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過去の記録
過去の記録 ～12/04｜本日 12/05 | 今後の予定 12/06～
2014年02月03日(月)
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
藤田 健人 氏 (京都大学数理解析研究所)
Classification of log del Pezzo surfaces of index three (JAPANESE)
藤田 健人 氏 (京都大学数理解析研究所)
Classification of log del Pezzo surfaces of index three (JAPANESE)
[ 講演概要 ]
Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.
Log del Pezzo surfaces constitute an interesting class of rational surfaces and naturally appear in the minimal model program. I will describe an algorithm to classify all the log del Pezzo surfaces of fixed (Q-Gorenstein) index $a$. Especially, I will focus on the case that $a$ is equal to three. This is joint work with Kazunori Yasutake.
GCOEセミナー
16:00-17:00 数理科学研究科棟(駒場) 118号室
Fatiha Alabau 氏 (University of Lorraine)
On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)
Fatiha Alabau 氏 (University of Lorraine)
On the influence of the coupling on the dynamics of under-observed cascade systems of PDE’s (ENGLISH)
[ 講演概要 ]
We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.
We consider observability of coupled dynamical systems of hyperbolic and parabolic type when the number of observations is strictly less that the number of unknowns. A main issue is to understand how the lack of observations of certain components is compensated by the coupling information. This talk will present a mathematical approach based on energy methods and some recent positive and negative results on these questions.
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 118号室
Piermarco Cannarsa 氏 (University of Rome Tor Vergata)
Compactness estimates for Hamilton-Jacobi equations (ENGLISH)
Piermarco Cannarsa 氏 (University of Rome Tor Vergata)
Compactness estimates for Hamilton-Jacobi equations (ENGLISH)
[ 講演概要 ]
For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.
For scalar conservations laws in one space dimension, P. Lax was the first to obtain compactness properties of the solution semigroup. Such properties were subsequently analyzed by several authors in quantitative terms using Kolmogorov's entropy. In this talk, we shall explain how to adapt such approach to the Hopf-Lax semigroup of solutions to first order Hamilton-Jacobi equations in arbitrary space dimension, and discuss related controllability issues.
2014年02月01日(土)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
Minimal submanifolds on type IV symmetric domains (ENGLISH)
Bayarmagnai, G. 氏 (National University of Mongolia) 13:30-14:30
On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)
[ 講演概要 ]
The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
織田孝幸 氏 (東京大学・数理科学研究科) 15:00-16:00The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.
Minimal submanifolds on type IV symmetric domains (ENGLISH)
[ 講演概要 ]
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.
2014年01月31日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 122号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Jean-Pierre Puel 氏 (Université de Versailles Saint-Quentin-en-Yvelines)
Controllability of fluid flows (ENGLISH)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Jean-Pierre Puel 氏 (Université de Versailles Saint-Quentin-en-Yvelines)
Controllability of fluid flows (ENGLISH)
[ 講演概要 ]
First of all we will describe in an abstract situation the various concepts
of controllability for evolution equations.
We will then present some problems and results concerning the
controllability of systems modeling fluid flows.
First of all we will consider the Euler equation describing the motion of an
incompressible inviscid fluid.
Then we will give some results concerning the Navier-Stokes equations,
modeling an incompressible viscous fluid, and some related systems.
Finally we will give a first result of controllability for the case of a
compressible fluid (in dimension 1) and some important open problems.
First of all we will describe in an abstract situation the various concepts
of controllability for evolution equations.
We will then present some problems and results concerning the
controllability of systems modeling fluid flows.
First of all we will consider the Euler equation describing the motion of an
incompressible inviscid fluid.
Then we will give some results concerning the Navier-Stokes equations,
modeling an incompressible viscous fluid, and some related systems.
Finally we will give a first result of controllability for the case of a
compressible fluid (in dimension 1) and some important open problems.
