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過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
2012年11月12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
安武 和範 氏 (九州大学大学院数理学研究院)
On Fano fourfolds with nef vector bundles $Λ^2T_X$ (JAPANESE)
安武 和範 氏 (九州大学大学院数理学研究院)
On Fano fourfolds with nef vector bundles $Λ^2T_X$ (JAPANESE)
[ 講演概要 ]
By using results about extremal contractions on smooth fourfolds, we give a classification of fano fourfolds whose the second exterior power of tangent bundles are numerically effective.
By using results about extremal contractions on smooth fourfolds, we give a classification of fano fourfolds whose the second exterior power of tangent bundles are numerically effective.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
A.G. Aleksandrov 氏 (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
A.G. Aleksandrov 氏 (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
[ 講演概要 ]
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.
2012年11月10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.
松山 登喜夫 氏 (中央大学) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
Spectral stability of the p-Laplacian (JAPANESE)
このセミナーは,月に1度程度,不定期に開催されます.
松山 登喜夫 氏 (中央大学) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
[ 講演概要 ]
In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
杉本 充 氏 (名古屋大学) 14:40-16:00In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
[ 講演概要 ]
Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for slutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Victor I. Burenkov 氏 (Russia/United Kingdom) 16:30-17:50Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for slutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Spectral stability of the p-Laplacian (JAPANESE)
[ 講演概要 ]
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).
References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).
References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.
2012年11月09日(金)
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
廣瀬 慧 氏 (大阪大学大学院基礎工学研究科)
Tuning parameter selection in sparse regression modeling (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
廣瀬 慧 氏 (大阪大学大学院基礎工学研究科)
Tuning parameter selection in sparse regression modeling (JAPANESE)
[ 講演概要 ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ 参考URL ]In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
2012年11月07日(水)
古典解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
岩木耕平 氏 (京都大学)
パンルヴェ函数のWKB解析とパラメトリックStokes現象 (JAPANESE)
岩木耕平 氏 (京都大学)
パンルヴェ函数のWKB解析とパラメトリックStokes現象 (JAPANESE)
[ 講演概要 ]
パンルヴェ函数の漸近挙動の研究、および接続問題は、他分野への応用という観点からも非常に重要なテーマである。今回は(2階の古典的な)パンルヴェ方程式を完全WKB解析の立場から考察する。特に、方程式に含まれる「独立変数以外のパラメータ」の値を変化させた際にもある種のStokes現象(パラメトリックStokes現象)が起こることを紹介し、漸近挙動の不連続な変化を記述する接続公式を導く。
パンルヴェ函数の漸近挙動の研究、および接続問題は、他分野への応用という観点からも非常に重要なテーマである。今回は(2階の古典的な)パンルヴェ方程式を完全WKB解析の立場から考察する。特に、方程式に含まれる「独立変数以外のパラメータ」の値を変化させた際にもある種のStokes現象(パラメトリックStokes現象)が起こることを紹介し、漸近挙動の不連続な変化を記述する接続公式を導く。
2012年11月06日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
古庄 英和 氏 (名古屋大学多元数理科学研究科)
結び目へのガロア作用 (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
古庄 英和 氏 (名古屋大学多元数理科学研究科)
結び目へのガロア作用 (JAPANESE)
[ 講演概要 ]
結び目に定まるモティーフの構造について説明する。
その後、有理数体の絶対ガロア群が'結び目全体が張る空間'に
非自明な方法で非自明に作用することを説明する。
結び目に定まるモティーフの構造について説明する。
その後、有理数体の絶対ガロア群が'結び目全体が張る空間'に
非自明な方法で非自明に作用することを説明する。
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
Thierry Ramond 氏 (Univ. Paris, Orsay)
Resonance free domains for homoclinic orbits (ENGLISH)
Thierry Ramond 氏 (Univ. Paris, Orsay)
Resonance free domains for homoclinic orbits (ENGLISH)
Lie群論・表現論セミナー
16:30-17:30 数理科学研究科棟(駒場) 126号室
奥田隆幸 氏 (東京大学)
An explicit construction of spherical designs on S^3 (JAPANESE)
奥田隆幸 氏 (東京大学)
An explicit construction of spherical designs on S^3 (JAPANESE)
[ 講演概要 ]
The existence of spherical t-designs on S^d for any t and d are proved by Seymour--Zaslavsky in 1984.
However, explicit constructions of spherical designs were not known for d > 2 and large t.
