本文印刷
全画面プリント
過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
2016年05月10日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
小鳥居 祐香 氏 (東京大学大学院数理科学研究科)
On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)
Tea: Common Room 16:30-17:00
小鳥居 祐香 氏 (東京大学大学院数理科学研究科)
On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)
[ 講演概要 ]
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.
2016年05月09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
厚地 淳 氏 (慶應義塾大学)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
厚地 淳 氏 (慶應義塾大学)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
[ 講演概要 ]
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
河本 陽介 氏 (九州大学大学院数理学府)
無限粒子系の拡散過程の密度保存性について
河本 陽介 氏 (九州大学大学院数理学府)
無限粒子系の拡散過程の密度保存性について
[ 講演概要 ]
無限個粒子を持つ平行移動不変な点過程には確率１で密度（densityもしくはintensity）が存在する。この点過程を可逆測度とする（配置空間値）拡散過程を考える。この拡散過程には任意の時刻で密度が存在し、かつ分布の意味で密度が不変であることは、平行移動不変点過程を可逆測度としていることから明らかである。当講演では、この拡散過程が時間発展において密度が不変であること、つまり容量のレベルで拡散過程は密度を変えないということを話す。
また、この密度保存性と長田-種村の結果を使うことによって、ある種類の無限次元SDEが一意的な強解を持つことを導出できる。時間があれば、どういう種類の無限次元SDEに応用できるかを説明したい。
無限個粒子を持つ平行移動不変な点過程には確率１で密度（densityもしくはintensity）が存在する。この点過程を可逆測度とする（配置空間値）拡散過程を考える。この拡散過程には任意の時刻で密度が存在し、かつ分布の意味で密度が不変であることは、平行移動不変点過程を可逆測度としていることから明らかである。当講演では、この拡散過程が時間発展において密度が不変であること、つまり容量のレベルで拡散過程は密度を変えないということを話す。
また、この密度保存性と長田-種村の結果を使うことによって、ある種類の無限次元SDEが一意的な強解を持つことを導出できる。時間があれば、どういう種類の無限次元SDEに応用できるかを説明したい。
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
田中健一郎 氏 (武蔵野大学工学部)
重み付きハーディ空間における関数近似公式および数値積分公式の設計に対するポテンシャル論的アプローチ (日本語)
田中健一郎 氏 (武蔵野大学工学部)
重み付きハーディ空間における関数近似公式および数値積分公式の設計に対するポテンシャル論的アプローチ (日本語)
[ 講演概要 ]
本発表では，重み付きハーディ空間というある解析関数の空間において，十分に高精度な関数近似公式および数値積分公式の設計法を報告する．ここで考える重み付きハーディ空間は，実軸を含む複素平面上の帯状領域で解析的で，重み関数で指定される重み付きノルムに関して有界となる関数の全体からなる空間である．この空間は，数値計算の対象となるような，一定の条件を満たす解析関数を，適当な変数変換によって変換したものの全体と見なすことができる．このような変数変換は，高精度な計算を実現するためになされる．例えば，有効な数値積分公式として知られている二重指数関数型（DE）公式では，二重指数関数型（DE）変換と呼ばれる変数変換によって，被積分関数を実軸上で二重指数関数的な減衰を持つ関数に変換することが行われる．また，有効な関数近似公式の一つであるDE-Sinc公式でもDE変換が用いられる．
このように，重み付きハーディ空間での関数や積分の近似は基本的な問題と言えるが，この空間において「最適」な公式はそれぞれどのようなものかは，これまで一部の場合についてしか分かっていなかった．本研究では，まず関数近似に対して，一般的な重み関数の場合について，最適な公式を求める問題をポテンシャル論の方法を用いて定式化した．そして，それを近似的に解くことで公式を設計し，また，それらの公式の理論的誤差評価も与えた．これらの公式の厳密な最適性はまだ示せてはいないものの，従来のSinc公式よりも高精度になることが数値実験で観察できている．さらに，数値積分に対しても，類似の方法によって構成した関数近似公式を積分することで公式を設計した．これらについては理論的な誤差評価は得られていないが，やはり数値実験によって，従来の公式よりも高精度な公式が得られていることが観察できた．特に，重み関数が二重指数関数的な減衰を持つ場合について，設計した公式がDE公式よりも高精度となることが観察できた．本研究は，岡山友昭氏（広島市立大学），杉原正顯氏（青山学院大学）との共同研究である．
本発表では，重み付きハーディ空間というある解析関数の空間において，十分に高精度な関数近似公式および数値積分公式の設計法を報告する．ここで考える重み付きハーディ空間は，実軸を含む複素平面上の帯状領域で解析的で，重み関数で指定される重み付きノルムに関して有界となる関数の全体からなる空間である．この空間は，数値計算の対象となるような，一定の条件を満たす解析関数を，適当な変数変換によって変換したものの全体と見なすことができる．このような変数変換は，高精度な計算を実現するためになされる．例えば，有効な数値積分公式として知られている二重指数関数型（DE）公式では，二重指数関数型（DE）変換と呼ばれる変数変換によって，被積分関数を実軸上で二重指数関数的な減衰を持つ関数に変換することが行われる．また，有効な関数近似公式の一つであるDE-Sinc公式でもDE変換が用いられる．
このように，重み付きハーディ空間での関数や積分の近似は基本的な問題と言えるが，この空間において「最適」な公式はそれぞれどのようなものかは，これまで一部の場合についてしか分かっていなかった．本研究では，まず関数近似に対して，一般的な重み関数の場合について，最適な公式を求める問題をポテンシャル論の方法を用いて定式化した．そして，それを近似的に解くことで公式を設計し，また，それらの公式の理論的誤差評価も与えた．これらの公式の厳密な最適性はまだ示せてはいないものの，従来のSinc公式よりも高精度になることが数値実験で観察できている．さらに，数値積分に対しても，類似の方法によって構成した関数近似公式を積分することで公式を設計した．これらについては理論的な誤差評価は得られていないが，やはり数値実験によって，従来の公式よりも高精度な公式が得られていることが観察できた．特に，重み関数が二重指数関数的な減衰を持つ場合について，設計した公式がDE公式よりも高精度となることが観察できた．本研究は，岡山友昭氏（広島市立大学），杉原正顯氏（青山学院大学）との共同研究である．
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
Mikael Pichot 氏 (McGIll大学/東大数理)
Surgery theory and discrete groups (English)