2014年01月30日(木)
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 128号室
Hans Jockers 氏 (The University of Bonn)
Characteristic classes from 2d renormalized sigma-models (ENGLISH)
Hans Jockers 氏 (The University of Bonn)
Characteristic classes from 2d renormalized sigma-models (ENGLISH)
[ 講演概要 ]
The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic
of holomorphic vector bundles to topological invariants of compact complex manifold.
I will explain a generalization of the Mukai's modified first Chern character map, which
introduces certain characteristic classes that have not been considered in this form by
Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma
function. The characteristic Gamma class has a surprising relation to the quantum theory
of certain 2d sigma-models with compact complex manifolds as their target spaces. I will
argue that the Gamma class describes perturbative quantum corrections to the classical
theory of those sigma models.
The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic
of holomorphic vector bundles to topological invariants of compact complex manifold.
I will explain a generalization of the Mukai's modified first Chern character map, which
introduces certain characteristic classes that have not been considered in this form by
Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma
function. The characteristic Gamma class has a surprising relation to the quantum theory
of certain 2d sigma-models with compact complex manifolds as their target spaces. I will
argue that the Gamma class describes perturbative quantum corrections to the classical
theory of those sigma models.
2014年01月28日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 118号室
教室がいつもと異なっていますので、ご注意ください
村川秀樹 氏 (九州大学大学院数理学研究院)
細胞接着の数理モデルについて (JAPANESE)
http://www.infsup.jp/utnas/
教室がいつもと異なっていますので、ご注意ください
村川秀樹 氏 (九州大学大学院数理学研究院)
細胞接着の数理モデルについて (JAPANESE)
[ 講演概要 ]
多細胞生物のからだを構成する細胞は独立に存在するのではなく、細胞同士が接着したり、細胞外基質に接着して存在している。細胞同士の接着は細胞接着または細胞間接着と呼ばれる。Armstrong、Painter、Sherratt (2006)は細胞集団の挙動を理解するために、細胞接着を考慮した数理モデルを提案した。そのモデルは多くの研究者の興味を引き、精力的に研究が進められているが、数値実験の結果からはそのモデルが現象を記述しているとは言い難い。その数理モデルの問題点を精査し、現象を記述する新たな数理モデルを提案する。
[ 参考URL ]多細胞生物のからだを構成する細胞は独立に存在するのではなく、細胞同士が接着したり、細胞外基質に接着して存在している。細胞同士の接着は細胞接着または細胞間接着と呼ばれる。Armstrong、Painter、Sherratt (2006)は細胞集団の挙動を理解するために、細胞接着を考慮した数理モデルを提案した。そのモデルは多くの研究者の興味を引き、精力的に研究が進められているが、数値実験の結果からはそのモデルが現象を記述しているとは言い難い。その数理モデルの問題点を精査し、現象を記述する新たな数理モデルを提案する。
http://www.infsup.jp/utnas/
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
This seminar is cosponsored by the GCOE program.
Arnaud Ducrot 氏 (ボルドー大学)
Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)
This seminar is cosponsored by the GCOE program.
Arnaud Ducrot 氏 (ボルドー大学)
Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.
In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.
GCOEセミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)
http://agusta.ms.u-tokyo.ac.jp/analysis.html
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.
[ 参考URL ]In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.
http://agusta.ms.u-tokyo.ac.jp/analysis.html
2014年01月27日(月)
複素解析幾何セミナー
11:00-12:00 数理科学研究科棟(駒場) 126号室
野口 潤次郎 氏 (東大数理)
Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)
野口 潤次郎 氏 (東大数理)
Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)
[ 講演概要 ]
The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.
In the talk we will fix an error in an application in [NW02], and we will show
Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.
For the finiteness we obtain
Theorem 2. Let the notation be as above.
(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.
Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,
recent due to A. Levin.
The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.
In the talk we will fix an error in an application in [NW02], and we will show
Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.
For the finiteness we obtain
Theorem 2. Let the notation be as above.
(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.
(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.
Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,
recent due to A. Levin.
