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過去の記録
過去の記録 ～04/25｜本日 04/26 | 今後の予定 04/27～
統計数学セミナー
13:00-17:00 数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
2016年01月19日(火)
FMSPレクチャーズ
13:30 -14:30 数理科学研究科棟(駒場) 056号室
全9回講演の(3)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (3) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(3)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (3) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
FMSPレクチャーズ
16:30 -18:00 数理科学研究科棟(駒場) 056号室
全9回講演の(4)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (4) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(4)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (4) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 118号室
戸松玲治 氏 (北大理)
$C^*$テンソル圏入門
戸松玲治 氏 (北大理)
$C^*$テンソル圏入門
トポロジー火曜セミナー
15:00-16:00 数理科学研究科棟(駒場) 056号室
山本 光 氏 (東京大学大学院数理科学研究科)
Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)
山本 光 氏 (東京大学大学院数理科学研究科)
Ricci-mean curvature flows in gradient shrinking Ricci solitons (JAPANESE)
[ 講演概要 ]
A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean
curvature flow and a Ricci flow.
In this talk, we consider a Ricci-mean curvature flow in a gradient
shrinking Ricci soliton, and give a generalization of a well-known result
of Huisken which states that if a mean curvature flow in a Euclidean space
develops a singularity of type I, then its parabolic rescaling near the singular
point converges to a self-shrinker.
A Ricci-mean curvature flow is a coupled parabolic PDE system of a mean
curvature flow and a Ricci flow.
In this talk, we consider a Ricci-mean curvature flow in a gradient
shrinking Ricci soliton, and give a generalization of a well-known result
of Huisken which states that if a mean curvature flow in a Euclidean space
develops a singularity of type I, then its parabolic rescaling near the singular
point converges to a self-shrinker.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Hao Wu 氏 (Fudan University)
Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows
Hao Wu 氏 (Fudan University)
Well-posedness and stability of the full Ericksen-Leslie system for incompressible nematic liquid crystal flows
[ 講演概要 ]
In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.
We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.
In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.
In this talk, the general Ericksen-Leslie (E-L) system modelling the incompressible nematic liquid crystal flow will be discussed.
We shall prove the well-posedness and long-time behavior of the E-L system under proper assumptions on the viscous Leslie coefficients.
In particular, we shall discuss the connection between Parodi's relation and stability of the E-L system.
2016年01月18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
志賀 啓成 氏 (東京工業大学)
Holomorphic motions and the monodromy (Japanese)
志賀 啓成 氏 (東京工業大学)
Holomorphic motions and the monodromy (Japanese)
[ 講演概要 ]
Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.
Holomorphic motions, which was introduced by Mane, Sad and Sullivan, is a useful tool for Teichmuller theory as well as for complex dynamics. In particular, Slodkowski’s theorem makes a significant contribution to them. The theorem says that every holomorphic motion of a closed set on the Riemann sphere parametrized by the unit disk is extended to a holomorphic motion of the whole Riemann sphere parametrized by the unit disk. In this talk, we consider a generalization of the theorem. If time permits, we will discuss applications of our results.
FMSPレクチャーズ
15:00-16:00 数理科学研究科棟(駒場) 056号室
全9回講演の(1)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (1) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(1)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (1) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
FMSPレクチャーズ
16:30-17:30 数理科学研究科棟(駒場) 056号室
全9回講演の(2)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (2) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(2)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (2) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
作用素環セミナー
15:00-17:00 数理科学研究科棟(駒場) 118号室
戸松玲治 氏 (北大理)
$C^*$テンソル圏入門 (日本語)
戸松玲治 氏 (北大理)
$C^*$テンソル圏入門 (日本語)
統計数学セミナー
13:00-17:00 数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
FMSPレクチャーズ
14:00-15:00 数理科学研究科棟(駒場) 126号室
Samuli Siltanen 氏 (University of Helsinki)
Blind deconvolution for human speech signals (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Siltanen.pdf
Samuli Siltanen 氏 (University of Helsinki)
Blind deconvolution for human speech signals (ENGLISH)
[ 講演概要 ]
The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.
