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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 126号室
白石 友一 氏 (統計数理研究所)
二値判別機の組合せによる多値判別問題へのゲーム理論的アプローチ
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html
白石 友一 氏 (統計数理研究所)
二値判別機の組合せによる多値判別問題へのゲーム理論的アプローチ
[ 講演概要 ]
多値判別という学習理論の問題に対して、ゲーム理論的なアプローチを試みた結果についてお話したいと思います。多値判別問題を解くために実用的に広く用いられている方法に、2値判別機を組み合わせる方法があります。その際に2値判別機の出力結果に誤り訂正符号のモデルを仮定し、MAP推定により出力を決める方法が一般的です。本発表では2値判別機の組合せによる多値判別の問題を、「決定者」と「自然」のゲームとして捉え、既存の手法の解析や新しい手法の提案を行います。まず、多値判別問題における、誤り訂正符号による方法がミニマックスとなるための条件をネットワークフローにより表します。そして、one-vs-oneやone-vs-allなどの方法が自然な条件下でミニマックス戦略となることを検証します。次に、誤り訂正符号による方法に拡張を加え、「自然」の範囲をデータからある程度特定したときのミニマックス戦略を求める方法を提案し、これを2次錐計画法により定式化します。またミニマックス定理やエントロピーなどとの関連についての考察を行います。キーワードとしては
・判別問題(特にクラス数が3以上の多値判別問題)
・誤り訂正符号
・ゲーム理論
・最適化理論(線形計画法、2次錐計画法)
・ネットワークフロー理論
・フォン=ノイマンのミニマックス定理
などが挙げられると思います。
[ 参考URL ]多値判別という学習理論の問題に対して、ゲーム理論的なアプローチを試みた結果についてお話したいと思います。多値判別問題を解くために実用的に広く用いられている方法に、2値判別機を組み合わせる方法があります。その際に2値判別機の出力結果に誤り訂正符号のモデルを仮定し、MAP推定により出力を決める方法が一般的です。本発表では2値判別機の組合せによる多値判別の問題を、「決定者」と「自然」のゲームとして捉え、既存の手法の解析や新しい手法の提案を行います。まず、多値判別問題における、誤り訂正符号による方法がミニマックスとなるための条件をネットワークフローにより表します。そして、one-vs-oneやone-vs-allなどの方法が自然な条件下でミニマックス戦略となることを検証します。次に、誤り訂正符号による方法に拡張を加え、「自然」の範囲をデータからある程度特定したときのミニマックス戦略を求める方法を提案し、これを2次錐計画法により定式化します。またミニマックス定理やエントロピーなどとの関連についての考察を行います。キーワードとしては
・判別問題(特にクラス数が3以上の多値判別問題)
・誤り訂正符号
・ゲーム理論
・最適化理論(線形計画法、2次錐計画法)
・ネットワークフロー理論
・フォン=ノイマンのミニマックス定理
などが挙げられると思います。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 056号室
Motohico Mulase 氏 (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
Motohico Mulase 氏 (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
[ 講演概要 ]
In this talk I will give a survey of recent developments in the intersection theory of tautological classes on the moduli spaces of stable algebraic curves. The emphasis is placed on explaining where the Virasoro constraint conditions are originated. Recently several authors have encountered the same combinatorial recursion relation from completely different contexts, that eventually leads to the Virasoro constraint. This mysterious structure of the theory will be surveyed.
In this talk I will give a survey of recent developments in the intersection theory of tautological classes on the moduli spaces of stable algebraic curves. The emphasis is placed on explaining where the Virasoro constraint conditions are originated. Recently several authors have encountered the same combinatorial recursion relation from completely different contexts, that eventually leads to the Virasoro constraint. This mysterious structure of the theory will be surveyed.
2008年04月22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
Sergey Yuzvinsky 氏 (University of Oregon)
Special fibers of pencils of hypersurfaces
Tea: 16:00 - 16:30 コモンルーム
Sergey Yuzvinsky 氏 (University of Oregon)
Special fibers of pencils of hypersurfaces
[ 講演概要 ]
We consider pencils of hypersurfaces of degree $d>1$ in the complex
$n$-dimensional projective space subject to the condition that the
generic fiber is irreducible. We study the set of completely reducible
fibers, i.e., the unions of hyperplanes. The first surprinsing result is
that the cardinality of thie set has very strict uniformed upper bound
(not depending on $d$ or $n$). The other one gives a characterization
of this set in terms of either topology of its complement or combinatorics
of hyperplanes. We also include into consideration more general special
fibers are iimportant for characteristic varieties of the hyperplane
complements.
