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Seminar information archive
Seminar information archive ～10/03｜Today's seminar 10/04 | Future seminars 10/05～
2009/05/18
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
本多宣博 (東京工業大学)
Conformal symmetries of self-dual hyperbolic monopole metrics (joint work with Jeff Viaclovsky)
本多宣博 (東京工業大学)
Conformal symmetries of self-dual hyperbolic monopole metrics (joint work with Jeff Viaclovsky)
2009/05/16
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
水野 義紀 (徳島大学工学部) 13:30-14:30
3次元上半空間のスペクトル理論とエルミート保型形式
The Eisenstein series for $GL(3,Z)$ induced from cusp forms
水野 義紀 (徳島大学工学部) 13:30-14:30
3次元上半空間のスペクトル理論とエルミート保型形式
[ Abstract ]
3次元上半空間のスペクトル理論のエルミート保型形式への応用につい
て述べます。内容はジーゲル保型形式に対して2次元上半空間のスペクトル理論を応用す
るという今井氏による発見、及びその実際的応用のエルミート版への類似です。具体的に
は小嶋氏により発見されたエルミート版斉藤・黒川リフトに逆定理による解析的証明を与
えること、レベル付エルミート・アイゼンシュタイン級数のフーリエ係数の決定、それを
用いたp進エルミート・アイゼンシュタイン級数のエルミート・アイゼンシュタイン級数
による記述、についてです。これらにおいて必要となる「3次元上半空間のマース形式の
特殊値のある平均が、2次元上半空間のマース形式のフーリエ係数になる」というカトッ
ク・サルナック型の結果についても述べます。(p進エルミート・アイゼンシュタイン級
数については菊田俊之氏との共同研究、その他はRoland Matthes氏との共同研究です。)
宮崎 直 (東京大学数理科学研究科) 15:00-16:003次元上半空間のスペクトル理論のエルミート保型形式への応用につい
て述べます。内容はジーゲル保型形式に対して2次元上半空間のスペクトル理論を応用す
るという今井氏による発見、及びその実際的応用のエルミート版への類似です。具体的に
は小嶋氏により発見されたエルミート版斉藤・黒川リフトに逆定理による解析的証明を与
えること、レベル付エルミート・アイゼンシュタイン級数のフーリエ係数の決定、それを
用いたp進エルミート・アイゼンシュタイン級数のエルミート・アイゼンシュタイン級数
による記述、についてです。これらにおいて必要となる「3次元上半空間のマース形式の
特殊値のある平均が、2次元上半空間のマース形式のフーリエ係数になる」というカトッ
ク・サルナック型の結果についても述べます。(p進エルミート・アイゼンシュタイン級
数については菊田俊之氏との共同研究、その他はRoland Matthes氏との共同研究です。)
The Eisenstein series for $GL(3,Z)$ induced from cusp forms
[ Abstract ]
GL(3,Z)$に関するEisenstein級数のFourier-Whittaker展開は,
指標から誘導された場合については,Bump氏とFriedberg氏によって
明示的な表示が与えられている.ここでは,それらの類似として,
尖点形式から誘導された場合について,Fourier-Whittaker展開の
明示的な表示を与える.
GL(3,Z)$に関するEisenstein級数のFourier-Whittaker展開は,
指標から誘導された場合については,Bump氏とFriedberg氏によって
明示的な表示が与えられている.ここでは,それらの類似として,
尖点形式から誘導された場合について,Fourier-Whittaker展開の
明示的な表示を与える.
2009/05/14
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
東海林 まゆみ (日本女子大学・理学部・数物科学科)
Particle trajectories around a running cylinder in Brinkman's porous-media flow
東海林 まゆみ (日本女子大学・理学部・数物科学科)
Particle trajectories around a running cylinder in Brinkman's porous-media flow
[ Abstract ]
Motion of fluid particles provides us with interesting problems of dynamical
systems. We consider here the movement of particles around a running cylinder.
Classically J. C. Maxwell (1870) considered the problem in irrotational flow of
inviscid fluid. He showed that the complete solution is given by the elliptic
functions and the trajectory forms one of the elastica curves. C. Darwin ('53)
considered a similar problem for a moving sphere. In this case, the solution
cannot be written in terms of elliptic functions but can be expressed by a
simple definite integral.
We consider a similar problem in Brinkman's porous-media flow which is proposed
by Brinkman ('49). Our numerical examinations reveals some new interesting
features of the particle trajectories which are not observed in the case of
irrotational flow. We will report them.