2014年01月25日(土)
調和解析駒場セミナー
13:00-18:00 数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
Jayson Cunanan 氏 (名古屋大学) 13:30-15:00
Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)
質量劣臨界非線型シュレディンガー方程式の解析 (JAPANESE)
このセミナーは,月に1度程度,不定期に開催されます.
Jayson Cunanan 氏 (名古屋大学) 13:30-15:00
Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)
[ 講演概要 ]
We study the boundedness of
unimodular Fourier multipliers on Wiener amalgam spaces.
For a real-valued homogeneous function ¥mu
on ¥mathbb{R}^n of degree ¥alpha¥ge 2,
we show the boundedness of the operator e^{i¥mu(D)}
between the weighted Wiener amalgam space
W_s^{p,q} and W^{p,q}
for all 1¥le p,q¥le¥infty and
s>n(¥alpha-2)|1/p-1/2|+n|1/p-1/q|.
This threshold is shown to be optimal for regions
¥max(1/q, 1/2)¥le 1/p
and
¥min(1/q, 1/2)¥geq 1/p.
Moreover,
we give sufficient conditions
for the boundedness of e^{i¥mu(D)}
on W^{p,q} for ¥alpha¥in(0,2).
眞崎 聡 氏 (広島大学) 15:30-17:00We study the boundedness of
unimodular Fourier multipliers on Wiener amalgam spaces.
For a real-valued homogeneous function ¥mu
on ¥mathbb{R}^n of degree ¥alpha¥ge 2,
we show the boundedness of the operator e^{i¥mu(D)}
between the weighted Wiener amalgam space
W_s^{p,q} and W^{p,q}
for all 1¥le p,q¥le¥infty and
s>n(¥alpha-2)|1/p-1/2|+n|1/p-1/q|.
This threshold is shown to be optimal for regions
¥max(1/q, 1/2)¥le 1/p
and
¥min(1/q, 1/2)¥geq 1/p.
Moreover,
we give sufficient conditions
for the boundedness of e^{i¥mu(D)}
on W^{p,q} for ¥alpha¥in(0,2).
質量劣臨界非線型シュレディンガー方程式の解析 (JAPANESE)
[ 講演概要 ]
短距離型かつ質量劣臨界である非線型シュレディンガー方程式を考える。
スケール臨界となる斉次重みつきソボレフ空間から初期値をとり、
対応する解を解析する。
興味があるのは解の時間大域挙動である。
散乱のシャープな判定を与えるいわゆる最小爆発解の存在と、
さらにそれが定在波解ではないことを示す。
スケール臨界の重みを上手く取り扱うために工夫が必要で、
例えば解の属する関数空間を、
単純なルベーグ・ルベーグ型の時空の関数空間ではなく、
中西-小澤により導入された、
空間に関してはシュレディンガー発展作用素の性質を考慮して
修正を施した斉次ベゾフ空間をとり、
時間に関してはローレンツ空間をとったものを考える。
短距離型かつ質量劣臨界である非線型シュレディンガー方程式を考える。
スケール臨界となる斉次重みつきソボレフ空間から初期値をとり、
対応する解を解析する。
興味があるのは解の時間大域挙動である。
散乱のシャープな判定を与えるいわゆる最小爆発解の存在と、
さらにそれが定在波解ではないことを示す。
スケール臨界の重みを上手く取り扱うために工夫が必要で、
例えば解の属する関数空間を、
単純なルベーグ・ルベーグ型の時空の関数空間ではなく、
中西-小澤により導入された、
空間に関してはシュレディンガー発展作用素の性質を考慮して
修正を施した斉次ベゾフ空間をとり、
時間に関してはローレンツ空間をとったものを考える。
2014年01月24日(金)
代数学コロキウム
16:40-18:50 数理科学研究科棟(駒場) 056号室
いつもと曜日が異なりますのご注意ください
Christopher Davis 氏 (University of Copenhagen) 16:40-17:40
An approach to p-adic Hodge theory over number fields (ENGLISH)
Canonical lifts of norm fields and applications (ENGLISH)
いつもと曜日が異なりますのご注意ください
Christopher Davis 氏 (University of Copenhagen) 16:40-17:40
An approach to p-adic Hodge theory over number fields (ENGLISH)
[ 講演概要 ]
As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.