In this talk, for a given spherical t-design Y on S^2, we give an
algorithm to make a spherical 2t-design X on S^3 which maps Y by a Hopf map. In particular, by combining with the results of Kuperberg in 2005, we have an explicit construction of spherical t-designs on S^3 for any t.
The existence of spherical t-designs on S^d for any t and d are proved by Seymour--Zaslavsky in 1984.
However, explicit constructions of spherical designs were not known for d > 2 and large t.
In this talk, for a given spherical t-design Y on S^2, we give an
algorithm to make a spherical 2t-design X on S^3 which maps Y by a Hopf map. In particular, by combining with the results of Kuperberg in 2005, we have an explicit construction of spherical t-designs on S^3 for any t.
2012年11月05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
馬 昭平 氏 (名古屋大学多元数理科学研究科)
トリゴナル曲線のモジュライの有理性 (JAPANESE)
馬 昭平 氏 (名古屋大学多元数理科学研究科)
トリゴナル曲線のモジュライの有理性 (JAPANESE)
[ 講演概要 ]
射影直線を3対1で被覆するような曲線はトリゴナル曲線と呼ばれ、超楕円曲線に次いで特殊な曲線である。Shepherd-Barron氏は種数が4で割って2余る場合にトリゴナル曲線のモジュライ空間が射影空間と双有理同型であることを証明した。本講演ではその結果を全ての種数に拡張する。
射影直線を3対1で被覆するような曲線はトリゴナル曲線と呼ばれ、超楕円曲線に次いで特殊な曲線である。Shepherd-Barron氏は種数が4で割って2余る場合にトリゴナル曲線のモジュライ空間が射影空間と双有理同型であることを証明した。本講演ではその結果を全ての種数に拡張する。
2012年10月31日(水)
幾何コロキウム
10:30-12:00 数理科学研究科棟(駒場) 128号室
入江慶 氏 (京都大学)
Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits (JAPANESE)
入江慶 氏 (京都大学)
Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits (JAPANESE)
[ 講演概要 ]
Hofer-Zehnder (HZ) capacity is an invariant of symplectic manifolds, which is important in symplectic topology and Hamiltonian dynamics. The energy-capacity inequality (due to Hofer and many others) claims that HZ capacity of a domain is bounded from above by its dispalcement energy.
In this talk, we prove a variant of this inequality, which is applicable to nondisplaceable domains. We also give some applications, including case of disc cotangent bundles.
Hofer-Zehnder (HZ) capacity is an invariant of symplectic manifolds, which is important in symplectic topology and Hamiltonian dynamics. The energy-capacity inequality (due to Hofer and many others) claims that HZ capacity of a domain is bounded from above by its dispalcement energy.
In this talk, we prove a variant of this inequality, which is applicable to nondisplaceable domains. We also give some applications, including case of disc cotangent bundles.
2012年10月30日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
川中子正 氏 (東京工業大学大学院理工学研究科)
半線形偏微分方程式に対するガレルキン法の誤差解析 (JAPANESE)
http://www.infsup.jp/utnas/
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
川中子正 氏 (東京工業大学大学院理工学研究科)
半線形偏微分方程式に対するガレルキン法の誤差解析 (JAPANESE)
[ 講演概要 ]
半線形偏微分方程式への応用を目的として、ヒルベルト空間上の抽象的非線形方程式に対するガレルキン近似解の存在および誤差解析に関する結果を紹介する。誤差解析に関する主な結果は次のようである:
真の解とガレルキン近似解との誤差は、ガレルキン近似解の残差と同位の無限小である。
真の解のガレルキン近似部分空間への直交射影とガレルキン近似解との誤差は、 真の解とガレルキン近似解との誤差より高位の無限小であり、また、前者の有用な減衰評価式を紹介する。
上述の結果は、半線形偏微分方程式の解の数値的検証アルゴリズムの品質を調べることに応用できる。
[ 参考URL ]半線形偏微分方程式への応用を目的として、ヒルベルト空間上の抽象的非線形方程式に対するガレルキン近似解の存在および誤差解析に関する結果を紹介する。誤差解析に関する主な結果は次のようである:
真の解とガレルキン近似解との誤差は、ガレルキン近似解の残差と同位の無限小である。
真の解のガレルキン近似部分空間への直交射影とガレルキン近似解との誤差は、 真の解とガレルキン近似解との誤差より高位の無限小であり、また、前者の有用な減衰評価式を紹介する。
上述の結果は、半線形偏微分方程式の解の数値的検証アルゴリズムの品質を調べることに応用できる。
http://www.infsup.jp/utnas/
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Tea: 16:00 - 16:30 コモンルーム
下川 航也 氏 (埼玉大学大学院理工学研究科)
Applications of knot theory to molecular biology (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
下川 航也 氏 (埼玉大学大学院理工学研究科)
Applications of knot theory to molecular biology (JAPANESE)
[ 講演概要 ]
In this talk we discuss applications of knot theory to studies of DNA
and proteins.
