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過去の記録
過去の記録 ～07/02｜本日 07/03 | 今後の予定 07/04～
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
このセミナーは悪天候の影響によりキャンセルになりました。
小櫃 邦夫 氏 (鹿児島大学)
Weil-Petersson 計量の漸近解析についての最近の進展 (Japanese)
このセミナーは悪天候の影響によりキャンセルになりました。
小櫃 邦夫 氏 (鹿児島大学)
Weil-Petersson 計量の漸近解析についての最近の進展 (Japanese)
[ 講演概要 ]
リーマン面のモジュライ空間上のWeil-Petersson 計量の境界における漸近展開は、H. Masurが1976年に与えた結果を初めとし、その後Yamada, Wolpert, Obitsu-Wolpert によって改良された。最近、Melrose, X. Zhu, Mazzeo, Swoboda により、その漸近展開の形が完全に決定された。彼らの仕事を紹介し、残された問題や関連する話題について解説する。
リーマン面のモジュライ空間上のWeil-Petersson 計量の境界における漸近展開は、H. Masurが1976年に与えた結果を初めとし、その後Yamada, Wolpert, Obitsu-Wolpert によって改良された。最近、Melrose, X. Zhu, Mazzeo, Swoboda により、その漸近展開の形が完全に決定された。彼らの仕事を紹介し、残された問題や関連する話題について解説する。
2016年01月22日(金)
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(8)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏 (ENGLISH)
Functor categories and stable homology of groups (8) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(8)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏 (ENGLISH)
Functor categories and stable homology of groups (8) (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(9)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (9) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(9)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (9) (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
2016年01月21日(木)
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(6)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (6) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(6)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (6) (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(7)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (7) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(7)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (7) (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
2016年01月20日(水)
FMSPレクチャーズ
16:00-18:00 数理科学研究科棟(駒場) 056号室
全9回講演の(5)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (5) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Djament%26Vespa.pdf
全9回講演の(5)
Aurelien Djament (Nantes/CNRS)氏(by video conference system) and Christine Vespa (Strasbourg) 氏
Functor categories and stable homology of groups (5) (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
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,dX). 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,dX). 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
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