We consider pencils of hypersurfaces of degree $d>1$ in the complex
$n$-dimensional projective space subject to the condition that the
generic fiber is irreducible. We study the set of completely reducible
fibers, i.e., the unions of hyperplanes. The first surprinsing result is
that the cardinality of thie set has very strict uniformed upper bound
(not depending on $d$ or $n$). The other one gives a characterization
of this set in terms of either topology of its complement or combinatorics
of hyperplanes. We also include into consideration more general special
fibers are iimportant for characteristic varieties of the hyperplane
complements.
2008年04月21日(月)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
高木寛通 氏 (東大数理)
Scorza quartics of trigonal spin curves and their varieties of power sums
高木寛通 氏 (東大数理)
Scorza quartics of trigonal spin curves and their varieties of power sums
[ 講演概要 ]
Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.
Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.
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
平地 健吾 氏 (東大数理)
Ambient realization of conformal jets and deformation complex
平地 健吾 氏 (東大数理)
Ambient realization of conformal jets and deformation complex
2008年04月17日(木)
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 126号室
中野 張 氏 (科学技術振興機構)
動的なリスク分散による保険料計算原理について
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html
中野 張 氏 (科学技術振興機構)
動的なリスク分散による保険料計算原理について
[ 講演概要 ]
生命保険や銀行貸付け等の長期の商品に対しては、
時間依存の安全割増によるリスク評価を行うことが求められる。
今回の発表では、効用関数の畳み込みにより生成される動的リスク尺度によるアプローチを紹介する。
[ 参考URL ]生命保険や銀行貸付け等の長期の商品に対しては、
時間依存の安全割増によるリスク評価を行うことが求められる。
今回の発表では、効用関数の畳み込みにより生成される動的リスク尺度によるアプローチを紹介する。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
小沢登高 氏 (東大数理)
On a class of II$_1$ factors with at most one Cartan subalgebra II
小沢登高 氏 (東大数理)
On a class of II$_1$ factors with at most one Cartan subalgebra II
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
WEISS Georg 氏 (東京大学大学院数理科学研究科)
Hidden dynamics and pulsating waves in self-propagating high temperature synthesis
WEISS Georg 氏 (東京大学大学院数理科学研究科)
Hidden dynamics and pulsating waves in self-propagating high temperature synthesis
[ 講演概要 ]
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.
In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.
In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).
2008年04月15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
村上 順 氏 (早稲田大学理工)
On the invariants of knots and 3-manifolds related to the restricted quantum group
Tea: 16:00 - 16:30 コモンルーム
村上 順 氏 (早稲田大学理工)
On the invariants of knots and 3-manifolds related to the restricted quantum group
[ 講演概要 ]
I would like to talk about the colored Alexander invariant and the logarithmic
invariant of knots and links. They are constructed from the universal R-matrices
of the semi-resetricted and restricted quantum groups of sl(2) respectively,
and they are related to the hyperbolic volumes of the cone manifolds along
the knot. I also would like to explain an attempt to generalize these invariants to
a three manifold invariant which relates to the volume of the manifold actually.
I would like to talk about the colored Alexander invariant and the logarithmic
invariant of knots and links. They are constructed from the universal R-matrices
of the semi-resetricted and restricted quantum groups of sl(2) respectively,
and they are related to the hyperbolic volumes of the cone manifolds along
the knot. I also would like to explain an attempt to generalize these invariants to
a three manifold invariant which relates to the volume of the manifold actually.
2008年04月14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
佐野 友二 氏 (東大IPMU)
トーリック・ファノ多様体のマルチプライア・イデアル層と二木不変量の関係について
佐野 友二 氏 (東大IPMU)
トーリック・ファノ多様体のマルチプライア・イデアル層と二木不変量の関係について
2008年04月08日(火)
Kavli IPMU Komaba Seminar
10:30-12:00 数理科学研究科棟(駒場) 002号室
Akihiro Tsuchiya 氏 (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)
Akihiro Tsuchiya 氏 (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)
[ 講演概要 ]
Tuesday, April -- July, 2008
First Lecture Aprl 8
Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.
(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres
The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra
Tuesday, April -- July, 2008
First Lecture Aprl 8
Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.
