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過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
2007年12月05日(水)
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 117号室
中村健太郎 氏 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
中村健太郎 氏 (東京大学大学院数理科学研究科)
Classification of two dimensional trianguline representations of p-adic fields
[ 講演概要 ]
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\\varphi, \\Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\\varphi,\\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
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
今野 良彦 氏 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
今野 良彦 氏 (日本女子大学理学部)
A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones
[ 講演概要 ]
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
[ 参考URL ]James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
2007年12月04日(火)
諸分野のための数学研究会
15:00-17:15 数理科学研究科棟(駒場) 122号室
Pavel Krejci 氏 (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov 氏 (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Pavel Krejci 氏 (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
[ 講演概要 ]
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
[ 参考URL ]We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov 氏 (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
[ 講演概要 ]
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
[ 参考URL ]We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
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
今野 宏 氏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
Tea: 16:00 - 16:30 コモンルーム
今野 宏 氏 (東京大学大学院数理科学研究科)
Morse theory for abelian hyperkahler quotients
[ 講演概要 ]
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
2007年12月03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
甲斐千舟 氏 (九州大学)
等質有界領域の対称性条件、性質の良い有界領域実現について
甲斐千舟 氏 (九州大学)
等質有界領域の対称性条件、性質の良い有界領域実現について
2007年11月29日(木)
講演会
10:40-12:10 数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007年11月27日(火)
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
Alexander Kuznetsov 氏 (Steklov Inst)
Categorical resolutions of singularities
Alexander Kuznetsov 氏 (Steklov Inst)
Categorical resolutions of singularities
[ 講演概要 ]
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.
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
小松 彦三郎 氏 (東大数理(名誉教授))
Heaviside's theory of signal transmission on submarine cables
小松 彦三郎 氏 (東大数理(名誉教授))
Heaviside's theory of signal transmission on submarine cables
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
石井 敦 氏 (京都大学数理解析研究所)
A quandle cocycle invariant for handlebody-links
Tea: 16:00 - 16:30 コモンルーム
石井 敦 氏 (京都大学数理解析研究所)
A quandle cocycle invariant for handlebody-links
[ 講演概要 ]
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.
2007年11月26日(月)
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 002号室
Mich\"ael Pevzner 氏 (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
Mich\"ael Pevzner 氏 (Universit\'e de Reims and the University of Tokyo)
Kontsevich quantization of Poisson manifolds and Duflo isomorphism.
[ 講演概要 ]
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.
The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.
The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.
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
金子宏 氏 (東京理科大学)
Analysis related to probability theory based on p-adic hierarchical structure
金子宏 氏 (東京理科大学)
Analysis related to probability theory based on p-adic hierarchical structure
2007年11月22日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
佐藤 洋平 氏 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
佐藤 洋平 氏 (早稲田大学・基幹理工学部・数学科)
Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解
[ 講演概要 ]
非線形シュレディンガー方程式
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。
もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。
非線形シュレディンガー方程式
$$ -\\epsilon2 \\Delta u +V(x)u= u^p, u>0 \\ \\hbox{in} \\R^N,
u\\in H1(\\R^N)$$
において、$\\epsilon \\to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\\liminf_{|x|\\to \\infty}V(x)>0$ を満たすとする。
もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\\epsilon$ を構成する。
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
張欽 氏 (東大数理)
Spatial property of the canonical map associated to von Neumann algebras
張欽 氏 (東大数理)
Spatial property of the canonical map associated to von Neumann algebras
講演会
10:40-12:10 数理科学研究科棟(駒場) 128号室
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
Mikael Pichot 氏 (東大数理)
Topics in ergodic theory, von Neumann algebras, and rigidity
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007年11月21日(水)
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 117号室
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
Christopher Rasmussen 氏 (京都大学数理解析研究所)
Abelian varieties with constrained torsion
[ 講演概要 ]
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\\Q$.