Motion of fluid particles provides us with interesting problems of dynamical
systems. We consider here the movement of particles around a running cylinder.
Classically J. C. Maxwell (1870) considered the problem in irrotational flow of
inviscid fluid. He showed that the complete solution is given by the elliptic
functions and the trajectory forms one of the elastica curves. C. Darwin ('53)
considered a similar problem for a moving sphere. In this case, the solution
cannot be written in terms of elliptic functions but can be expressed by a
simple definite integral.
We consider a similar problem in Brinkman's porous-media flow which is proposed
by Brinkman ('49). Our numerical examinations reveals some new interesting
features of the particle trajectories which are not observed in the case of
irrotational flow. We will report them.
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (東大数理)
Noncommutative geometry and lower dimensional volumes in Riemannian and CR geometry
Raphael Ponge (東大数理)
Noncommutative geometry and lower dimensional volumes in Riemannian and CR geometry
Mathematical Biology Seminar
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
岩見真吾 (静岡大学創造科学技術大学院)
AIDSワクチン開発への理論的介入-SHIV感染実験と数理モデル-
岩見真吾 (静岡大学創造科学技術大学院)
AIDSワクチン開発への理論的介入-SHIV感染実験と数理モデル-
[ Abstract ]
慢性感染症であるという特性を有するHIV感染症の拡大を阻止するためには、予防・治療AIDSワクチンの開発が不可欠である。しかし、1998年にヒトでは初めての国際的な臨床試験が始まったバックスジェン社のAIDSワクチンは、2003年に失敗だと発表された。また、2004年メルク社の最も有望だったワクチン候補も大規模な臨床試験にまで進んだが、効果がないどころか悪影響がある可能性が判明し、2007年に打ち切られた。HIV単離からすでに25年たった今でも、まだ効果的なワクチンは開発されていない。このように、HIVに対して従来のワクチン製造法では有効なワクチンを作れなかったとなれば、何かこれまでとは違う革新的な治療戦略が必要である。そこで、本研究では、HIVとその体内での振る舞いに関する基本的な疑問と取り組み、HIVを無力化する新しい方法を見つけ出すこと目指す。まず身体に備わった免疫応答が通常どのように機能するのかを知るために、HIVとよく似たSHIVの感染実験と数理モデルを用いて、SHIVの性状、病原性、免疫反応性を明らかにする。今回のセミナーでは、培養細胞での実験データから推定可能であるウイルスの増殖率と感染力によって特徴づけられるSHIVの病原性評価理論を紹介する。
慢性感染症であるという特性を有するHIV感染症の拡大を阻止するためには、予防・治療AIDSワクチンの開発が不可欠である。しかし、1998年にヒトでは初めての国際的な臨床試験が始まったバックスジェン社のAIDSワクチンは、2003年に失敗だと発表された。また、2004年メルク社の最も有望だったワクチン候補も大規模な臨床試験にまで進んだが、効果がないどころか悪影響がある可能性が判明し、2007年に打ち切られた。HIV単離からすでに25年たった今でも、まだ効果的なワクチンは開発されていない。このように、HIVに対して従来のワクチン製造法では有効なワクチンを作れなかったとなれば、何かこれまでとは違う革新的な治療戦略が必要である。そこで、本研究では、HIVとその体内での振る舞いに関する基本的な疑問と取り組み、HIVを無力化する新しい方法を見つけ出すこと目指す。まず身体に備わった免疫応答が通常どのように機能するのかを知るために、HIVとよく似たSHIVの感染実験と数理モデルを用いて、SHIVの性状、病原性、免疫反応性を明らかにする。今回のセミナーでは、培養細胞での実験データから推定可能であるウイルスの増殖率と感染力によって特徴づけられるSHIVの病原性評価理論を紹介する。
2009/05/13
Number Theory Seminar
16:30-18:45 Room #056 (Graduate School of Math. Sci. Bldg.)