(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres
The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra
2008年03月19日(水)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Juergen Saal 氏 (Department of Mathematics and Statistics, University of Konstanz)
Maximal Regularity for Mixed Order Systems
Juergen Saal 氏 (Department of Mathematics and Statistics, University of Konstanz)
Maximal Regularity for Mixed Order Systems
[ 講演概要 ]
In classical boundary value problems the related symbols are homogeneous in space and time. This allows for the application of a standard compactness argument in order to obtain the important maximal regularity. However, quasilinear systems arising e.g. from free boundary problems are in general of mixed order. In other words the related symbols are of intricate structure and in particular highly inhomogeneous. Therefore, the standard compactness argument fails. The purpose of this talk is to introduce the Newton polygon method, which gives a systematic approach to such mixed order systems and to demonstrate its strength by applications to the Stefan problem and a free boundary problem for the Navier-Stokes equations.
In classical boundary value problems the related symbols are homogeneous in space and time. This allows for the application of a standard compactness argument in order to obtain the important maximal regularity. However, quasilinear systems arising e.g. from free boundary problems are in general of mixed order. In other words the related symbols are of intricate structure and in particular highly inhomogeneous. Therefore, the standard compactness argument fails. The purpose of this talk is to introduce the Newton polygon method, which gives a systematic approach to such mixed order systems and to demonstrate its strength by applications to the Stefan problem and a free boundary problem for the Navier-Stokes equations.
2008年03月14日(金)
代数幾何学セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
David Morrison 氏 (UC Santa Barbara)
Understanding singular algebraic varieties via string theory
David Morrison 氏 (UC Santa Barbara)
Understanding singular algebraic varieties via string theory
[ 講演概要 ]
String theory has helped to formulate two major new insights in the study of singular algebraic varieties. The first -- which also arose from symplectic geometry -- is that families of Kaehler metrics are an important tool in uncovering the structure of singular algebraic varieties. The second, more recent insight -- related to independent work in the representation theory of associative algebras -- is that one's understanding of a singular (affine) algebraic variety is enhanced if one can find a non-commutative ring whose center is the coordinate ring of the variety. We will describe both of these insights, and explain how they are related to string theory.
String theory has helped to formulate two major new insights in the study of singular algebraic varieties. The first -- which also arose from symplectic geometry -- is that families of Kaehler metrics are an important tool in uncovering the structure of singular algebraic varieties. The second, more recent insight -- related to independent work in the representation theory of associative algebras -- is that one's understanding of a singular (affine) algebraic variety is enhanced if one can find a non-commutative ring whose center is the coordinate ring of the variety. We will describe both of these insights, and explain how they are related to string theory.
2008年03月13日(木)
解析学火曜セミナー
15:00-17:30 数理科学研究科棟(駒場) 117号室
「解析学(臨時)セミナー」と名称変更し,曜日,部屋も臨時に変更.
伊藤健一 氏 (東京大学大学院数理科学研究科) 15:00-16:00
Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI 氏 (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ 参考URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf
「解析学(臨時)セミナー」と名称変更し,曜日,部屋も臨時に変更.
伊藤健一 氏 (東京大学大学院数理科学研究科) 15:00-16:00
Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI 氏 (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ 参考URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf
2008年02月23日(土)
東京無限可積分系セミナー
13:00-16:30 数理科学研究科棟(駒場) 270号室
岩尾慎介 氏 (東大数理) 13:00-14:30
Solutions of hungry periodic discrete Toda equation and its ultradiscretization
A tropical analogue of Fay's trisecant identity and its application to the ultra-discrete periodic Toda equation.
岩尾慎介 氏 (東大数理) 13:00-14:30
Solutions of hungry periodic discrete Toda equation and its ultradiscretization
[ 講演概要 ]
The hungry discrete Toda equation is a generalization of the discrete Toda
equation. Through the method of ultradiscretization, the generalized
Box-ball system (gBBS) with finitely many kinds of balls is obtained from
hungry discrete Toda eq.. It is to be expected that the general solution of
gBBS should be obtained from the solution of hungry discrete Toda eq.
through ultradiscretization. In this talk, we derive the solutions of hungry
periodic discrete Toda eq. (hpd Toda eq.), by using inverse scattering
method. Although the hpd Toda equation does not linearlized in the usual
sense on the Picard group of the spectral curve, it is possible to determine
its behavior on the Picard group.
