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過去の記録
過去の記録 ～04/18｜本日 04/19 | 今後の予定 04/20～
講演会
17:00-18:00 数理科学研究科棟(駒場) 128号室
Guoniu Han 氏 (Université de Strasbourg/CNRS)
Integer partitions and hook length formulas (ENGLISH)
www-irma.u-strasbg.fr/~guoniu/
Guoniu Han 氏 (Université de Strasbourg/CNRS)
Integer partitions and hook length formulas (ENGLISH)
[ 講演概要 ]
Integer partitions were first studied by Euler.
The Ferrers diagram of an integer partition is a very useful tool for
visualizing partitions. A Ferrers diagram is turned into a Young tableau
by filling each cell with a unique integer satisfying some conditions.
The number of Young tableaux is given by the famous hook length formula,
discovered by Frame-Robinson-Thrall.
In this talk, we introduce the hook length expansion technique and
explain how to find old and new hook length formulas for integer
partitions. In particular, we derive an expansion formula for the
powers of the Euler Product in terms of hook lengths, which is also
discovered by Nekrasov-Okounkov and Westburg. We obtain an extension
by adding two more parameters. It appears to be a discrete
interpolation between the Macdonald identities and the generating
function for t-cores. Several other summations involving hook length,
in particular, the Okada-Panova formula, will also be discussed.
[ 参考URL ]Integer partitions were first studied by Euler.
The Ferrers diagram of an integer partition is a very useful tool for
visualizing partitions. A Ferrers diagram is turned into a Young tableau
by filling each cell with a unique integer satisfying some conditions.
The number of Young tableaux is given by the famous hook length formula,
discovered by Frame-Robinson-Thrall.
In this talk, we introduce the hook length expansion technique and
explain how to find old and new hook length formulas for integer
partitions. In particular, we derive an expansion formula for the
powers of the Euler Product in terms of hook lengths, which is also
discovered by Nekrasov-Okounkov and Westburg. We obtain an extension
by adding two more parameters. It appears to be a discrete
interpolation between the Macdonald identities and the generating
function for t-cores. Several other summations involving hook length,
in particular, the Okada-Panova formula, will also be discussed.
www-irma.u-strasbg.fr/~guoniu/
2017年10月16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
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically $k$-convex domains in terms of hyperbolic metric
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically $k$-convex domains in terms of hyperbolic metric
[ 講演概要 ]
It is known that a plane domain $X$ with hyperbolic metric $h_X=h_X(z)|dz|$ of constant curvature $-4$ is (Euclidean) convex if and only if $h_X(z)d_X(z)\ge 1/2$, where $d_X(z)$ denotes the Euclidean distance from a point $z$ in $X$ to the boundary of $X$. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic $k$-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density $h_X(z)$ near the boundary.
It is known that a plane domain $X$ with hyperbolic metric $h_X=h_X(z)|dz|$ of constant curvature $-4$ is (Euclidean) convex if and only if $h_X(z)d_X(z)\ge 1/2$, where $d_X(z)$ denotes the Euclidean distance from a point $z$ in $X$ to the boundary of $X$. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic $k$-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density $h_X(z)$ near the boundary.
2017年10月11日(水)
講演会
11:00-12:00 数理科学研究科棟(駒場) 128号室
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
Ahmed Abbes 氏 (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
[ 講演概要 ]
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
Michael Temkin 氏 (The Hebrew University of Jerusalem)
Logarithmic resolution of singularities (ENGLISH)
Michael Temkin 氏 (The Hebrew University of Jerusalem)
Logarithmic resolution of singularities (ENGLISH)
[ 講演概要 ]
The famous Hironaka's theorem asserts that any integral algebraic variety X of characteristic zero can be modified to a smooth variety X_res by a sequence of blowings up. Later it was shown that one can make this compatible with smooth morphisms Y --> X in the sense that Y_res --> Y is the pullback of X_res --> X. In a joint project with D. Abramovich and J. Wlodarczyk, we construct a new algorithm which is compatible with all log smooth morphisms (e.g. covers ramified along exceptional divisors). We expect that this algorithm will naturally extend to an algorithm of resolution of morphisms to log smooth ones. In particular, this should lead to functorial semistable reduction theorems. In my talk I will tell about main ideas of the classical algorithm and will then discuss logarithmic and stack-theoretic modifications we had to make in the new algorithm.