[ 参考URL ]The structure of vowel sounds in human speech can be divided into two independent components. One of them is the “excitation signal,” which is a kind of buzzing sound created by the vocal folds flapping against each other. The other is the “filtering effect” caused by resonances in the vocal tract, or the confined space formed by the mouth and throat. The Glottal Inverse Filtering (GIF) problem is to (algorithmically) divide a microphone recording of a vowel sound into its two components. This “blind deconvolution” type task is an ill-posed inverse problem. Good-quality GIF filtering is essential for computer-generated speech needed for example by disabled people (think Stephen Hawking). Also, GIF affects the quality of synthetic speech in automatic information announcements and car navigation systems. Accurate estimation of the voice source from recorded speech is known to be difficult with current glottal inverse filtering (GIF) techniques, especially in the case of high-pitch speech of female or child subjects. In order to tackle this problem, the present study uses two different solution methods for GIF: Bayesian inversion and alternating minimization. The first method takes advantage of the Markov chain Monte Carlo (MCMC) modeling in defining the parameters of the vocal tract inverse filter. The filtering results are found to be superior to those achieved by the standard iterative adaptive inverse filtering (IAIF), but the computation is much slower than IAIF. Alternating minimization cuts down the computation time while retaining most of the quality improvement.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Siltanen.pdf
FMSPレクチャーズ
14:45-15:25 数理科学研究科棟(駒場) 126号室
Tapio Helin 氏 (University of Helsinki)
Inverse scattering from random potential (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Helin.pdf
Tapio Helin 氏 (University of Helsinki)
Inverse scattering from random potential (ENGLISH)
[ 講演概要 ]
We consider an inverse scattering problem with a random potential. We assume that our far-field data at multiple angles and all frequencies are generated by a single realization of the potential. From the frequency-correlated data our aim is to demonstrate that one can recover statistical properties of the potential. More precisely, the potential is assumed to be Gaussian with a covariance operator that can be modelled by a classical pseudodifferential operator. Our main result is to show that the principal symbol of this
covariance operator can be determined uniquely. What is important, our method does not require any approximation and we can analyse also the multiple scattering. This is joint work with Matti Lassas and Pedro Caro.
[ 参考URL ]We consider an inverse scattering problem with a random potential. We assume that our far-field data at multiple angles and all frequencies are generated by a single realization of the potential. From the frequency-correlated data our aim is to demonstrate that one can recover statistical properties of the potential. More precisely, the potential is assumed to be Gaussian with a covariance operator that can be modelled by a classical pseudodifferential operator. Our main result is to show that the principal symbol of this
covariance operator can be determined uniquely. What is important, our method does not require any approximation and we can analyse also the multiple scattering. This is joint work with Matti Lassas and Pedro Caro.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Helin.pdf
FMSPレクチャーズ
15:25-16:05 数理科学研究科棟(駒場) 126号室
Matti Lassas 氏 (University of Helsinki)
Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lassas.pdf
Matti Lassas 氏 (University of Helsinki)
Geometric Whitney problem: Reconstruction of a manifold from a point cloud (ENGLISH)
[ 講演概要 ]
We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.
We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.
Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.
The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.
The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.
References:
[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674
[ 参考URL ]We study the geometric Whitney problem on how a Riemannian manifold $(M,g)$ can be constructed to approximate a metric space $(X,d_X)$. This problem is closely related to manifold interpolation (or manifold learning) where a smooth $n$-dimensional surface $S¥subset {¥mathbb R}^m$, $m>n$ needs to be constructed to approximate a point cloud in ${¥mathbb R}^m$. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric.
We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary.
Moreover, we characterise the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius.
The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalisation of the Whitney embedding construction where approximative coordinate charts are embedded in ${¥mathbb R}^m$ and interpolated to a smooth surface. We also give algorithms that solve the problems for finite data.
The results are done in collaboration with C. Fefferman, S. Ivanov, Y. Kurylev, and H. Narayanan.
References:
[1] C. Fefferman, S. Ivanov, Y. Kurylev, M. Lassas, H. Narayanan: Reconstruction and interpolation of manifolds I: The geometric Whitney problem. ArXiv:1508.00674
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Lassas.pdf
2016年01月15日(金)
統計数学セミナー
13:00-17:00 数理科学研究科棟(駒場) 123号室
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
Enzo Orsingher 氏 (Sapienza University of Rome)
Fractional calculus and some applications to stochastic processes
[ 講演概要 ]
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
1) Riemann-Liouville fractional integrals and derivatives
2) integrals of derivatives and derivatives of integrals
3) Dzerbayshan-Caputo fractional derivatives
4) Marchaud derivative
5) Riesz potential and fractional derivatives
6) Hadamard derivatives and also Erdelyi-Kober derivatives
7) Laplace transforms of Riemann.Liouville and Dzerbayshan-Caputo fractional derivatives
8) Fractional diffusion equations and related special functions (Mittag-Leffler and Wright functions)
9) Fractional telegraph equations (space-time fractional equations and also their mutidimensional versions)
10) Time-fractional telegraph Poisson process
11) Space fractional Poisson process
13) Other fractional point processes (birth and death processes)
14) We shall present the relationship between solutions of wave and Euler-Poisson-Darboux equations through the Erdelyi-Kober integrals.