竹縄知之 氏 (東京海洋大・海洋工) 15:00-16:30The hungry discrete Toda equation is a generalization of the discrete Toda
equation. Through the method of ultradiscretization, the generalized
Box-ball system (gBBS) with finitely many kinds of balls is obtained from
hungry discrete Toda eq.. It is to be expected that the general solution of
gBBS should be obtained from the solution of hungry discrete Toda eq.
through ultradiscretization. In this talk, we derive the solutions of hungry
periodic discrete Toda eq. (hpd Toda eq.), by using inverse scattering
method. Although the hpd Toda equation does not linearlized in the usual
sense on the Picard group of the spectral curve, it is possible to determine
its behavior on the Picard group.
A tropical analogue of Fay's trisecant identity and its application to the ultra-discrete periodic Toda equation.
[ 講演概要 ]
The ultra-discrete Toda equation is essentially equivalent to the integrable
Box and Ball system, and considered to be a fundamental object in
ultra-discrete integrable systems. In this talk, we construct the general
solution of ultra-discrete Toda equation with periodic boundary condition,
by using the tropical theta function and the bilinear form. The tropical
theta function is associated with the tropical curve defined through the Lax
matrix of (not ultra-) discrete periodic Toda equation. For the proof, we
introduce a tropical analogue of Fay's trisecant identity. (This talk is
based on the joint work with R. Inoue.)
The ultra-discrete Toda equation is essentially equivalent to the integrable
Box and Ball system, and considered to be a fundamental object in
ultra-discrete integrable systems. In this talk, we construct the general
solution of ultra-discrete Toda equation with periodic boundary condition,
by using the tropical theta function and the bilinear form. The tropical
theta function is associated with the tropical curve defined through the Lax
matrix of (not ultra-) discrete periodic Toda equation. For the proof, we
introduce a tropical analogue of Fay's trisecant identity. (This talk is
based on the joint work with R. Inoue.)
2008年02月20日(水)
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 122号室
大屋 幸輔 氏 (大阪大学大学院経済学研究科)
A Test for Cross-sectional Dependence of Microstructure Noises and their Cross-Covariance Estimator
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/21.html
大屋 幸輔 氏 (大阪大学大学院経済学研究科)
A Test for Cross-sectional Dependence of Microstructure Noises and their Cross-Covariance Estimator
[ 講演概要 ]
高頻度観測される約定データにもとづく Integrated Volatility や Integrated Covariance の推定量は Bid-Ask Bounce に代表される Market Microstructure Noise の存在により、バイアスをもち、その分散も過大なものになっている。さ まざまな推定量の改良が提案されているが、それらの多くは Microstructure Noise の dependence の構造を既知としたものである。この従属性の構造を明ら かにするために、本報告では直接観測できない Microstructure Noise の相互自 己共分散がゼロであるかどうかを検定する統計量と相互自己共分散関数の推定量 を提案する。
[ 参考URL ]高頻度観測される約定データにもとづく Integrated Volatility や Integrated Covariance の推定量は Bid-Ask Bounce に代表される Market Microstructure Noise の存在により、バイアスをもち、その分散も過大なものになっている。さ まざまな推定量の改良が提案されているが、それらの多くは Microstructure Noise の dependence の構造を既知としたものである。この従属性の構造を明ら かにするために、本報告では直接観測できない Microstructure Noise の相互自 己共分散がゼロであるかどうかを検定する統計量と相互自己共分散関数の推定量 を提案する。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/21.html
講演会
13:30-17:45 数理科学研究科棟(駒場) 123号室
乙部厳己 氏 (信州大理) 13:30-14:00
Divergence formulae on the space of continuous functions and Malliavin calculus
長田博文 氏 (九大数理) 14:15-15:15
Ginibre random point field and a notion of convergence of Dirichlet forms
Lorenzo Zambotti 氏 (パリ第6大学) 15:30-16:30
Stochastic PDEs and infinite dimensional integration by parts formulae
志賀徳造 氏 (東工大理工) 16:45-17:45
ランダム環境下の確率モデルに関連する問題
(A problem arising in stochastic models in random environments)
乙部厳己 氏 (信州大理) 13:30-14:00
Divergence formulae on the space of continuous functions and Malliavin calculus
長田博文 氏 (九大数理) 14:15-15:15
Ginibre random point field and a notion of convergence of Dirichlet forms
Lorenzo Zambotti 氏 (パリ第6大学) 15:30-16:30
Stochastic PDEs and infinite dimensional integration by parts formulae
志賀徳造 氏 (東工大理工) 16:45-17:45
ランダム環境下の確率モデルに関連する問題
(A problem arising in stochastic models in random environments)
2008年02月19日(火)
講演会
16:30-17:30 数理科学研究科棟(駒場) 118号室
Eric Stade 氏 (Colorado University)
An overview on archimedean L-factors for G_1xG_2
Eric Stade 氏 (Colorado University)
An overview on archimedean L-factors for G_1xG_2
[ 講演概要 ]
When G_1xG_2 is one of pairs GL(n)xGL(n), GL(n)xGL(n+1), GL(n)xSO(2n+1), and GL(n+1)xSO(2n+1), we have evaluation of the archimedian L-factors of automorphic L-functions obtained by Rankin-Selberg convolution.