The famous Hironaka's theorem asserts that any integral algebraic variety X of characteristic zero can be modified to a smooth variety X_res by a sequence of blowings up. Later it was shown that one can make this compatible with smooth morphisms Y --> X in the sense that Y_res --> Y is the pullback of X_res --> X. In a joint project with D. Abramovich and J. Wlodarczyk, we construct a new algorithm which is compatible with all log smooth morphisms (e.g. covers ramified along exceptional divisors). We expect that this algorithm will naturally extend to an algorithm of resolution of morphisms to log smooth ones. In particular, this should lead to functorial semistable reduction theorems. In my talk I will tell about main ideas of the classical algorithm and will then discuss logarithmic and stack-theoretic modifications we had to make in the new algorithm.
2017年10月10日(火)
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
與倉 昭治 氏 (鹿児島大学)
Poset-stratified spaces and some applications (JAPANESE)
Tea: Common Room 17:00-17:30
與倉 昭治 氏 (鹿児島大学)
Poset-stratified spaces and some applications (JAPANESE)
[ 講演概要 ]
A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).
A poset-stratified space is a continuous map from a topological space to a poset with the Alexandroff topology. In this talk I will discuss some thoughts about poset-stratified spaces from a naive general-topological viewpoint, some applications such as hyperplane arrangements and poset-stratified space structures of hom-sets, and related topics such as characteristic classes of vector bundles, dependence of maps (by Borsuk) and dependence of cohomology classes (by Thom).
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
中野張 氏 (東京工業大学大学院情報理工学院)
線形・非線形放物型偏微分方程式に対するメッシュフリー選点法
中野張 氏 (東京工業大学大学院情報理工学院)
線形・非線形放物型偏微分方程式に対するメッシュフリー選点法
[ 講演概要 ]
一般に，後退確率微分方程式や確率最適制御の解は非線形放物型偏微分方程式により記述される．これらの非線形偏微分方程式の多くに対しては，滑らかさが期待できないため古典解ではなく粘性解の枠組みが採用される．よって応用のためは，解くべき偏微分方程式の粘性解に収束し，かつ多次元の問題に適用可能な数値解法が必要とされるが，既存手法の中には未だ決定的なものは存在しない状況である．
本講演では，上述の問題を解決するためにメッシュフリー選点法の適用を提案し，最近の研究成果について報告する．この目的のため，(1) 種々の確率論的問題と放物型偏微分方程式の関係の概説，(2) 粘性解の紹介，(3) 既存数値解法の紹介，(4) 動径基底関数による補間理論の紹介，(5) メッシュフリー選点法の導出，(6) 収束証明に関する結果の紹介，
という流れで話を進める．
また，フィルタリング問題に現れる線形確率偏微分方程式を対象に，メッシュフリー選点法の収束が保証される動径基底関数やグリッド点の具体例について報告する．
一般に，後退確率微分方程式や確率最適制御の解は非線形放物型偏微分方程式により記述される．これらの非線形偏微分方程式の多くに対しては，滑らかさが期待できないため古典解ではなく粘性解の枠組みが採用される．よって応用のためは，解くべき偏微分方程式の粘性解に収束し，かつ多次元の問題に適用可能な数値解法が必要とされるが，既存手法の中には未だ決定的なものは存在しない状況である．
本講演では，上述の問題を解決するためにメッシュフリー選点法の適用を提案し，最近の研究成果について報告する．この目的のため，(1) 種々の確率論的問題と放物型偏微分方程式の関係の概説，(2) 粘性解の紹介，(3) 既存数値解法の紹介，(4) 動径基底関数による補間理論の紹介，(5) メッシュフリー選点法の導出，(6) 収束証明に関する結果の紹介，
という流れで話を進める．
また，フィルタリング問題に現れる線形確率偏微分方程式を対象に，メッシュフリー選点法の収束が保証される動径基底関数やグリッド点の具体例について報告する．
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
金光 秋博 氏 (東大数理)
Classification of Mukai pairs with corank 3 (English or Japanese)
金光 秋博 氏 (東大数理)
Classification of Mukai pairs with corank 3 (English or Japanese)
[ 講演概要 ]
A Mukai pair $(X,E)$ is a pair of a Fano manifold $X$ and an ample vector bundle $E$ of rank $r$ on $X$ such that $c_1(X)=c_1(E)$. Study of such pairs was proposed by Mukai. It is known that, for a Mukai pair $(X,E)$, the rank $r$ of the bundle $E$ is at most $\dim X +1$, and Mukai conjectured the explicit
classification with $r \geq \dim X$. The above conjecture was solved independently by Fujita, Peternell and Ye-Zhang. Also the classification of Mukai pairs with $r= \dim X -1$ was given by Peternell-Szurek-Wi\'sniewski. In this talk I will give the classification of Mukai pairs with $r= \dim X -2$ and $\dim X \geq 5$.