大久保 俊 (東京大学大学院数理科学研究科) 16:30-17:30
剰余体が非完全な場合のB_dR^+のGalois理論
斎藤 秀司 (東京大学大学院数理科学研究科) 17:45-18:45
A counterexample of Bloch-Kato conjecture over a local field and infinite torsion in algebraic cycles of codimension two
大久保 俊 (東京大学大学院数理科学研究科) 16:30-17:30
剰余体が非完全な場合のB_dR^+のGalois理論
斎藤 秀司 (東京大学大学院数理科学研究科) 17:45-18:45
A counterexample of Bloch-Kato conjecture over a local field and infinite torsion in algebraic cycles of codimension two
2009/05/12
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
松田 能文 (東京大学大学院数理科学研究科)
Discrete subgroups of the group of circle diffeomorphisms
松田 能文 (東京大学大学院数理科学研究科)
Discrete subgroups of the group of circle diffeomorphisms
[ Abstract ]
Typical examples of discrete subgroups of the group of circle diffeomorphisms
are Fuchsian groups.
In this talk, we construct discrete subgroups of the group of
orientation-preserving
real analytic cirlcle diffeomorphisms
which are not topologically conjugate to finite coverings of Fuchsian groups.
Typical examples of discrete subgroups of the group of circle diffeomorphisms
are Fuchsian groups.
In this talk, we construct discrete subgroups of the group of
orientation-preserving
real analytic cirlcle diffeomorphisms
which are not topologically conjugate to finite coverings of Fuchsian groups.
Seminar on Probability and Statistics
16:20-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
塩濱 敬之 (東京理科大学, 工学部)
Asymptitically efficient estimation of multiple change points in GARCH types models
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/03.html
塩濱 敬之 (東京理科大学, 工学部)
Asymptitically efficient estimation of multiple change points in GARCH types models
[ Abstract ]
Instability of volatility parameters in GARCH models in an important issue for analyzing financial time series. In this paper we investigate the asymptotic theory for multiple change point estimators of GARCH$(p,q)$ models. When the parameters of a GARCH models have changed within an observed realization, two types estimators, Maximum likelihood estimator (MLE) and Bayesian estimator (BE), are proposed. Then we derive the asymptotic distributions for these estimators. The MLE and BE have different limit laws, and the BE is asymptotically efficient. Monte Carlo studies on the finite sample behaviors are conducted. Applications to Nikkei 225 index are discussed.
[ Reference URL ]Instability of volatility parameters in GARCH models in an important issue for analyzing financial time series. In this paper we investigate the asymptotic theory for multiple change point estimators of GARCH$(p,q)$ models. When the parameters of a GARCH models have changed within an observed realization, two types estimators, Maximum likelihood estimator (MLE) and Bayesian estimator (BE), are proposed. Then we derive the asymptotic distributions for these estimators. The MLE and BE have different limit laws, and the BE is asymptotically efficient. Monte Carlo studies on the finite sample behaviors are conducted. Applications to Nikkei 225 index are discussed.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/03.html
2009/05/11
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
林本厚志 (長野高専)
CR幾何学でのドラーム分解型定理
林本厚志 (長野高専)
CR幾何学でのドラーム分解型定理
2009/05/07
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
見村万佐人 (東大数理)
A fixed point property and the Kazhdan property of
$SL(n, \\mathbb{Z} [X_1, \\ldots , X_k])$ for Banach spaces
見村万佐人 (東大数理)
A fixed point property and the Kazhdan property of
$SL(n, \\mathbb{Z} [X_1, \\ldots , X_k])$ for Banach spaces
2009/04/30
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
池田 幸太 (明治大 研究・知財戦略機構)
ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性
池田 幸太 (明治大 研究・知財戦略機構)
ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性
[ Abstract ]
生物の形態形成に関するモデル方程式である、ギーラー・マインハルト方程式に対するシャドウ系を考える。
この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。
実は、パラメータと領域を固定しても、単一のスポットだけからなるものや、2つ以上のスポットを持つ定常解、多重スポットが同時に存在しうるが、多重スポットは常に不安定であると予想されている。
本講演では、この予想を数学的に保証するために、多重スポットが適当な条件を満たせば不安定であることを示したい。
生物の形態形成に関するモデル方程式である、ギーラー・マインハルト方程式に対するシャドウ系を考える。
この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。
実は、パラメータと領域を固定しても、単一のスポットだけからなるものや、2つ以上のスポットを持つ定常解、多重スポットが同時に存在しうるが、多重スポットは常に不安定であると予想されている。
本講演では、この予想を数学的に保証するために、多重スポットが適当な条件を満たせば不安定であることを示したい。
Operator Algebra Seminars
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
酒匂宏樹 (東大数理)
Measure Equivalence Rigidity and Bi-exactness of Groups
酒匂宏樹 (東大数理)
Measure Equivalence Rigidity and Bi-exactness of Groups
2009/04/28
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
平地 健吾 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
平地 健吾 (東京大学大学院数理科学研究科)
The ambient metric in conformal geometry
[ Abstract ]
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
下村 明洋 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
下村 明洋 (首都大学東京)
非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)
2009/04/27
Algebraic Geometry Seminar
15:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Prof. Alessandra Sarti (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
) 17:00-18:00
The cohomological crepant resolution conjecture
Prof. Alessandra Sarti (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
[ Abstract ]
I will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.