In these lessons we will introduce the main ideas of the classical fractional calculus. The results and theorems will be presented with all details and calculations. We shall study some fundamental fractional equations and their interplay with stochastic processes. Some details on the iterated Brownian motion will also be given.
2016年01月13日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Alexander Kumjian 氏 (Univ. Nevada, Reno)
A Stabilization Theorem for Fell Bundles over Groupoids
Alexander Kumjian 氏 (Univ. Nevada, Reno)
A Stabilization Theorem for Fell Bundles over Groupoids
FMSPレクチャーズ
16:00-17:30 数理科学研究科棟(駒場) 122号室
Yves Dermenjian 氏 (Aix-Marseille Universite)
A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dermenjian.pdf
Yves Dermenjian 氏 (Aix-Marseille Universite)
A Carleman estimate for an elliptic operator in a partially anisotropic and discontinuous media (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Dermenjian.pdf
2016年01月12日(火)
トポロジー火曜セミナー
16:30-18:30 数理科学研究科棟(駒場) 056号室
川崎 盛通 氏 (東京大学大学院数理科学研究科) 16:30-17:30
重い部分集合と非可縮周期軌道 (JAPANESE)
On codimension two contact embeddings in the standard spheres (JAPANESE)
川崎 盛通 氏 (東京大学大学院数理科学研究科) 16:30-17:30
重い部分集合と非可縮周期軌道 (JAPANESE)
[ 講演概要 ]
ビランとポルテロヴィッチ、サラモンによる研究では、開シンプレクティック多
様体Mとその部分集合$X$, $M$内の自由ホモトピー類αに対する相対的なシンプレクテ
ィック容量$C_{BPS}(M,X,α)$を定義した。
$C_{BPS}(M,X,α)$はM上のハミルトン函数がXで十分大きい値を取る場合にαを代表
する周期軌道が存在するかという問題に関わって定義される。
一方で、エントフとポルテロヴィッチは非交叉配置性の文脈でシンプレクティッ
ク多様体の「重い」部分集合というものを定義している。
本講演ではビラン・ポルテロヴィッチ・サラモン容量$C_{BPS}(M,X,α)$の有限性
(適当な設定下での周期軌道の存在)を重い部分集合を用いて示す方法について解
説する。
これまでの研究では(自由ループの)ホモトピー類αを代表する周期軌道の検出に
は、αを代表する軌道のハミルトン・フレアー理論を用いるのが一般的であった。
重い部分集合は(可縮軌道のハミルトン・フレアー理論の)スペクトル不変量を用
いて定義される概念であるので、今回の手法では可縮軌道のハミルトン・フレア
ー理論を用いて非可縮軌道を検出することになる。
古川 遼 氏 (東京大学大学院数理科学研究科) 17:30-18:30ビランとポルテロヴィッチ、サラモンによる研究では、開シンプレクティック多
様体Mとその部分集合$X$, $M$内の自由ホモトピー類αに対する相対的なシンプレクテ
ィック容量$C_{BPS}(M,X,α)$を定義した。
$C_{BPS}(M,X,α)$はM上のハミルトン函数がXで十分大きい値を取る場合にαを代表
する周期軌道が存在するかという問題に関わって定義される。
一方で、エントフとポルテロヴィッチは非交叉配置性の文脈でシンプレクティッ
ク多様体の「重い」部分集合というものを定義している。
本講演ではビラン・ポルテロヴィッチ・サラモン容量$C_{BPS}(M,X,α)$の有限性
(適当な設定下での周期軌道の存在)を重い部分集合を用いて示す方法について解
説する。
これまでの研究では(自由ループの)ホモトピー類αを代表する周期軌道の検出に
は、αを代表する軌道のハミルトン・フレアー理論を用いるのが一般的であった。
重い部分集合は(可縮軌道のハミルトン・フレアー理論の)スペクトル不変量を用
いて定義される概念であるので、今回の手法では可縮軌道のハミルトン・フレア
ー理論を用いて非可縮軌道を検出することになる。
On codimension two contact embeddings in the standard spheres (JAPANESE)
[ 講演概要 ]
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.