A Mukai pair $(X,E)$ is a pair of a Fano manifold $X$ and an ample vector bundle $E$ of rank $r$ on $X$ such that $c_1(X)=c_1(E)$. Study of such pairs was proposed by Mukai. It is known that, for a Mukai pair $(X,E)$, the rank $r$ of the bundle $E$ is at most $\dim X +1$, and Mukai conjectured the explicit
classification with $r \geq \dim X$. The above conjecture was solved independently by Fujita, Peternell and Ye-Zhang. Also the classification of Mukai pairs with $r= \dim X -1$ was given by Peternell-Szurek-Wi\'sniewski. In this talk I will give the classification of Mukai pairs with $r= \dim X -2$ and $\dim X \geq 5$.
2017年10月06日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 002号室
宮地晶彦 氏 (東京女子大学)
調和解析における特異積分と実関数論の方法 (JAPANESE)
http://lab.twcu.ac.jp/miyachi/English.html
宮地晶彦 氏 (東京女子大学)
調和解析における特異積分と実関数論の方法 (JAPANESE)
[ 講演概要 ]
フーリエ級数の収束など古典的な調和解析の問題の多くは、
特異積分の評価の問題に帰着される。特異積分を調べる
実関数論の方法で繰り返し現れるのは最大関数と２乗型関数である。
講演では、特異積分の評価に関わる古典的な方法を振り返りながら、
双線形の特異積分など最近の話題の一端を紹介してみたい。
[ 参考URL ]フーリエ級数の収束など古典的な調和解析の問題の多くは、
特異積分の評価の問題に帰着される。特異積分を調べる
実関数論の方法で繰り返し現れるのは最大関数と２乗型関数である。
講演では、特異積分の評価に関わる古典的な方法を振り返りながら、
双線形の特異積分など最近の話題の一端を紹介してみたい。
http://lab.twcu.ac.jp/miyachi/English.html
2017年10月03日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Athanase Papadopoulos 氏 (IRMA, Université de Strasbourg)
Transitional geometry (ENGLISH)
Tea: Common Room 16:30-17:00
Athanase Papadopoulos 氏 (IRMA, Université de Strasbourg)
Transitional geometry (ENGLISH)
[ 講演概要 ]
I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.
I will describe transitions, that is, paths between hyperbolic and spherical geometry, passing through the Euclidean. This is based on joint work with Norbert A’Campo and recent joint work with A’Campo and Yi Huang.
2017年10月02日(月)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Mikael Pichot 氏 (RIMS, Kyoto Univ./McGill Univ.)
Introduction to intermediate rank geometry (English)
Mikael Pichot 氏 (RIMS, Kyoto Univ./McGill Univ.)
Introduction to intermediate rank geometry (English)
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
千葉 優作 氏 (お茶の水女子大学)
The extension of holomorphic functions on a non-pluriharmonic locus
千葉 優作 氏 (お茶の水女子大学)
The extension of holomorphic functions on a non-pluriharmonic locus
[ 講演概要 ]
Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. In this talk, we show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function on $\Omega$.
Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. In this talk, we show that any holomorphic function defined on a connected open neighborhood of the support of $(i\partial \overline{\partial}\varphi)^{n-3}$ can be extended to the holomorphic function on $\Omega$.
2017年09月27日(水)
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
加藤和也 氏 (University of Chicago)
Height functions for motives, Hodge analogues, and Nevanlinna analogues (ENGLISH)
加藤和也 氏 (University of Chicago)
Height functions for motives, Hodge analogues, and Nevanlinna analogues (ENGLISH)
[ 講演概要 ]
We compare height functions for (1) points of an algebraic variety over a number field, (2) motives over a number field, (3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field, (4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain. Usual Nevanlinna theory uses height functions for (5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study.