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
宮尾 祐介 氏 (東京大学理学部情報科学科)
自然言語処理における構造的・統計的モデル
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html
宮尾 祐介 氏 (東京大学理学部情報科学科)
自然言語処理における構造的・統計的モデル
[ 講演概要 ]
本発表では,自然言語処理において代表的な問題である機械翻訳と構文解析に ついて,言語の構造的性質と統計的性質をどのようなモデルで表現するかにつ いて概説する.これらの問題に対しては,古くは構造的規則性に着目し,翻訳 規則や文法などの規則体系を明らかにすることが主な研究目標であった.しか し,統計モデルの自然言語処理への応用が90年代に提案され,大きな成功をお さめたことから,現在では主流となっている.最近では,統計モデルを構造化 することによって言語の複雑な構造をとらえるアプローチがさかんに研究され ており,本発表では,これらの構造的・統計的モデルが言語の構造をどのよう にモデル化しているかを述べる.
[ 参考URL ]本発表では,自然言語処理において代表的な問題である機械翻訳と構文解析に ついて,言語の構造的性質と統計的性質をどのようなモデルで表現するかにつ いて概説する.これらの問題に対しては,古くは構造的規則性に着目し,翻訳 規則や文法などの規則体系を明らかにすることが主な研究目標であった.しか し,統計モデルの自然言語処理への応用が90年代に提案され,大きな成功をお さめたことから,現在では主流となっている.最近では,統計モデルを構造化 することによって言語の複雑な構造をとらえるアプローチがさかんに研究され ており,本発表では,これらの構造的・統計的モデルが言語の構造をどのよう にモデル化しているかを述べる.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html
2007年11月20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
長郷 文和 氏 (東京工業大学大学院理工学研究科)
A certain slice of the character variety of a knot group
and the knot contact homology
Tea: 16:00 - 16:30 コモンルーム
長郷 文和 氏 (東京工業大学大学院理工学研究科)
A certain slice of the character variety of a knot group
and the knot contact homology
[ 講演概要 ]
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.
In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.
We will mainly explain these facts.
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.
In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.
We will mainly explain these facts.
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
西山 享 氏 (京都大学)
Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
西山 享 氏 (京都大学)
Asymptotic cone for semisimple elements and the associated variety of degenerate principal series
[ 講演概要 ]
Let $ a $ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $ K $ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $ a $ under the adjoint action by $ K $. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $ a $.
[ 参考URL ]Let $ a $ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $ K $ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $ a $ under the adjoint action by $ K $. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $ a $.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007年11月19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
藤野修 氏 (名古屋大学)
乗数イデアル層の類似物
藤野修 氏 (名古屋大学)
乗数イデアル層の類似物
2007年11月17日(土)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
小島教知 氏 (東京工業大学理学研究科) 13:30-14:30
Pullback formula for vector valued Siegel modular forms and its applications
Congruences connecting Tate-Shafarevich groups with Hurwitz numbers
小島教知 氏 (東京工業大学理学研究科) 13:30-14:30
Pullback formula for vector valued Siegel modular forms and its applications
[ 講演概要 ]
$H_n$ を $n$ 次 Siegel 上半空間, $E^n_k$ を次数 $n$, 重さ $k$ のSiegel Eisenstein 級数とする. いま $p$, $q$ を自然数としたとき,$H_p\\times H_q$ は $H_{p+q}$ の中に埋め込むことができる. Garrett は $E^{p+q}_k$ を $H_p\\times H_q$ 上に制限したときに Klingen Eisenstein 級数や Siegel 保型形式の standard $L$ 函数の値などで表示する公式を与へた. この公式は pullback formula とよばれてゐる.
この pullback formula はBoecherer によつて複素パラメータつきの Eisenstein 級数の場合に拡張され, Klingen Eisenstein 級数や standard $L$ 函数についての結果が得られてゐる.
本講演ではこれらの結果がベクトル値 Siegel 保型形式の場合にどれくらゐ拡張できるかについて述べる.