In this talk we consider codimension two contact
embedding problem by using higher dimensional braids.
First, we focus on embeddings of contact $3$-manifolds to the standard $
S^5$ and give some results, for example, any contact structure on $S^3$
can embed so that it is smoothly isotopic to the standard embedding.
These are joint work with John Etnyre. Second, we consider the relative
Euler number of codimension two contact submanifolds and its Seifert
hypersurfaces which is a generalization of the self-linking number of
transverse knots in contact $3$-manifolds. We give a way to calculate
the relative Euler number of certain contact submanifolds obtained by
braids and as an application we give examples of embeddings of one
contact manifold which are isotopic as smooth embeddings but not
isotopic as contact embeddings in higher dimension.
2016年01月09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
田中 仁 氏 (東京大学) 13:30-15:00
The n linear embedding theorem
(日本語)
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain
(日本語)
田中 仁 氏 (東京大学) 13:30-15:00
The n linear embedding theorem
(日本語)
[ 講演概要 ]
実関数論の方法による調和解析の分野において，2進立方体を用いた解析は長い歴史を持ち，豊かな内容を持っています．
しかし，それは単純なモデルを与え，それゆえ実験的な考察のための，もしくは最良の定数を決定するための，補助的なものとしての位置づけのみをこれまで与えられてきたように思われます．
ところが，この分野で基本的かつ重要な作用素の一つである特異積分作用素が，この2進立方体が作る正作用素の族によって，各点において支配されることが発見され，2進立方体を用いた解析はその重要性が再認識されるようになりました．
本講演では，この2進立方体が作る加重付多重正作用素の有界性を保証する「n重線形埋蔵定理」について紹介します．
平田賢太郎 氏 (広島大学) 15:30-17:00実関数論の方法による調和解析の分野において，2進立方体を用いた解析は長い歴史を持ち，豊かな内容を持っています．
しかし，それは単純なモデルを与え，それゆえ実験的な考察のための，もしくは最良の定数を決定するための，補助的なものとしての位置づけのみをこれまで与えられてきたように思われます．
ところが，この分野で基本的かつ重要な作用素の一つである特異積分作用素が，この2進立方体が作る正作用素の族によって，各点において支配されることが発見され，2進立方体を用いた解析はその重要性が再認識されるようになりました．
本講演では，この2進立方体が作る加重付多重正作用素の有界性を保証する「n重線形埋蔵定理」について紹介します．
An improved growth estimate for positive solutions of a semilinear heat equation in a Lipschitz domain
(日本語)
[ 講演概要 ]
2007年にPolacik-Quittner-Soupletは，任意の領域において半線形熱方程式$u_t-\Delta u=u^p$の正値解に対して初期時刻，爆発時刻，領域の境界付近の増大度に関する先験的評価を与えた．
爆発時刻における増大度は最良であるが，初期時刻および領域の境界付近での増大度は最良ではない．
本講演では，調和関数の評価，放物型ポテンシャル論の結果や熱核評価を上手く用いると，$p$が$1$に近い時にはLipschitz領域上の正値解に対してもっと良い評価が得られることを報告する．
2007年にPolacik-Quittner-Soupletは，任意の領域において半線形熱方程式$u_t-\Delta u=u^p$の正値解に対して初期時刻，爆発時刻，領域の境界付近の増大度に関する先験的評価を与えた．
爆発時刻における増大度は最良であるが，初期時刻および領域の境界付近での増大度は最良ではない．
本講演では，調和関数の評価，放物型ポテンシャル論の結果や熱核評価を上手く用いると，$p$が$1$に近い時にはLipschitz領域上の正値解に対してもっと良い評価が得られることを報告する．
2016年01月08日(金)
談話会・数理科学講演会
16:50-17:50 数理科学研究科棟(駒場) 123号室
小木曽啓示 氏 (東京大学大学院数理科学研究科)
Birational geometry through complex dymanics (ENGLISH)
小木曽啓示 氏 (東京大学大学院数理科学研究科)
Birational geometry through complex dymanics (ENGLISH)
[ 講演概要 ]
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so
mpressed.
The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be
observed.
In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:
(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;
(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;
(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus
quotient.