We compare height functions for (1) points of an algebraic variety over a number field, (2) motives over a number field, (3) variations of Hodge structure with log degeneration on a projective smooth curve over the complex number field, (4) horizontal maps from the complex plane C to a toroidal partial compactification of the period domain. Usual Nevanlinna theory uses height functions for (5) holomorphic maps f from C to a compactification of an agebraic variety V and considers how often the values of f lie outside V. Vojta compares (1) and (5). In (4), V is replaced by a period domain. The comparisons of (1)--(4) provide many new questions to study.
2017年09月26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, Lie群論・表現論セミナーと合同
関口 英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (JAPANESE)
Tea: Common Room 16:30-17:00, Lie群論・表現論セミナーと合同
関口 英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (JAPANESE)
[ 講演概要 ]
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds,
namely, that of positive $k$-planes and that of negative $k$-planes.
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds,
namely, that of positive $k$-planes and that of negative $k$-planes.
Lie群論・表現論セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同
関口英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (Japanese)
トポロジー火曜セミナーと合同
関口英子 氏 (東京大学大学院数理科学研究科)
Representations of Semisimple Lie Groups and Penrose Transform (Japanese)
[ 講演概要 ]
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.
The classical Penrose transform is generalized to an intertwining operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of (real) semisimple Lie groups.
I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold.
To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain.
Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes.
2017年09月25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
Christophe Mourougane 氏 (Université de Rennes 1)
Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties
Christophe Mourougane 氏 (Université de Rennes 1)
Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties
[ 講演概要 ]
It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.
Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.
It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.
Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.
2017年09月11日(月)
講演会
15:30-16:30 数理科学研究科棟(駒場) 002号室
Jean Zinn-Justin 氏 (CEA Saclay)
3D field theories with Chern-Simons term for large N in the Weyl gauge
(ENGLISH)
Jean Zinn-Justin 氏 (CEA Saclay)
3D field theories with Chern-Simons term for large N in the Weyl gauge
(ENGLISH)
[ 講演概要 ]
ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.
We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.
We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.
Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.
ADS/CFT correspondance has led to a number of conjectures concerning, conformal invariant, U(N) symmetric 3D field theories with Chern-Simons term for N large. An example is boson-fermion duality. This has prompted a number of calculations to shed extra light on the ADS/CFT correspondance.
We study here the example of gauge invariant fermion matter coupled to a Chern-Simons term. In contrast with previous calculations, which employ the light-cone gauge, we use the more conventional temporal gauge. We calculate several gauge invariant correlation functions. We consider general massive matter and determine the conditions for conformal invariance. We compare massless results with previous calculations, providing a check of gauge independence.
We examine also the possibility of spontaneous breaking of scale invariance and show that this requires the addition of an auxiliary scalar field.
Our method is based on field integral and steepest descent. The saddle point equations involve non-local fields and take the form of a set of integral equations that we solve exactly.
