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Seminar information archive
Seminar information archive ～04/19｜Today's seminar 04/20 | Future seminars 04/21～
2009/01/14
Lectures
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
片山 統裕 (東北大学 大学院情報科学研究科 応用情報科学専攻)
中枢ニューロン樹状突起における酵素活性化ウェーブとその数理モデル
片山 統裕 (東北大学 大学院情報科学研究科 応用情報科学専攻)
中枢ニューロン樹状突起における酵素活性化ウェーブとその数理モデル
[ Abstract ]
ニューロンの興奮性の調節やシナプス可塑性において重要な役割を担っているC型タンパク質リン酸化酵素(PKC)は,その酵素活性と関連して細胞内局在が変化する性質を有する(トランスロケーション).GFP-γPKC融合タンパクを発現させたマウス小脳プルキンエ細胞において,平行線維シナプスの高頻度刺激に伴い,刺激部位近傍から樹状突起に沿ってトランスロケーションが伝播する現象が報告されている.最近,坪川は,同じ刺激条件で樹状突起内をほぼ同速度で伝播する細胞内Ca2+波が生じることを見出し,これがγPKCトランスロケーション波をリードしている可能性を指摘した.本研究では,生理学的・解剖学的知見に基づいたプルキンエ細胞の数理モデルを構築し,Ca2+波の再現を試みた.その結果に基づき,トランスロケーション伝播のメカニズムと機能的意義について考察する.
ニューロンの興奮性の調節やシナプス可塑性において重要な役割を担っているC型タンパク質リン酸化酵素(PKC)は,その酵素活性と関連して細胞内局在が変化する性質を有する(トランスロケーション).GFP-γPKC融合タンパクを発現させたマウス小脳プルキンエ細胞において,平行線維シナプスの高頻度刺激に伴い,刺激部位近傍から樹状突起に沿ってトランスロケーションが伝播する現象が報告されている.最近,坪川は,同じ刺激条件で樹状突起内をほぼ同速度で伝播する細胞内Ca2+波が生じることを見出し,これがγPKCトランスロケーション波をリードしている可能性を指摘した.本研究では,生理学的・解剖学的知見に基づいたプルキンエ細胞の数理モデルを構築し,Ca2+波の再現を試みた.その結果に基づき,トランスロケーション伝播のメカニズムと機能的意義について考察する.
2009/01/13
Lectures
10:30-11:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Gieri Simonett (Vanderbilt University, USA)
Analytic semigroups, maximal regularity and nonlinear parabolic problems
[ Reference URL ]
http://www.math.sci.hokudai.ac.jp/sympo/090113/index.html
Gieri Simonett (Vanderbilt University, USA)
Analytic semigroups, maximal regularity and nonlinear parabolic problems
[ Reference URL ]
http://www.math.sci.hokudai.ac.jp/sympo/090113/index.html
Tuesday Seminar on Topology
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
山下 温 (東京大学大学院数理科学研究科)
Compactification of the homeomorphism group of a graph
山下 温 (東京大学大学院数理科学研究科)
Compactification of the homeomorphism group of a graph
[ Abstract ]
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\\Gamma$ with countably many components,
the homeomorphism group $\\mathcal{H}(\\Gamma)$
and its identity component $\\mathcal{H}_+(\\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\\overline{\\mathcal{H}}(\\Gamma)$ and
$\\overline{\\mathcal{H}}_+(\\Gamma)$ of these groups and describe the
topological type of the pair $(\\overline{\\mathcal{H}}_+(\\Gamma), \\mathcal{H}_+(\\Gamma))$
using the data of $\\Gamma$. I will also discuss the topological structure of
$\\overline{\\mathcal{H}}(\\Gamma)$ where $\\Gamma$ is the circle.
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\\Gamma$ with countably many components,
the homeomorphism group $\\mathcal{H}(\\Gamma)$
and its identity component $\\mathcal{H}_+(\\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\\overline{\\mathcal{H}}(\\Gamma)$ and
$\\overline{\\mathcal{H}}_+(\\Gamma)$ of these groups and describe the
topological type of the pair $(\\overline{\\mathcal{H}}_+(\\Gamma), \\mathcal{H}_+(\\Gamma))$
using the data of $\\Gamma$. I will also discuss the topological structure of
$\\overline{\\mathcal{H}}(\\Gamma)$ where $\\Gamma$ is the circle.
2009/01/12
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
西岡斉治 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
西岡斉治 (東京大学大学院数理科学研究科博士課程)
代数的差分方程式の可解性と既約性
[ Abstract ]
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)
2009/01/09
GCOE lecture series
17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
Lectures
16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
Leevan Ling (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
[ Abstract ]
The condition number of a matrix is commonly used for investigating the
stability of solutions to linear algebraic systems. Recent meshless
techniques for solving PDEs have been known to give rise to
ill-conditioned matrices, yet are still able to produce results that are
close to machine accuracy. In this work, we consider the method of
fundamental solutions (MFS), which is known to solve, with extremely high
accuracy, certain
partial differential equations, namely those for which a fundamental
solution is known. To investigate the applicability of the MFS, either when
the boundary is not analytic or when the boundary data is not harmonic, we
examine the relationship between its accuracy and the effective condition
number.
