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Seminar information archive
Seminar information archive ～04/29｜Today's seminar 04/30 | Future seminars 05/01～
Infinite Analysis Seminar Tokyo
10:00-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)
岩尾 慎介 (東大数理) 10:00-11:00
離散周期KP方程式の簡約と、初期値問題の解の構成
Laplacian on graphs: Examples from physics
岩尾 慎介 (東大数理) 10:00-11:00
離散周期KP方程式の簡約と、初期値問題の解の構成
[ Abstract ]
様々に簡約された離散周期KP方程式に対して、スペクトル曲線を用いた逆散乱解法を考える。 このとき、簡約の種類によっては、超楕円とは限らない代数曲線が多数あらわれてくる。 本講演では、簡約周期KP方程式の初期値問題の解を構成する方法を紹介する。この方法はFayの恒等式を用いない構成的なもので、わかりやすいものである。
Y. Avishai (Ben Gurion University) 13:00-14:00様々に簡約された離散周期KP方程式に対して、スペクトル曲線を用いた逆散乱解法を考える。 このとき、簡約の種類によっては、超楕円とは限らない代数曲線が多数あらわれてくる。 本講演では、簡約周期KP方程式の初期値問題の解を構成する方法を紹介する。この方法はFayの恒等式を用いない構成的なもので、わかりやすいものである。
Laplacian on graphs: Examples from physics
[ Abstract ]
When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.
I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.
When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.
I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.
2009/12/21
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
源 泰幸 (京都大学理学部数学教室)
Ampleness of two-sided tilting complexes
源 泰幸 (京都大学理学部数学教室)
Ampleness of two-sided tilting complexes
[ Abstract ]
From the view point of noncommutative algebraic geometry (NCAG),
a two-sided tilting complex is an analog of a line bundle.
In this talk we introduce the notion of ampleness for two-sided
tilting complexes over finite dimensional algebras.
From the view point of NCAG, the Serre functors are considered to be
shifted canonical bundles. We show by examples that the property
of shifted canonical bundle captures some representation theoretic
property of algebras.
From the view point of noncommutative algebraic geometry (NCAG),
a two-sided tilting complex is an analog of a line bundle.
In this talk we introduce the notion of ampleness for two-sided
tilting complexes over finite dimensional algebras.
From the view point of NCAG, the Serre functors are considered to be
shifted canonical bundles. We show by examples that the property
of shifted canonical bundle captures some representation theoretic
property of algebras.
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Thomas Simon (Universite de Lille 1)
Absolute continuity of Ornstein-Uhlenbeck processes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html
Thomas Simon (Universite de Lille 1)
Absolute continuity of Ornstein-Uhlenbeck processes
[ Abstract ]
Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.
dX = AX + dB
where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.
[ Reference URL ]Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.
dX = AX + dB
where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html
2009/12/18
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)
山下 浩 (数理システム代表取締役)
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅡ
山下 浩 (数理システム代表取締役)
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅡ
Colloquium
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
小澤登高 (東京大学大学院数理科学研究科)
Dixmierの相似問題
小澤登高 (東京大学大学院数理科学研究科)
Dixmierの相似問題
[ Abstract ]
群のユニタリ表現に関しては美しい理論があるが, ユニタリでない無限次元表現はまったくとらえがたい対象である. そこで, 群のヒルベルト空間上の表現がいつユニタリ表現と相似(共役ともいう)になるかを問うのがDixmierの相似問題である. この問題は従順性という概念と深い関わりを持ち, 従って群の従順性の代数的な特徴づけを問うたvon Neumannの問題とも関わっている. von Neumannの問題は, 1980年代に否定的に解かれたものの, 近年の測度論的群論の発展により予想外の展開を見た. 講演では, これらのストーリ ーと測度論的群論の相似問題への応用(Monod氏との共同研究)を話す予定である. 予備知識はほとんど仮定しないので, 学部生にも聞きに来てもらいたい.
群のユニタリ表現に関しては美しい理論があるが, ユニタリでない無限次元表現はまったくとらえがたい対象である. そこで, 群のヒルベルト空間上の表現がいつユニタリ表現と相似(共役ともいう)になるかを問うのがDixmierの相似問題である. この問題は従順性という概念と深い関わりを持ち, 従って群の従順性の代数的な特徴づけを問うたvon Neumannの問題とも関わっている. von Neumannの問題は, 1980年代に否定的に解かれたものの, 近年の測度論的群論の発展により予想外の展開を見た. 講演では, これらのストーリ ーと測度論的群論の相似問題への応用(Monod氏との共同研究)を話す予定である. 予備知識はほとんど仮定しないので, 学部生にも聞きに来てもらいたい.