Especially we will consider (1)topological characterization of
mechanisms of site-specific recombination systems,
(2)modeling knotted DNA and proteins in confined regions using lattice
knots, and
(3)mechanism of topoisomerases and signed crossing changes.
In this talk we discuss applications of knot theory to studies of DNA
and proteins.
Especially we will consider (1)topological characterization of
mechanisms of site-specific recombination systems,
(2)modeling knotted DNA and proteins in confined regions using lattice
knots, and
(3)mechanism of topoisomerases and signed crossing changes.
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
Francis Nier 氏 (Univ. Rennes 1)
About the method of characteristics (ENGLISH)
Francis Nier 氏 (Univ. Rennes 1)
About the method of characteristics (ENGLISH)
[ 講演概要 ]
While studying the mean field dynamics of a systems of bosons, one is led to solve a transport equation for a probability measure in an infinite dimensional phase-space. Since those probability measures are characterized after testing with cylindrical or polynomial observables, which make classes which are not invariant after composing with a nonlinear flow. Thus the standard method of characteristics for transport equations cannot be extended at once to the infinite dimensional case. A solution comes from techniques developed for optimal transport and a probabilistic interpretation of trajectories.
While studying the mean field dynamics of a systems of bosons, one is led to solve a transport equation for a probability measure in an infinite dimensional phase-space. Since those probability measures are characterized after testing with cylindrical or polynomial observables, which make classes which are not invariant after composing with a nonlinear flow. Thus the standard method of characteristics for transport equations cannot be extended at once to the infinite dimensional case. A solution comes from techniques developed for optimal transport and a probabilistic interpretation of trajectories.
講演会
17:00-18:00 数理科学研究科棟(駒場) 470号室
Frank Lutz 氏 (ベルリン工科大学)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
Frank Lutz 氏 (ベルリン工科大学)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
[ 講演概要 ]
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).
For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct ``complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
``complicatedness'' of complexes.
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).
For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct ``complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
``complicatedness'' of complexes.
2012年10月29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)
The Mukai conjecture for log Fano manifolds (JAPANESE)
藤田 健人 氏 (京都大学数理解析研究所)
The Mukai conjecture for log Fano manifolds (JAPANESE)
[ 講演概要 ]
The concept of log Fano manifolds is one of the most natural generalization of the concept of Fano manifolds. We will give some structure theorems of log Fano manifolds. For example, we will show that the Mukai conjecture for Fano manifolds implies the `log Mukai conjecture' for log Fano manifolds.
The concept of log Fano manifolds is one of the most natural generalization of the concept of Fano manifolds. We will give some structure theorems of log Fano manifolds. For example, we will show that the Mukai conjecture for Fano manifolds implies the `log Mukai conjecture' for log Fano manifolds.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
厚地淳 氏 (慶応大学)
葉層構造を持つ多様体上の有理型関数の値分布, II (JAPANESE)
厚地淳 氏 (慶応大学)
葉層構造を持つ多様体上の有理型関数の値分布, II (JAPANESE)
2012年10月26日(金)
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
廣瀬 慧 氏 (大阪大学大学院基礎工学研究科)
Tuning parameter selection in sparse regression modeling (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
廣瀬 慧 氏 (大阪大学大学院基礎工学研究科)
Tuning parameter selection in sparse regression modeling (JAPANESE)
[ 講演概要 ]
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
[ 参考URL ]In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html
2012年10月23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) 002号室
Elliott Lieb 氏 (Princeton Univ.)
Topics in quantum entropy and entanglement (ENGLISH)
Elliott Lieb 氏 (Princeton Univ.)