The condition number of a matrix is commonly used for investigating the
stability of solutions to linear algebraic systems. Recent meshless
techniques for solving PDEs have been known to give rise to
ill-conditioned matrices, yet are still able to produce results that are
close to machine accuracy. In this work, we consider the method of
fundamental solutions (MFS), which is known to solve, with extremely high
accuracy, certain
partial differential equations, namely those for which a fundamental
solution is known. To investigate the applicability of the MFS, either when
the boundary is not analytic or when the boundary data is not harmonic, we
examine the relationship between its accuracy and the effective condition
number.
GCOE Seminars
16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
Leevan Ling (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations
[ Abstract ]
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
2009/01/08
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors
Seminar on Mathematics for various disciplines
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
伊東一文 (North Carolina State University)
Calibration problems for Black-Scholes American Options under the GMMY process
伊東一文 (North Carolina State University)
Calibration problems for Black-Scholes American Options under the GMMY process
[ Abstract ]
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.
GCOE lecture series
17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications
第1講: Reductive p-adic groups and Hecke algebras
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications
第1講: Reductive p-adic groups and Hecke algebras
[ Abstract ]
Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.
We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
[ Reference URL ]Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.
We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009/01/06
Lectures
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)
[ Abstract ]
第3回: 心臓の電気生理
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
第3回: 心臓の電気生理
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
Lectures
14:00-15:30 Room #123 (Graduate School of Math. Sci. Bldg.)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)
[ Abstract ]
第2回: 神経細胞の電気生理
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
第2回: 神経細胞の電気生理
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
2009/01/05
Lectures
16:00-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)
森洋一朗 (ミネソタ大学)
GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)
[ Abstract ]
第1回: 電気生理学の基礎概念入門 (5日 16:00-17:30)
・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性
第2回: 神経細胞の電気生理 (6日 14:00-15:30)
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
第3回: 心臓の電気生理 (6日 16:00-17:30)
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
数理生理学は生理現象を数理モデルを用いて解明しようとする営みであって,実験生物学の定量化,計算機の高速化にともなって急速に発展してきている分野です.この講義では数理生理学の中でも古典的な分野である電気生理学の数理について解説します.
生物学の予備知識は仮定しません.ごく初等的な微分方程式の知識で十分理解できる内容ですが,一部で応用数学の標準的手法(接合漸近展開、均質化極限など)を用います.第1回目の内容が講義全体の基礎となりますが,第2回目と第3回目の講義を独立に聴講することも可能です.またテーマにあわせて最近の話題についても触れる予定です。
講演者のプロフィール:
森洋一朗氏は,東京大学医学部を卒業後,渡米してニューヨーク大学(クーラント研究所)で数学の学位を得ました.すでに数々の賞を受賞しており,数理生物学における若手のホープとして国際的に高く評価されています.
第1回: 電気生理学の基礎概念入門 (5日 16:00-17:30)
・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性
第2回: 神経細胞の電気生理 (6日 14:00-15:30)
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
第3回: 心臓の電気生理 (6日 16:00-17:30)
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
数理生理学は生理現象を数理モデルを用いて解明しようとする営みであって,実験生物学の定量化,計算機の高速化にともなって急速に発展してきている分野です.この講義では数理生理学の中でも古典的な分野である電気生理学の数理について解説します.
生物学の予備知識は仮定しません.ごく初等的な微分方程式の知識で十分理解できる内容ですが,一部で応用数学の標準的手法(接合漸近展開、均質化極限など)を用います.第1回目の内容が講義全体の基礎となりますが,第2回目と第3回目の講義を独立に聴講することも可能です.またテーマにあわせて最近の話題についても触れる予定です。
講演者のプロフィール:
森洋一朗氏は,東京大学医学部を卒業後,渡米してニューヨーク大学(クーラント研究所)で数学の学位を得ました.すでに数々の賞を受賞しており,数理生物学における若手のホープとして国際的に高く評価されています.