Birational geometry and complex dymanics are rich subjects having
interactions with many branches of mathematics. On the other hand,
though these two subjects share many common interests hidden especially
when one considers group symmetry of manifolds, it seems rather recent
that their rich interations are really notified, perhaps after breaking
through works for surface automorphisms in the view of topological
entropy by Cantat and McMullen early in this century, by which I was so
mpressed.
The notion of entropy of automorphism is a fundamental invariant which
measures how fast two general points spread out fast under iteration. So,
the exisitence of surface automorphism of positive entropy with Siegel
disk due to McMullen was quite surprizing. The entropy also measures, by
the fundamenal theorem of Gromov-Yomdin, the
logarithmic growth of the degree of polarization under iteration. For
instance, the Mordell-Weil group of an elliptic fibration is a very
intersting rich subject in algebraic geometry and number theory, but the
group preserves the fibration so that it might not be so interesting
from dynamical view point. However, if the surface admits two different
elliptic fibrations, which often happens in K3 surfaces of higher Picard
number, then highly non-commutative dynamically rich phenomena can be
observed.
In this talk, I would like to explain the above mentioned phenomena with
a few unexpected applications that I noticed in these years:
(1) Kodaira problem on small deformation of compact Kaehler manifolds in
higher dimension via K3 surface automorphism with Siegel disk;
(2) Geometric liftability problem of automorphisms in positive
characteristic to chacateristic 0 via Mordell-Weil groups and number
theoretic aspect of entropy;
(3) Existence problem on primitive automorphisms of projective manifolds,
through (relative) dynamical degrees due to Dinh-Sibony, Dinh-Nguyen-
Troung, a powerful refinement of the notion of entropy, with by-product
for Ueno-Campana's problem on (uni)rationality of manifolds of torus
quotient.
2016年01月06日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Benoit Collins 氏 (京大理)
Quantum channels from the free orthogonal quantum group (English)
Benoit Collins 氏 (京大理)
Quantum channels from the free orthogonal quantum group (English)
2016年01月05日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
Eric Skibsted 氏 (Aarhus University, Denmark)
Stationary scattering theory on manifolds (English)
Eric Skibsted 氏 (Aarhus University, Denmark)
Stationary scattering theory on manifolds (English)
[ 講演概要 ]
We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).
We present a stationary scattering theory for the Schrödinger operator on Riemannian manifolds with the structure of ends each of which is equipped with an escape function (for example a convex distance function). This includes manifolds with ends modeled as cone-like subsets of the Euclidean space and/or the hyperbolic space. Our results include Rellich’s theorem, the limiting absorption principle, radiation condition bounds, the Sommerfeld uniqueness result, and we give complete characterization/asymptotics of the generalized eigenfunctions in a certain Besov space and show asymptotic completeness (with K. Ito).
2015年12月21日(月)
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
David Croydon 氏 (University of Warwick)
Scaling limits of random walks on trees (English)
David Croydon 氏 (University of Warwick)
Scaling limits of random walks on trees (English)
[ 講演概要 ]
I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.
I will survey some recent work regarding the scaling limits of random walks on trees, as well as the scaling of the associated local times and cover time. The trees considered will include self-similar pre-fractal graphs, critical Galton-Watson trees and the uniform spanning tree in two dimensions.
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
山ノ井 克俊 氏 (大阪大学)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
山ノ井 克俊 氏 (大阪大学)
On pseudo Kobayashi hyperbolicity of subvarieties of abelian varieties
(Japanese)
[ 講演概要 ]
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
A subvariety of an abelian variety is of general type if and only if it is pseudo Kobayashi hyperbolic. I will discuss the proof of this result.
2015年12月17日(木)
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
このセミナーは講演者が急病のためキャンセルになりました。This seminer is canceled due to the speaker 's sick.
Dulip Piyaratne 氏 (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
http://db.ipmu.jp/member/personal/3989en.html
このセミナーは講演者が急病のためキャンセルになりました。This seminer is canceled due to the speaker 's sick.
Dulip Piyaratne 氏 (IPMU)
Polarization and stability on a derived equivalent abelian variety (English)
[ 講演概要 ]
In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
[ 参考URL ]In this talk I will explain how one can define a polarization on a derived equivalent abelian variety by using Fourier-Mukai theory. Furthermore, we see how such a realisations is connected with stability conditions on their derived categories. Then I will discuss these ideas for abelian surfaces and abelian 3-folds in detail.
http://db.ipmu.jp/member/personal/3989en.html
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