Topics in quantum entropy and entanglement (ENGLISH)
[ 講演概要 ]
Several recent results on quantum entropy and the uncertainty
principle will be discussed. This is partly joint work with Eric Carlen
on lower bounds for entanglement, which has no classical analog, in terms
of the negative of the conditional entropy, S1 - S12, whose negativity,
when it occurs, also has no classical analog. (see arXiv:1203.4719)
It is also partly joint work with Rupert Frank on the uncertaintly
principle for quantum entropy which compares the quantum von Neumann
entropy with the classical entropies with respect to two different
bases. We prove an extension to the product of two and three spaces, which
has applications in quantum information theory. (see arxiv:1204.0825)
Several recent results on quantum entropy and the uncertainty
principle will be discussed. This is partly joint work with Eric Carlen
on lower bounds for entanglement, which has no classical analog, in terms
of the negative of the conditional entropy, S1 - S12, whose negativity,
when it occurs, also has no classical analog. (see arXiv:1203.4719)
It is also partly joint work with Rupert Frank on the uncertaintly
principle for quantum entropy which compares the quantum von Neumann
entropy with the classical entropies with respect to two different
bases. We prove an extension to the product of two and three spaces, which
has applications in quantum information theory. (see arxiv:1204.0825)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
河澄 響矢 氏 (東京大学大学院数理科学研究科)
A geometric approach to the Johnson homomorphisms (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
河澄 響矢 氏 (東京大学大学院数理科学研究科)
A geometric approach to the Johnson homomorphisms (JAPANESE)
[ 講演概要 ]
ジョンソン準同型を、完備化されたゴールドマン・トゥラエフ・リー双代数への
トレリ群の
埋め込みとして捉え直す。その際、ジョンソン準同型像はトゥラエフ余括弧積の
核に含まれる。
境界成分が1の場合、このことから森田トレースの幾何的な意味が明らかになる。
時間が許せば、穴あき円板の場合についても議論する。
ジョンソン準同型を、完備化されたゴールドマン・トゥラエフ・リー双代数への
トレリ群の
埋め込みとして捉え直す。その際、ジョンソン準同型像はトゥラエフ余括弧積の
核に含まれる。
境界成分が1の場合、このことから森田トレースの幾何的な意味が明らかになる。
時間が許せば、穴あき円板の場合についても議論する。
2012年10月22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) 126号室
千葉優作 氏 (東大数理)
ヒルベルトモジュラー曲面への整曲線に対する第2主要定理 (JAPANESE)
千葉優作 氏 (東大数理)
ヒルベルトモジュラー曲面への整曲線に対する第2主要定理 (JAPANESE)
2012年10月19日(金)
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
清水 泰隆 氏 (大阪大学大学院基礎工学研究科)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
清水 泰隆 氏 (大阪大学大学院基礎工学研究科)
Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)
[ 講演概要 ]
An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.
[ 参考URL ]An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks
is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of
the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.
This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html
2012年10月18日(木)
統計数学セミナー
15:15-16:25 数理科学研究科棟(駒場) 006号室
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
加藤 賢悟 氏 (広島大学大学院理学研究科数学専攻)
Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html
参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
加藤 賢悟 氏 (広島大学大学院理学研究科数学専攻)
Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)
[ 講演概要 ]
This paper aims at developing a quasi-Bayesian analysis
of the nonparametric instrumental variables model, with a focus on the
asymptotic properties of quasi-posterior distributions. In this paper,
instead of assuming a distributional assumption on the data generating
process, we consider a quasi-likelihood induced from the conditional
moment restriction, and put priors on the function-valued parameter.
We call the resulting posterior quasi-posterior, which corresponds to
``Gibbs posterior'' in the literature. Here we shall focus on sieve
priors, which are priors that concentrate on finite dimensional sieve
spaces. The dimension of the sieve space should increase as the sample
size. We derive rates of contraction and a non-parametric Bernstein-von
Mises type result for the quasi-posterior distribution, and rates of
convergence for the quasi-Bayes estimator defined by the posterior
expectation. We show that, with priors suitably chosen, the
quasi-posterior distribution (the quasi-Bayes estimator) attains the
minimax optimal rate of contraction (convergence, respectively). These
results greatly sharpen the previous related work.
[ 参考URL ]This paper aims at developing a quasi-Bayesian analysis
of the nonparametric instrumental variables model, with a focus on the
asymptotic properties of quasi-posterior distributions. In this paper,
instead of assuming a distributional assumption on the data generating
process, we consider a quasi-likelihood induced from the conditional
moment restriction, and put priors on the function-valued parameter.
We call the resulting posterior quasi-posterior, which corresponds to
``Gibbs posterior'' in the literature. Here we shall focus on sieve
priors, which are priors that concentrate on finite dimensional sieve
spaces. The dimension of the sieve space should increase as the sample
size. We derive rates of contraction and a non-parametric Bernstein-von
Mises type result for the quasi-posterior distribution, and rates of
convergence for the quasi-Bayes estimator defined by the posterior
expectation. We show that, with priors suitably chosen, the
quasi-posterior distribution (the quasi-Bayes estimator) attains the
minimax optimal rate of contraction (convergence, respectively). These
results greatly sharpen the previous related work.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html
講演会
16:00-17:00 数理科学研究科棟(駒場) 470号室
Anatoly Yagola 氏 (Lomonosov Moscow State University)
Multidimensional ill-posed problems (ENGLISH)
Anatoly Yagola 氏 (Lomonosov Moscow State University)
Multidimensional ill-posed problems (ENGLISH)
[ 講演概要 ]
It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.