Mikael Pichot 氏 (McGIll大学/東大数理)
Surgery theory and discrete groups (English)
FMSPレクチャーズ
15:00-17:00 数理科学研究科棟(駒場) 002号室
Michael Tuite 氏 (National University of Ireland, Galway)
Vertex Operator Algebras according to Newton (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tuite.pdf
Michael Tuite 氏 (National University of Ireland, Galway)
Vertex Operator Algebras according to Newton (ENGLISH)
[ 講演概要 ]
In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.
[ 参考URL ]In this lecture I will give an introduction to Vertex Operator Algebras (VOAs) using elementary methods originally due to Isaac Newton. I will also discuss a class of exceptional VOAs including the Moonshine module which share a number of fundamental properties in common.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Tuite.pdf
2016年04月27日(水)
PDE実解析研究会
15:00-16:00 数理科学研究科棟(駒場) 056号室
通常の曜日、時刻と異なります。
Elijah Liflyand 氏 (Bar-Ilan University, Israel)
Fourier transform versus Hilbert transform (English)
http://u.math.biu.ac.il/~liflyand/
通常の曜日、時刻と異なります。
Elijah Liflyand 氏 (Bar-Ilan University, Israel)
Fourier transform versus Hilbert transform (English)
[ 講演概要 ]
We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.
1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?
We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.
2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.
We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.
3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.
There are multidimensional generalizations of these results.
[ 参考URL ]We present several results in which the interplay between the Fourier transform and the Hilbert transform is of special form and importance.
1. In 50-s (Kahane, Izumi-Tsuchikura, Boas, etc.), the following problem in Fourier Analysis attracted much attention: Let $\{a_k\},$ $k=0,1,2...,$ be the sequence of the Fourier coefficients of the absolutely convergent sine (cosine) Fourier series of a function $f:\mathbb T=[-\pi,\pi)\to \mathbb C,$ that is $\sum |a_k|<\infty.$ Under which conditions on $\{a_k\}$ the re-expansion of $f(t)$ ($f(t)-f(0)$, respectively) in the cosine (sine) Fourier series will also be absolutely convergent?
We solve a similar problem for functions on the whole axis and their Fourier transforms. Generally, the re-expansion of a function with integrable cosine (sine) Fourier transform in the sine (cosine) Fourier transform is integrable if and only if not only the initial Fourier transform is integrable but also the Hilbert transform of the initial Fourier transform is integrable.
2. The following result is due to Hardy and Littlewood: If a (periodic) function $f$ and its conjugate $\widetilde f$ are both of bounded variation, their Fourier series converge absolutely.
We generalize the Hardy-Littlewood theorem (joint work with U. Stadtmüller) to the Fourier transform of a function on the real axis and its modified Hilbert transform. The initial Hardy-Littlewood theorem is a partial case of this extension, when the function is taken to be with compact support.
3. These and other problems are integrated parts of harmonic analysis of functions of bounded variation. We have found the maximal space for the integrability of the Fourier transform of a function of bounded variation. Along with those known earlier, various interesting new spaces appear in this study. Their inter-relations lead, in particular, to improvements of Hardy's inequality.