2017年08月30日(水)
博士論文発表会
10:00-11:15 数理科学研究科棟(駒場) 128号室
佐藤 僚 氏 (東京大学大学院数理科学研究科)
Modular invariant representations over the N=2 superconformal algebra
（モジュラー不変性をもつN=2 超共形代数の表現について） (JAPANESE)
佐藤 僚 氏 (東京大学大学院数理科学研究科)
Modular invariant representations over the N=2 superconformal algebra
（モジュラー不変性をもつN=2 超共形代数の表現について） (JAPANESE)
2017年08月25日(金)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 128号室
CLINET, Simon 氏 (東京大学大学院数理科学研究科)
Statistical inference for point processes and application to Limit Order Book
（点過程に対する統計的推測及びリミットオーダーブックへの応用） (ENGLISH)
CLINET, Simon 氏 (東京大学大学院数理科学研究科)
Statistical inference for point processes and application to Limit Order Book
（点過程に対する統計的推測及びリミットオーダーブックへの応用） (ENGLISH)
2017年08月23日(水)
統計数学セミナー
13:30-14:40 数理科学研究科棟(駒場) 052号室
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
[ 講演概要 ]
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
2017年07月28日(金)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Benoit Collins 氏 (京大理)
Free orthogonal groups and quantum information (English)
Benoit Collins 氏 (京大理)
Free orthogonal groups and quantum information (English)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 128号室
江尻 祥 氏 (東京大学大学院数理科学研究科)
Studies on algebraic fiber spaces in positive characteristic
（正標数の代数的ファイバー空間に関する研究） (JAPANESE)
江尻 祥 氏 (東京大学大学院数理科学研究科)
Studies on algebraic fiber spaces in positive characteristic
（正標数の代数的ファイバー空間に関する研究） (JAPANESE)
博士論文発表会
15:45-17:00 数理科学研究科棟(駒場) 128号室
金光 秋博 氏 (東京大学大学院数理科学研究科)
Studies on Fano manifolds and vector bundles
（Fano多様体とベクトル束の研究） (JAPANESE)
金光 秋博 氏 (東京大学大学院数理科学研究科)
Studies on Fano manifolds and vector bundles
（Fano多様体とベクトル束の研究） (JAPANESE)
2017年07月25日(火)
博士論文発表会
15:00-16:15 数理科学研究科棟(駒場) 128号室
桑垣 樹 氏 (東京大学大学院数理科学研究科)
The nonequivariant coherent-constructible correspondence for toric stacks
(トーリックスタックにおける連接-構成可能対応) (JAPANESE)
桑垣 樹 氏 (東京大学大学院数理科学研究科)
The nonequivariant coherent-constructible correspondence for toric stacks
(トーリックスタックにおける連接-構成可能対応) (JAPANESE)
2017年07月21日(金)
社会数理コロキウム
16:30-17:30 数理科学研究科棟(駒場) 123号室
17:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
数理科学を原理とする第4次産業革命 (JAPANESE)
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20170721.pdf
17:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
数理科学を原理とする第4次産業革命 (JAPANESE)
[ 講演概要 ]
第1次産業革命は、力学を原理としてイギリスで生まれた紡績機械・蒸気機関・石炭製鉄の発明で、海運業・鉄道業というサービス産業を産み出した。第2次産業革命は、化学反応を原理として、ドイツで生まれた物質科学による内燃機関の発明によってアメリカで発展したもので、自動車物流・電力供給というサービス産業を産み出した。第3次産業革命は、量子物理学を原理として、アメリカで生まれた通信・コンピュータ・半導体の発明によって金融・流通というサービス産業を革新的に発展させた。このように、産業革命とは、ものづくりがサービスと連携することにその本質がある。すなわち、第2次産業と第3次産業との連携にその本質がある。
そこで、第4次産業革命を数理科学を原理とする「デジタル・トランスフォーメーション革命」と捉え、従来成立しているあらゆる産業をデジタル化すること、すなわちビジネスモデルを転換する新たな産業革命であると考えることが重要である。
本講義では、この新たな産業革命は、IoT/ビッグデータ/AI（人工知能）とこれを支える数理科学の役割について述べることとする。
[ 参考URL ]第1次産業革命は、力学を原理としてイギリスで生まれた紡績機械・蒸気機関・石炭製鉄の発明で、海運業・鉄道業というサービス産業を産み出した。第2次産業革命は、化学反応を原理として、ドイツで生まれた物質科学による内燃機関の発明によってアメリカで発展したもので、自動車物流・電力供給というサービス産業を産み出した。第3次産業革命は、量子物理学を原理として、アメリカで生まれた通信・コンピュータ・半導体の発明によって金融・流通というサービス産業を革新的に発展させた。このように、産業革命とは、ものづくりがサービスと連携することにその本質がある。すなわち、第2次産業と第3次産業との連携にその本質がある。
そこで、第4次産業革命を数理科学を原理とする「デジタル・トランスフォーメーション革命」と捉え、従来成立しているあらゆる産業をデジタル化すること、すなわちビジネスモデルを転換する新たな産業革命であると考えることが重要である。
本講義では、この新たな産業革命は、IoT/ビッグデータ/AI（人工知能）とこれを支える数理科学の役割について述べることとする。
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20170721.pdf
2017年07月18日(火)
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
呼子 笛太郎 氏 (東北大理)
On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)
呼子 笛太郎 氏 (東北大理)
On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)
[ 講演概要 ]
In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.
In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.
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