2009/12/17
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
佐藤康彦 (北海道大理)
Almost commuting unitaries and ${\\mathbb{Z}}^2$-action
佐藤康彦 (北海道大理)
Almost commuting unitaries and ${\\mathbb{Z}}^2$-action
Seminar on Geometric Complex Analysis
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Alan Huckleberry (Ruhr-Universität Bochum)
Hyperbolicity of cycle spaces and automorphism groups of flag domains
Alan Huckleberry (Ruhr-Universität Bochum)
Hyperbolicity of cycle spaces and automorphism groups of flag domains
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Hatem Zaag (CNRS / パリ北大学)
A Liouville theorem for a semilinear heat equation with no gradient structure
Hatem Zaag (CNRS / パリ北大学)
A Liouville theorem for a semilinear heat equation with no gradient structure
[ Abstract ]
We prove a Liouville Theorem for entire solutions of a vector
valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.
We prove a Liouville Theorem for entire solutions of a vector
valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.
2009/12/16
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Stefano Maria Iacus (Department of Economics, Business and Statistics, University of Milan, Italy)
ecent results on volatility change point analysis for discretely sampled stochastic differential equations
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html
Stefano Maria Iacus (Department of Economics, Business and Statistics, University of Milan, Italy)
ecent results on volatility change point analysis for discretely sampled stochastic differential equations
[ Abstract ]
In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.
Join work with Prof. Nakahiro Yoshida.
[ Reference URL ]In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.
Join work with Prof. Nakahiro Yoshida.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html
2009/12/15
Lie Groups and Representation Theory
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
砂田利一氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
砂田利一氏 (明治大学理工学部)
Open Problems in Discrete Geometric Analysis
[ Abstract ]
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
[ Reference URL ]Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
砂田 利一 (明治大学)
Open Problems in Discrete Geometric Analysis
砂田 利一 (明治大学)
Open Problems in Discrete Geometric Analysis
[ Abstract ]
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
2009/12/14
Seminar on Probability and Statistics
14:00-15:10 Room #128 (Graduate School of Math. Sci. Bldg.)
L. VOSTRIKOVA (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
On the stability of contingent claimes in incomplet models under statistical estimations.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html
L. VOSTRIKOVA (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
On the stability of contingent claimes in incomplet models under statistical estimations.
[ Abstract ]
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.
[ Reference URL ]In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html
Algebraic Geometry Seminar
14:40-16:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Sergey Galkin (IPMU)
Invariants of Fano varieties via quantum D-module
Sergey Galkin (IPMU)
Invariants of Fano varieties via quantum D-module
[ Abstract ]
We will introduce and compute Apery characteristic
class and Frobenius genera - invariants of Fano variety derived from
it's Gromov-Witten invariants. Then we will show how to compute them
and relate with other invariants.
We will introduce and compute Apery characteristic
class and Frobenius genera - invariants of Fano variety derived from
it's Gromov-Witten invariants. Then we will show how to compute them
and relate with other invariants.
2009/12/11
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #117 (Graduate School of Math. Sci. Bldg.)
山下 浩 (数理システム代表取締役 )
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅠ
山下 浩 (数理システム代表取締役 )
数理科学をビジネスに - 最適化とデータマイニングの周辺でⅠ
2009/12/10
Lectures
10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (9)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (9)
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
張欽 (東大数理)
Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra
張欽 (東大数理)
Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra
2009/12/09
Lectures
14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (8)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (8)
Seminar on Probability and Statistics
15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
佐藤 整尚 (統計数理研究所)
分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html
佐藤 整尚 (統計数理研究所)
分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について
[ Abstract ]
近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。
[ Reference URL ]近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html
2009/12/08
Lectures
14:40-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (7)
竹崎正道 (UCLA)
冨田竹崎理論とその応用 (7)
GCOE Seminars
17:30-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Giovanni Felder (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
Giovanni Felder (ETH Zurich)
Gaudin subalgebras and stable rational curves. (ENGLISH)
[ Abstract ]
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
2009/12/07
Kavli IPMU Komaba Seminar
17:30-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Weiping Zhang (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
Weiping Zhang (Chern Institute of Mathematics, Nankai University)
Geometric quantization on noncompact manifolds
[ Abstract ]
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.
2009/12/03
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
見村万佐人 (東大数理)
Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings
見村万佐人 (東大数理)
Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings
2009/12/02
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Juergen Saal (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
Juergen Saal (University of Konstanz)
A hyperbolic fluid model based on Cattaneo's law
[ Abstract ]
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.
2009/12/01
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes)
Non-Abelian Novikov homology
Andrei Pajitnov (Univ. de Nantes)
Non-Abelian Novikov homology
[ Abstract ]
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.
In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.
In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.
2009/11/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
奥山裕介 (京都工芸繊維大学)
Equidistribution and Nevanlinna theory
奥山裕介 (京都工芸繊維大学)
Equidistribution and Nevanlinna theory
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