There are multidimensional generalizations of these results.
http://u.math.biu.ac.il/~liflyand/
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 056号室
大井雅雄 氏 (東京大学数理科学研究科)
On the endoscopic lifting of simple supercuspidal representations (Japanese)
大井雅雄 氏 (東京大学数理科学研究科)
On the endoscopic lifting of simple supercuspidal representations (Japanese)
2016年04月26日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
松原 宰栄 氏 (東大数理)
On microlocal analysis of Gauss-Manin connections for boundary singularities (Japanese)
松原 宰栄 氏 (東大数理)
On microlocal analysis of Gauss-Manin connections for boundary singularities (Japanese)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
This talk is given in Japanese due to the speaker's intension.
尾高悠志 氏 (京大数学教室)
A gentle introduction to K-stability and its recent development (Japanese)
https://sites.google.com/site/yujiodaka2013/
This talk is given in Japanese due to the speaker's intension.
尾高悠志 氏 (京大数学教室)
A gentle introduction to K-stability and its recent development (Japanese)
[ 講演概要 ]
K安定性とは複素代数多様体上の「標準的な」ケーラー計量の存在問題に端を発する，代数幾何的な概念です．二木先生や満渕先生等の先駆的な仕事に感化されて導入され，特に近年ホットに研究され始めている一方，未だその大半はより微分幾何的な研究者の方々や背景の中でなされているように講演者には感じられます．
代数幾何的にもどのように面白いか，どういった意義があるかに私見で軽く触れた上で，その基礎付けをより拡張した枠組みで説明しつつ，最先端でどのようなことが問題になっているかをいくらか（私の力量と時間の許す限り）解説しつつ，文献をご紹介できればと思っています
[ 参考URL ]K安定性とは複素代数多様体上の「標準的な」ケーラー計量の存在問題に端を発する，代数幾何的な概念です．二木先生や満渕先生等の先駆的な仕事に感化されて導入され，特に近年ホットに研究され始めている一方，未だその大半はより微分幾何的な研究者の方々や背景の中でなされているように講演者には感じられます．
代数幾何的にもどのように面白いか，どういった意義があるかに私見で軽く触れた上で，その基礎付けをより拡張した枠組みで説明しつつ，最先端でどのようなことが問題になっているかをいくらか（私の力量と時間の許す限り）解説しつつ，文献をご紹介できればと思っています
https://sites.google.com/site/yujiodaka2013/
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
植木 潤 氏 (東京大学大学院数理科学研究科)
Arithmetic topology on branched covers of 3-manifolds (JAPANESE)
Tea: Common Room 16:30-17:00
植木 潤 氏 (東京大学大学院数理科学研究科)
Arithmetic topology on branched covers of 3-manifolds (JAPANESE)
[ 講演概要 ]
The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.
In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.
The analogy between 3-dimensional topology and number theory was first pointed out by Mazur in the 1960s, and it has been studied systematically by Kapranov, Reznikov, Morishita, and others. In their analogies, for example, knots and 3-manifolds correspond to primes and number rings respectively. The study of these analogies is called arithmetic topology now.
In my talk, based on their dictionary of analogies, we study analogues of idelic class field theory, Iwasawa theory, and Galois deformation theory in the context of 3-dimensional topology, and establish various foundational analogies in arithmetic topology.
統計数学セミナー
16:10-17:10 数理科学研究科棟(駒場) 123号室
Teppei Ogihara 氏 (Institute of Statistical Mathematics, JST PRESTO, JST CREST)
LAMN property and optimal estimation for diffusion with non synchronous observations
Teppei Ogihara 氏 (Institute of Statistical Mathematics, JST PRESTO, JST CREST)
LAMN property and optimal estimation for diffusion with non synchronous observations
[ 講演概要 ]
We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.
We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.
統計数学セミナー
13:00-14:20 数理科学研究科棟(駒場) 123号室
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 1
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 1
[ 講演概要 ]
In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.
In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.
統計数学セミナー
14:30-15:50 数理科学研究科棟(駒場) 123号室
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 2
Ciprian Tudor 氏 (Université de Lille 1)
Stochastic heat equation with fractional noise 2
[ 講演概要 ]
We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.
We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.
数理人口学・数理生物学セミナー
15:00-16:00 数理科学研究科棟(駒場) 128演習室号室
Lev Idels 氏 (Vanvouver Island University)
Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)
https://web.viu.ca/idelsl/
Lev Idels 氏 (Vanvouver Island University)
Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)
[ 講演概要 ]
In general, delay differential equations provide a richer mathematical
framework (compared with ordinary differential equations) for the
analysis of biosystems dynamics. The inclusion of explicit time lags in
tumor growth models allows direct reference to experimentally measurable
and/or controllable cell growth characteristics. For three different
types of angiogenesis models with variable delays, we consider either
continuous or impulse therapy that eradicates tumor cells and suppresses
angiogenesis. It was shown that with the growth of delays, even
constant, the equilibrium can lose its stability, and sustainable
oscillation, as well as chaotic behavior, can be observed. The analysis
outlines the difficulties which occur in the case of unbounded growth
rates, such as classical Gompertz model, for small volumes of cancer
cells compared to available blood vessels. The Wheldon model (1975) of a
Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of
recent discovery that this model has a major drawback.