Bryden Cais 氏 (University of Arizona) 17:50-18:50As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.
Canonical lifts of norm fields and applications (ENGLISH)
[ 講演概要 ]
In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.
In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 002号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Bo Berndtsson 氏 (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Bo Berndtsson 氏 (Chalmers University of Technology)
Complex Brunn-Minkowski theory (ENGLISH)
[ 講演概要 ]
The classical Brunn-Minkowski theory deals with the volume of convex sets.
It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.
The classical Brunn-Minkowski theory deals with the volume of convex sets.
It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.
2014年01月23日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Thomas Giletti 氏 (Univ. of Lorraine at Nancy)
Inside dynamics of pushed and pulled fronts (ENGLISH)
Thomas Giletti 氏 (Univ. of Lorraine at Nancy)
Inside dynamics of pushed and pulled fronts (ENGLISH)
[ 講演概要 ]
Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.
Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.
2014年01月22日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 117号室
いつもと場所が異なりますのでご注意ください
柏原正樹 氏 (京都大学数理解析研究所)
Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)
いつもと場所が異なりますのでご注意ください
柏原正樹 氏 (京都大学数理解析研究所)
Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)
[ 講演概要 ]
The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.
(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.)
The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.
(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.)
代数幾何学セミナー
15:00-16:30 数理科学研究科棟(駒場) 122号室
いつもと曜日・時間が異なります
Thomas Ducat 氏 (University of Warwick)
Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)
いつもと曜日・時間が異なります
Thomas Ducat 氏 (University of Warwick)
Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)
[ 講演概要 ]
Consider a singular curve C contained in a smooth 3-fold X.
Assuming the existence of a Du Val general elephant S containing C,
I give a normal form for the equations of C in X and an outline of how to
construct a divisorial extraction from this curve. If the general S is
Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit
conditions for the existence of a terminal extraction. A treatment of
the D_{2k+1} case should be possible by similar means.
Consider a singular curve C contained in a smooth 3-fold X.
Assuming the existence of a Du Val general elephant S containing C,
I give a normal form for the equations of C in X and an outline of how to
construct a divisorial extraction from this curve. If the general S is
Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit
conditions for the existence of a terminal extraction. A treatment of
the D_{2k+1} case should be possible by similar means.
2014年01月21日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
浜向 直 氏 (東大数理)
符号付き距離関数との比較に基づく改良された等高面法 (JAPANESE)
浜向 直 氏 (東大数理)
符号付き距離関数との比較に基づく改良された等高面法 (JAPANESE)
[ 講演概要 ]
等高面法では、各時刻における曲面をある補助関数のゼロ等高面として表示し、
その補助関数に対する偏微分方程式を解くことで曲面の動きを求める。 しかし
時間が経つにつれて解の傾きが小さくなることがあり、 計算機では等高面を取
り出すことが困難となる。 そこで本講演では、方程式を適当に修正すること
で、 ゼロ等高面付近で傾きが小さくならない解が得られることを、 符号付き距
離関数との比較を通して示す。
等高面法では、各時刻における曲面をある補助関数のゼロ等高面として表示し、
その補助関数に対する偏微分方程式を解くことで曲面の動きを求める。 しかし
時間が経つにつれて解の傾きが小さくなることがあり、 計算機では等高面を取
り出すことが困難となる。 そこで本講演では、方程式を適当に修正すること
で、 ゼロ等高面付近で傾きが小さくならない解が得られることを、 符号付き距
離関数との比較を通して示す。
トポロジー火曜セミナー
16:30-17:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)
[ 講演概要 ]
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.
We prove that the Chern class of a closed contact manifold is an
obstruction for codimension two contact embeddings in the odd
dimensional Euclidean space.
By Gromov's h-principle,
for any closed contact $3$-manifold with trivial first Chern class,
there is a contact structure on $\\mathbb{R}^5$ which admits a contact
embedding.
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