The last two cases are joint works with Taku Ishii (Chiba Inst. of Tech) which are in progress.
When G_1xG_2 is one of pairs GL(n)xGL(n), GL(n)xGL(n+1), GL(n)xSO(2n+1), and GL(n+1)xSO(2n+1), we have evaluation of the archimedian L-factors of automorphic L-functions obtained by Rankin-Selberg convolution.
The last two cases are joint works with Taku Ishii (Chiba Inst. of Tech) which are in progress.
2008年02月13日(水)
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 123号室
増田 弘毅 氏 (九大数理)
Realized multipower variationの統計推測への応用について
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/20.html
増田 弘毅 氏 (九大数理)
Realized multipower variationの統計推測への応用について
[ 講演概要 ]
確率過程からの高頻度データに基づいて定義されるMultipower variation (MPV)は,飛躍に対して頑健な累積ボラティリティ推定量や,飛躍の検出のための統 計量として,近年計量経済において脚光を浴びている.MPVはモデルの複雑さに依ら ずその計算が容易であるため,飛躍付確率過程に関する様々な統計推測問題への適用 が期待される.本報告では特に,最近Lee and Mykland (The Review of Financial Studies, to appear)によって提案された,MPVを介した飛躍時点(微小区間)の検出 手法を,複合ポアソン型飛躍付拡散過程の漸近推測へ応用することを考える.
[ 参考URL ]確率過程からの高頻度データに基づいて定義されるMultipower variation (MPV)は,飛躍に対して頑健な累積ボラティリティ推定量や,飛躍の検出のための統 計量として,近年計量経済において脚光を浴びている.MPVはモデルの複雑さに依ら ずその計算が容易であるため,飛躍付確率過程に関する様々な統計推測問題への適用 が期待される.本報告では特に,最近Lee and Mykland (The Review of Financial Studies, to appear)によって提案された,MPVを介した飛躍時点(微小区間)の検出 手法を,複合ポアソン型飛躍付拡散過程の漸近推測へ応用することを考える.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/20.html
2008年02月12日(火)
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 056号室
Katrin Wendland 氏 (University of Augrburg)
How to lift a construction by Hiroshi Inose to conformal field theory
Katrin Wendland 氏 (University of Augrburg)
How to lift a construction by Hiroshi Inose to conformal field theory
[ 講演概要 ]
The moduli space of Einstein metrics is well known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is well understood as well. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from conformal field theory. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem. The only known constructions which allow to deal with families of CFTs give CFTs associated to K3 surfaces with orbifold singularities.
We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed.
We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds.
The moduli space of Einstein metrics is well known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is well understood as well. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from conformal field theory. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem. The only known constructions which allow to deal with families of CFTs give CFTs associated to K3 surfaces with orbifold singularities.
We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed.
We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds.
2008年02月07日(木)
講演会
16:30-18:00 数理科学研究科棟(駒場) 002号室
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
連続講演
Luc Illusie 氏 (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ 講演概要 ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008年02月06日(水)
統計数学セミナー
13:30-14:40 数理科学研究科棟(駒場) 056号室
Jean JACOD 氏 (Universite Paris 6)
Estimation of the integrated volatility in presence of microstructure noise
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/17.html
Jean JACOD 氏 (Universite Paris 6)
Estimation of the integrated volatility in presence of microstructure noise
[ 講演概要 ]
The aim is to estimate the integrated volatility of a process observed discretely, in the setting of high frequency data, and when there is a microstructure noise. We use a kind of pre-averaging approach, which is rate-optimal when the noise is i.i.d., and may probably be even variance-optimal for a good choice of the kernel involved. However, the main innovative aspect is that it accommodates other types of noise, and in particular the case where the observations are rounded values of the underlying process plus an additive noise.