We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].
Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral
equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].
2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.
This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.
It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.
We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].
Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral
equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].
2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.
This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.
2012年10月17日(水)
幾何コロキウム
10:30-12:00 数理科学研究科棟(駒場) 128号室
見村万佐人 氏 (東北大学)
p-カジュダン定数と非エクスパンダー族 (JAPANESE)
見村万佐人 氏 (東北大学)
p-カジュダン定数と非エクスパンダー族 (JAPANESE)
[ 講演概要 ]
グラフや有限生成群(ケーリーグラフと思う)に道距離を入れて距離空間と思って研究をするとき,基本的な指針の一つが"線型化"することである.より正確には,性質の良いバナッハ空間への良い埋め込みを考えることである.特にヒルベルト空間や一般のl^p空間への埋め込みは大変研究されている.有名な結果として,"エクスパンダー族"がヒルベルト空間やl^p空間に一様埋め込みをもたない,ことが挙げられる.ここで,エクスパンダー族とは,次数が一様有限な有限グラフの族であって,各グラフのスペクトルギャップが下から一様におさえられているようなものである(この条件は,各グラフのチーガー定数が下から一様におさえられていることと同値である).
今回の講演では,有限生成群の族のケーリーグラフから作られるような,"非"エクスパンダー族についての研究をお話しする.有限生成群に対してヒルベルト空間上の表現からカジュダン定数や性質tauに関する定数というものが定義され,ケーリーグラフのスペクトルギャップと関連する.本講演ではl^p空間での一般化を定義し,それらを用いて,上記の設定でのグラフの族のp-スペクトルギャップの減衰の状況を記述する.これにより,上記のグラフの族の距離幾何的な情報を取り出す.主な例は,3以上の整数で番号付けされた群の族(SL_n(Z/k_nZ))_nのケーリーグラフたちである.ここで(k_n)はk_n>2なる整数たちの列であり,ケーリーグラフは各nに対して,標準的な4元からなる生成集合から構成する.この講演は,"ケーリーグラフ"・"エクスパンダー族"・"カジュダン定数"のような基本的な定義から始める予定である.
グラフや有限生成群(ケーリーグラフと思う)に道距離を入れて距離空間と思って研究をするとき,基本的な指針の一つが"線型化"することである.より正確には,性質の良いバナッハ空間への良い埋め込みを考えることである.特にヒルベルト空間や一般のl^p空間への埋め込みは大変研究されている.有名な結果として,"エクスパンダー族"がヒルベルト空間やl^p空間に一様埋め込みをもたない,ことが挙げられる.ここで,エクスパンダー族とは,次数が一様有限な有限グラフの族であって,各グラフのスペクトルギャップが下から一様におさえられているようなものである(この条件は,各グラフのチーガー定数が下から一様におさえられていることと同値である).
今回の講演では,有限生成群の族のケーリーグラフから作られるような,"非"エクスパンダー族についての研究をお話しする.有限生成群に対してヒルベルト空間上の表現からカジュダン定数や性質tauに関する定数というものが定義され,ケーリーグラフのスペクトルギャップと関連する.本講演ではl^p空間での一般化を定義し,それらを用いて,上記の設定でのグラフの族のp-スペクトルギャップの減衰の状況を記述する.これにより,上記のグラフの族の距離幾何的な情報を取り出す.主な例は,3以上の整数で番号付けされた群の族(SL_n(Z/k_nZ))_nのケーリーグラフたちである.ここで(k_n)はk_n>2なる整数たちの列であり,ケーリーグラフは各nに対して,標準的な4元からなる生成集合から構成する.この講演は,"ケーリーグラフ"・"エクスパンダー族"・"カジュダン定数"のような基本的な定義から始める予定である.
講演会
15:00-16:00 数理科学研究科棟(駒場) 370号室
Vjacheslav Yurko 氏 (Saratov University)
Inverse problems for differential operators on spatial networks (ENGLISH)
Vjacheslav Yurko 氏 (Saratov University)
Inverse problems for differential operators on spatial networks (ENGLISH)
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