[ 参考URL ]In general, delay differential equations provide a richer mathematical
framework (compared with ordinary differential equations) for the
analysis of biosystems dynamics. The inclusion of explicit time lags in
tumor growth models allows direct reference to experimentally measurable
and/or controllable cell growth characteristics. For three different
types of angiogenesis models with variable delays, we consider either
continuous or impulse therapy that eradicates tumor cells and suppresses
angiogenesis. It was shown that with the growth of delays, even
constant, the equilibrium can lose its stability, and sustainable
oscillation, as well as chaotic behavior, can be observed. The analysis
outlines the difficulties which occur in the case of unbounded growth
rates, such as classical Gompertz model, for small volumes of cancer
cells compared to available blood vessels. The Wheldon model (1975) of a
Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of
recent discovery that this model has a major drawback.
https://web.viu.ca/idelsl/
2016年04月25日(月)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
山下真 氏 (お茶の水女子大)
Graded twisting of quantum groups, actions, and categories
山下真 氏 (お茶の水女子大)
Graded twisting of quantum groups, actions, and categories
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
山盛 厚伺 氏 (台湾中央研究院)
The representative domain and its applications (JAPANESE)
山盛 厚伺 氏 (台湾中央研究院)
The representative domain and its applications (JAPANESE)
[ 講演概要 ]
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
中島 秀太 氏 (数理解析研究所)
Concentration results for directed polymer with unbouded jumps
中島 秀太 氏 (数理解析研究所)
Concentration results for directed polymer with unbouded jumps
2016年04月22日(金)
統計数学セミナー
10:30-11:50 数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 1
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 1
[ 講演概要 ]
In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.
In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.
統計数学セミナー
12:50-14:10 数理科学研究科棟(駒場) 002号室
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 2
Ciprian Tudor 氏 (Université de Lille 1)
Stein method and Malliavin calculus : theory and some applications to limit theorems 2
[ 講演概要 ]
In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.
In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.
統計数学セミナー
14:20-15:50 数理科学研究科棟(駒場) 002号室
Seiichiro Kusuoka 氏 (Okayama University)
Equivalence between the convergence in total variation and that of the Stein factor to the invariant measures of diffusion processes
Seiichiro Kusuoka 氏 (Okayama University)
Equivalence between the convergence in total variation and that of the Stein factor to the invariant measures of diffusion processes
[ 講演概要 ]
We consider the characterization of the convergence of distributions to a given distribution in a certain class by using Stein's equation and Malliavin calculus with respect to the invariant measures of one-dimensional diffusion processes. Precisely speaking, we obtain an estimate between the so-called Stein factor and the total variation norm, and the equivalence between the convergence of the distributions in total variation and that of the Stein factor. This talk is based on the joint work with C.A.Tudor (arXiv:1310.3785).
We consider the characterization of the convergence of distributions to a given distribution in a certain class by using Stein's equation and Malliavin calculus with respect to the invariant measures of one-dimensional diffusion processes. Precisely speaking, we obtain an estimate between the so-called Stein factor and the total variation norm, and the equivalence between the convergence of the distributions in total variation and that of the Stein factor. This talk is based on the joint work with C.A.Tudor (arXiv:1310.3785).
統計数学セミナー
16:10-17:10 数理科学研究科棟(駒場) 002号室
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Asymptotic expansion and estimation of volatility
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Asymptotic expansion and estimation of volatility
[ 講演概要 ]
Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.
Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.
2016年04月21日(木)
幾何コロキウム
17:00-18:00 数理科学研究科棟(駒場) 123号室
集中講義に続いて行います.いつもと違う部屋ですのでご注意下さい.
本多正平 氏 (東北大学)
Spectral convergence under bounded Ricci curvature (Japanese)
集中講義に続いて行います.いつもと違う部屋ですのでご注意下さい.
本多正平 氏 (東北大学)
Spectral convergence under bounded Ricci curvature (Japanese)
[ 講演概要 ]
For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.
For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.
FMSPレクチャーズ
15:00-16:00, 16:10-17:10 数理科学研究科棟(駒場) 002号室
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf
2016年04月20日(水)
FMSPレクチャーズ
15:00-16:00, 16:10-17:10 数理科学研究科棟(駒場) 002号室
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf
Aniceto Murillo et al 氏 (Universidad de Malaga)
Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Murillo.pdf
< 前へ 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186 次へ >