[ 参考URL ]The aim is to estimate the integrated volatility of a process observed discretely, in the setting of high frequency data, and when there is a microstructure noise. We use a kind of pre-averaging approach, which is rate-optimal when the noise is i.i.d., and may probably be even variance-optimal for a good choice of the kernel involved. However, the main innovative aspect is that it accommodates other types of noise, and in particular the case where the observations are rounded values of the underlying process plus an additive noise.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/17.html
統計数学セミナー
14:50-16:00 数理科学研究科棟(駒場) 056号室
Jean JACOD 氏 (Universite Paris 6)
Estimating the Degree of Activity of jumps in High Frequency Data
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/18.html
Jean JACOD 氏 (Universite Paris 6)
Estimating the Degree of Activity of jumps in High Frequency Data
[ 講演概要 ]
Suppose that a continuous-time process X = (X_t )_{t >= 0} is observed at finitely many times, regularly spaced, on the fixed time interval [0, T ]. We suppose that this process is an It\\^o semimartingale, with a non-vanishing diffusion coefficient, and with jumps. The aim is to estimate the so-called ”Blumenthal-Getoor” index of the (partially observed) path on [0, T ], which is the (random) infimum of all reals r such that the sum \\sum_{s\\le T} |\\Delta X_s|^r is finite (\\Delta X_s denotes the jump size at time s). When X is a L'evy process, this infimum is non-random, and also independent of T , and has been introduced by Blumenthal and Getoor. Under appropriate assumptions, unfortunately rather restrictive, we provide an estimator, which is consistent when the step size between observations goes to 0, and satisfies in addition a Central Limit Theorem. We also show the (surprising) values that this estimator takes, when applied to real financial data.
[ 参考URL ]Suppose that a continuous-time process X = (X_t )_{t >= 0} is observed at finitely many times, regularly spaced, on the fixed time interval [0, T ]. We suppose that this process is an It\\^o semimartingale, with a non-vanishing diffusion coefficient, and with jumps. The aim is to estimate the so-called ”Blumenthal-Getoor” index of the (partially observed) path on [0, T ], which is the (random) infimum of all reals r such that the sum \\sum_{s\\le T} |\\Delta X_s|^r is finite (\\Delta X_s denotes the jump size at time s). When X is a L'evy process, this infimum is non-random, and also independent of T , and has been introduced by Blumenthal and Getoor. Under appropriate assumptions, unfortunately rather restrictive, we provide an estimator, which is consistent when the step size between observations goes to 0, and satisfies in addition a Central Limit Theorem. We also show the (surprising) values that this estimator takes, when applied to real financial data.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/18.html
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 056号室
竹原 浩太 氏 (東京大学大学院経済学研究科)
A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/19.html
竹原 浩太 氏 (東京大学大学院経済学研究科)
A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options
[ 講演概要 ]
In this session we develop a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates.
Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained.
Moreover, the hybrid scheme develops Fourier transform method with an asymptotic expansion to utilize closed-form characteristic functions obtainable in parts of a model.
Our scheme also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of closed-form characteristic functions.
Finally, a series of numerical examples shows the validity of our scheme.
(This is a collaborative research with Professor Akihiko Takahashi(Graduate School of Economics, The University of Tokyo).)
[ 参考URL ]In this session we develop a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates.
Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained.
Moreover, the hybrid scheme develops Fourier transform method with an asymptotic expansion to utilize closed-form characteristic functions obtainable in parts of a model.
Our scheme also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of closed-form characteristic functions.
Finally, a series of numerical examples shows the validity of our scheme.
(This is a collaborative research with Professor Akihiko Takahashi(Graduate School of Economics, The University of Tokyo).)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/19.html
数理ファイナンスセミナー
18:00-19:30 数理科学研究科棟(駒場) 128号室
Daniel Bloch 氏 ( )
Fast calibration of some Affine and Quadratic models with applications to derivatives on variance swaps
Daniel Bloch 氏 ( )
Fast calibration of some Affine and Quadratic models with applications to derivatives on variance swaps
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