2008/12/26
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
軍司圭一 (Postech) 13:30-14:30
On Siegel Eisenstein series of degree two and weight 2
未定
軍司圭一 (Postech) 13:30-14:30
On Siegel Eisenstein series of degree two and weight 2
[ Abstract ]
Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。
未定 (未定) 15:00-16:00Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。
未定
2008/12/19
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)
高野 康 (みずほ第一フィナンシャルテクノロジー)
金融リスク管理と数理Ⅱ(応用編)
高野 康 (みずほ第一フィナンシャルテクノロジー)
金融リスク管理と数理Ⅱ(応用編)
2008/12/18
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Benoit Collins (東大数理/Ottawa 大学)
Some geometric and probabilistic properties of the free quantum group $A_o(n)$
Benoit Collins (東大数理/Ottawa 大学)
Some geometric and probabilistic properties of the free quantum group $A_o(n)$
2008/12/17
Seminar on Probability and Statistics
13:40-14:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Ilia Negri (University of Bergamo, Italy)
Goodness of fit tests for ergodic diffusions by discrete sampling schemes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/09.html
Ilia Negri (University of Bergamo, Italy)
Goodness of fit tests for ergodic diffusions by discrete sampling schemes
[ Abstract ]
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct two kinds of tests based on different types of discrete observations, namely, the data observed discretely in time or in space. We prove that the limit distribution of our tests is the supremum of the standard Brownian motion, and thus our tests are asymptotically distribution free. We also show that our tests are consistent under any fixed alternatives.
joint with Yoichi Nishiyama (Inst. Statist. Math.)
[ Reference URL ]We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct two kinds of tests based on different types of discrete observations, namely, the data observed discretely in time or in space. We prove that the limit distribution of our tests is the supremum of the standard Brownian motion, and thus our tests are asymptotically distribution free. We also show that our tests are consistent under any fixed alternatives.
joint with Yoichi Nishiyama (Inst. Statist. Math.)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/09.html
Seminar on Probability and Statistics
15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Stefano Maria Iacus (Universita degli Studi di Milano, Italy)
Divergences Test Statistics for Discretely Observed Diffusion Processes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html
Stefano Maria Iacus (Universita degli Studi di Milano, Italy)
Divergences Test Statistics for Discretely Observed Diffusion Processes
[ Abstract ]
In this paper we propose the use of $\\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.
joint work with A. De Gregorio
[ Reference URL ]In this paper we propose the use of $\\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.
joint work with A. De Gregorio
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html
Seminar on Probability and Statistics
16:20-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Nicolas Privault (City University of Hong Kong)
Stein estimation of Poisson process intensities
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html
Nicolas Privault (City University of Hong Kong)
Stein estimation of Poisson process intensities
[ Abstract ]
In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
[ Reference URL ]In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html
2008/12/12
Lecture Series on Mathematical Sciences in Soceity
16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)
吉野 伸 (東京電力)
ガスタービン翼の伝熱について
吉野 伸 (東京電力)
ガスタービン翼の伝熱について
2008/12/11
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
佐藤康彦 (北大理)
Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras
佐藤康彦 (北大理)
Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras
2008/12/10
Geometry Seminar
14:45-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
吉田 尚彦 (明治大学大学院理工学研究科) 14:45-16:15
Acyclic polarizations and localization of Riemann-Roch numbers
The topology of symplectic and hyperkahler quotients
吉田 尚彦 (明治大学大学院理工学研究科) 14:45-16:15
Acyclic polarizations and localization of Riemann-Roch numbers
[ Abstract ]
前量子化可能な閉シンプレクティック多様体が(特異)Lagrange ファイバー空間の構造を持つ場合,Riemann-Roch 数が Bohr-Sommerfeld ファイバーの個数と一致することがトーリック多様体,ユニタリー群の Gelfand-Cetlin 系や Riemann 面上の平坦 SU(2) 束のモジュライなどの例で,双方を別々に計算し比較することにより,確かめられている.本講演では,spin^c Dirac 作用素の指数に対する Witten 流の局所化を用いることによって,Riemann-Roch 数が非特異 Bohr-Sommerfeld ファイバー及び特異ファイバーに局所化することを示す.(古田幹雄氏(東大数理),藤田玄氏(学習院大学)との共同研究.論文:arXiv:0804.3258)
Megumi Harada (McMaster University) 16:30-18:00前量子化可能な閉シンプレクティック多様体が(特異)Lagrange ファイバー空間の構造を持つ場合,Riemann-Roch 数が Bohr-Sommerfeld ファイバーの個数と一致することがトーリック多様体,ユニタリー群の Gelfand-Cetlin 系や Riemann 面上の平坦 SU(2) 束のモジュライなどの例で,双方を別々に計算し比較することにより,確かめられている.本講演では,spin^c Dirac 作用素の指数に対する Witten 流の局所化を用いることによって,Riemann-Roch 数が非特異 Bohr-Sommerfeld ファイバー及び特異ファイバーに局所化することを示す.(古田幹雄氏(東大数理),藤田玄氏(学習院大学)との共同研究.論文:arXiv:0804.3258)
The topology of symplectic and hyperkahler quotients
[ Abstract ]
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.
2008/12/09
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Bertrand Deroin (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
Bertrand Deroin (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
[ Abstract ]
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.
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