011年05月30日(月)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
[ 講演概要 ]
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
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
山盛厚伺 氏 (明治大学)
On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)
山盛厚伺 氏 (明治大学)
On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)
2011年05月26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
深尾武史 氏 (京都教育大学)
Obstacle problem of Navier-Stokes equations in thermohydraulics (JAPANESE)
深尾武史 氏 (京都教育大学)
Obstacle problem of Navier-Stokes equations in thermohydraulics (JAPANESE)
[ 講演概要 ]
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.
2011年05月25日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 056号室
松本雄也 氏 (東京大学数理科学研究科)
On good reduction of some K3 surfaces (JAPANESE)
松本雄也 氏 (東京大学数理科学研究科)
On good reduction of some K3 surfaces (JAPANESE)
[ 講演概要 ]
局所体 K 上の多様体がいつ良い還元をもつかを調べる.
多様体 X が良い還元をもつならば,
X の l 進エタールコホモロジーから定まるガロア表現は不分岐表現となる
(ここで l は K の剰余体の標数と異なる素数).
では逆に,このガロア表現が不分岐ならば良い還元をもつか …(*)
という問題を考えると,
X がアーベル多様体ならば (*) は成り立つ(Serre--Tate)が,
一般の多様体では成り立たない.
そこで,(*) が成り立つような多様体のクラスを探すことを考える.
この講演では,ある種の K3 曲面について (*) をやや弱めた主張が成り立つことを紹介する.
局所体 K 上の多様体がいつ良い還元をもつかを調べる.
多様体 X が良い還元をもつならば,
X の l 進エタールコホモロジーから定まるガロア表現は不分岐表現となる
(ここで l は K の剰余体の標数と異なる素数).
では逆に,このガロア表現が不分岐ならば良い還元をもつか …(*)
という問題を考えると,
X がアーベル多様体ならば (*) は成り立つ(Serre--Tate)が,
一般の多様体では成り立たない.
そこで,(*) が成り立つような多様体のクラスを探すことを考える.
この講演では,ある種の K3 曲面について (*) をやや弱めた主張が成り立つことを紹介する.
2011年05月24日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
村井大介 氏 (名古屋大学大学院情報科学研究科)
密度型位相最適化問題に対するある解法の誤差解析 (JAPANESE)
http://www.infsup.jp/utnas/
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
村井大介 氏 (名古屋大学大学院情報科学研究科)
密度型位相最適化問題に対するある解法の誤差解析 (JAPANESE)
[ 講演概要 ]
偏微分方程式が定義された領域の最適な穴の配置を求める問題を位相最適化問題という。この問題に対して、密度を設計変数にした密度型位相最適化問題が定式化され、数値不安定現象が起こらない解法が提案されている。本公演では、この解法によって得られた数値解に含まれる誤差を解析した結果を報告する。Poisson問題を例にした数値誤差の結果も紹介する予定である。
[ 講演参考URL ]偏微分方程式が定義された領域の最適な穴の配置を求める問題を位相最適化問題という。この問題に対して、密度を設計変数にした密度型位相最適化問題が定式化され、数値不安定現象が起こらない解法が提案されている。本公演では、この解法によって得られた数値解に含まれる誤差を解析した結果を報告する。Poisson問題を例にした数値誤差の結果も紹介する予定である。
http://www.infsup.jp/utnas/
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
吉永 正彦 氏 (京都大学大学院理学研究科)
Minimal Stratifications for Line Arrangements (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
吉永 正彦 氏 (京都大学大学院理学研究科)
Minimal Stratifications for Line Arrangements (JAPANESE)
[ 講演概要 ]
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
椋野純一 氏 (名古屋大学)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
椋野純一 氏 (名古屋大学)
Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds (JAPANESE)
[ 講演概要 ]
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\\Gamma$ of $G$ via the left action, the quotient space $\\Gamma \\backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
博士論文発表会
13:15-14:30 数理科学研究科棟(駒場) 128号室
高岡 浩一郎 氏 (東京大学大学院数理科学研究科)
マルチンゲール理論およびその数理ファイナンスへの応用に関する幾つかの性質 (JAPANESE)
高岡 浩一郎 氏 (東京大学大学院数理科学研究科)
マルチンゲール理論およびその数理ファイナンスへの応用に関する幾つかの性質 (JAPANESE)
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