大西良博 氏 (岩手大学) 15:00-16:00$H_n$ を $n$ 次 Siegel 上半空間, $E^n_k$ を次数 $n$, 重さ $k$ のSiegel Eisenstein 級数とする. いま $p$, $q$ を自然数としたとき,$H_p\\times H_q$ は $H_{p+q}$ の中に埋め込むことができる. Garrett は $E^{p+q}_k$ を $H_p\\times H_q$ 上に制限したときに Klingen Eisenstein 級数や Siegel 保型形式の standard $L$ 函数の値などで表示する公式を与へた. この公式は pullback formula とよばれてゐる.
この pullback formula はBoecherer によつて複素パラメータつきの Eisenstein 級数の場合に拡張され, Klingen Eisenstein 級数や standard $L$ 函数についての結果が得られてゐる.
本講演ではこれらの結果がベクトル値 Siegel 保型形式の場合にどれくらゐ拡張できるかについて述べる.
Congruences connecting Tate-Shafarevich groups with Hurwitz numbers
[ 講演概要 ]
奇素数 $p$ について, 虚2次体 $\\mathbf{Q} (\\sqrt{-p})$ の類数を $h(-p)$ と書くことにします. このとき $p≡1, 3 mod 4$ に応じて
$h(-p)≡2^{-1}E_{(p-1)/2} mod p$
$h(-p)≡ -2B_{(p+1)/2} mod p$
となり, 右辺の最小の剰余は左辺そのものを与へます. 但し $B_n$ は Bernoulli 数, $E_n$ は Euler 数. この合同式の一般化として, ある種の楕円曲線の Tate-Shafarevich 群の位数の平方根と Hurwitz 数との間の同様な合同式を与へます.
奇素数 $p$ について, 虚2次体 $\\mathbf{Q} (\\sqrt{-p})$ の類数を $h(-p)$ と書くことにします. このとき $p≡1, 3 mod 4$ に応じて
$h(-p)≡2^{-1}E_{(p-1)/2} mod p$
$h(-p)≡ -2B_{(p+1)/2} mod p$
となり, 右辺の最小の剰余は左辺そのものを与へます. 但し $B_n$ は Bernoulli 数, $E_n$ は Euler 数. この合同式の一般化として, ある種の楕円曲線の Tate-Shafarevich 群の位数の平方根と Hurwitz 数との間の同様な合同式を与へます.
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) 126号室
Gleb Novichkov 氏 (Keio Univ.) 13:00-14:30
Dynamical r-matrices coupled with dual Poisson Lie group
Yang-Baxter Equation and Quantum Geometry
Gleb Novichkov 氏 (Keio Univ.) 13:00-14:30
Dynamical r-matrices coupled with dual Poisson Lie group
[ 講演概要 ]
The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Vladimir V. Bazhanov 氏 (Australian National Univ.) 15:00-16:30The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Yang-Baxter Equation and Quantum Geometry
[ 講演概要 ]
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\\'e,
Darboux and Bianchi in differential geometry.
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\\'e,
Darboux and Bianchi in differential geometry.
2007年11月15日(木)
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
水田有一 氏 (東大数理)
Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介
水田有一 氏 (東大数理)
Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介
2007年11月14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
塚原 英敦 氏 (成城大学経済学部)
Estimation of Distortion Risk Measures
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html
塚原 英敦 氏 (成城大学経済学部)
Estimation of Distortion Risk Measures
[ 講演概要 ]
By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.
[ 参考URL ]By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html
2007年11月13日(火)
講演会
16:00-17:30 数理科学研究科棟(駒場) 052号室
Jens Starke 氏 (Technical University of Denmark)
Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb
Jens Starke 氏 (Technical University of Denmark)
Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb
[ 講演概要 ]
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.
(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.
(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.
(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.
This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.
(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.
(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.
(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.
This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.
2007年11月12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
野口 潤次郎 氏 (東京大学)
蕭の有理型接続と関連する話題 (Siu's meromorphic connection and related topics)
野口 潤次郎 氏 (東京大学)
蕭の有理型接続と関連する話題 (Siu's meromorphic connection and related topics)
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