Prof. Samuel Boissier (Universite de NiceI will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.
) 17:00-18:00
The cohomological crepant resolution conjecture
[ Abstract ]
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.
2009/04/23
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
内藤克利 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
内藤克利 (首都大)
Entire Cyclic Cohomology of Noncommutative 2-Tori
2009/04/22
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Wilhelm Klingenberg (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
Wilhelm Klingenberg (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
[ Abstract ]
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.
Geometry Seminar
14:45-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
中田文憲 (東京工業大学理工学研究科) 14:45-16:15
Einstein-Weyl structures on 3-dimensional Severi varieties
Toric non-Abelian Hodge theory
中田文憲 (東京工業大学理工学研究科) 14:45-16:15
Einstein-Weyl structures on 3-dimensional Severi varieties
[ Abstract ]
The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Tamas Hausel (Oxford University) 16:30-18:00The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Toric non-Abelian Hodge theory
[ Abstract ]
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Arnaud DOUCET (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
Arnaud DOUCET (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
[ Abstract ]
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
[ Reference URL ]We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
2009/04/21
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ivan Marin (Univ. Paris VII)
Some algebraic aspects of KZ systems
Ivan Marin (Univ. Paris VII)
Some algebraic aspects of KZ systems
[ Abstract ]
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.
2009/04/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
鎌田博行 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
鎌田博行 (宮城教育大学)
Indefinite Kähler surfaces of constant scalar curvature
2009/04/18
Infinite Analysis Seminar Tokyo
11:00-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Vladimir Dobrev (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
TBA
Vladimir Dobrev (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00-12:00
Invariant Differential Operators for Non-Compact Lie Groups
[ Abstract ]
We present a canonical procedure for the explicit construction of
invariant differential operators. The exposition is for semi-simple
Lie algebras, but is easily generalized to the supersymmetric and
quantum group settings. Especially important is a narrow class of
algebras, which we call 'conformal Lie algebras', which have very
similar properties to the conformal algebras of n-dimensional
Minkowski space-time. Examples are given in detail, including diagrams of
intertwining operators, or equivalently, multiplets of elementary
representations (generalized Verma modules).
笠谷昌弘 (東大数理) 13:30-14:30We present a canonical procedure for the explicit construction of
invariant differential operators. The exposition is for semi-simple
Lie algebras, but is easily generalized to the supersymmetric and
quantum group settings. Especially important is a narrow class of
algebras, which we call 'conformal Lie algebras', which have very
similar properties to the conformal algebras of n-dimensional
Minkowski space-time. Examples are given in detail, including diagrams of
intertwining operators, or equivalently, multiplets of elementary
representations (generalized Verma modules).
TBA
[ Abstract ]
TBA
TBA
2009/04/16
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
緒方芳子 (東大数理)
Large Deviations in Quantum Spin Chains
緒方芳子 (東大数理)
Large Deviations in Quantum Spin Chains
2009/04/15
Lectures
15:30-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Wilhelm Stannat (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
Wilhelm Stannat (Darmstadt 工科大学)
Invariant measures for stochastic partial differential equations: new a priori estimates and applications
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jean JACOD (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
Jean JACOD (Universite Paris VI)
Estimating the successive Blumenthal-Getoor indices for a discretely observed process
[ Abstract ]
Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
[ Reference URL ]Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\\sigma_{i\\ge 1} a_i/x^\\beta$ as $x \\rightarrow 0$, we call $\\beta_1 > \\beta_2 >...$ the successive Blumenthal-Getoor indices, since $\\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\\beta_i$ and $a_i$ for those $i$'s such that $\\beta_i > \\beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\\beta_i < \\beta_1 /2$. On the other hand, a central limit theorem for $\\beta_1$ is available only when $\\beta_i < \\beta_1 /2$: consequently, when we can actually consistently estimate some $\\beta_i$'s besides $\\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
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