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Seminar information archive
Seminar information archive ～04/26｜Today's seminar 04/27 | Future seminars 04/28～
2006/11/20
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
野口潤次郎 (東大数理)
Advances and examples in the value distribution theory
野口潤次郎 (東大数理)
Advances and examples in the value distribution theory
2006/11/18
Seminar for Mathematical Past of Asia
16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
安 大玉 (東京大学大学院人文社会系研究科、東アジア思想文化)
17 世紀西洋実用幾何学の東伝と徐光啓の数学観
─『測量法義』『測量異同』『句股義』を中心として─
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.
安 大玉 (東京大学大学院人文社会系研究科、東アジア思想文化)
17 世紀西洋実用幾何学の東伝と徐光啓の数学観
─『測量法義』『測量異同』『句股義』を中心として─
[ Abstract ]
『測量法義』『測量異同』『句股義』は、いずれも 1607 年イエズス会士宣教師マテオ・リッチ(漢名:利瑪竇)と徐光啓によって刊行された『幾何原本』に続いて刊行された測量法および句股術に関する実用数学書である。『幾何原本』が演繹論理にもとづく“度数の宗”といわれる理論書であるのに対し、これら三部作は、いずれも実用レベルの応用数学の範疇に属するものである。
(1)『測量法義』は、西洋の測量用の観測機器である象限義(geometric quadrant)による測高・測深・測遠の方法を中心に西洋の測量術を紹介した書物である。
(2)『測量異同』は、呉敬の『九章算法比類大全』から六つの類型の問題を抽出し、その解法を通じて西法と中法の異同を論じる小論である。
(3)『句股義』は、中法と西法の比較を経て、中法の欠点として「ただ解法を知るのみで、その義は知らない(第能言其法、不能言其義也)」ことを取り上げ、選別された 15 問について、その“義”を論じたものである。
今回の報告は、かかる三部作の内容分析を通じて、徐光啓の三部作構想の狙いがどこにあるかを明らかにし、また三部作のもつ意義を考えてみたい。
[ Reference URL ]『測量法義』『測量異同』『句股義』は、いずれも 1607 年イエズス会士宣教師マテオ・リッチ(漢名:利瑪竇)と徐光啓によって刊行された『幾何原本』に続いて刊行された測量法および句股術に関する実用数学書である。『幾何原本』が演繹論理にもとづく“度数の宗”といわれる理論書であるのに対し、これら三部作は、いずれも実用レベルの応用数学の範疇に属するものである。
(1)『測量法義』は、西洋の測量用の観測機器である象限義(geometric quadrant)による測高・測深・測遠の方法を中心に西洋の測量術を紹介した書物である。
(2)『測量異同』は、呉敬の『九章算法比類大全』から六つの類型の問題を抽出し、その解法を通じて西法と中法の異同を論じる小論である。
(3)『句股義』は、中法と西法の比較を経て、中法の欠点として「ただ解法を知るのみで、その義は知らない(第能言其法、不能言其義也)」ことを取り上げ、選別された 15 問について、その“義”を論じたものである。
今回の報告は、かかる三部作の内容分析を通じて、徐光啓の三部作構想の狙いがどこにあるかを明らかにし、また三部作のもつ意義を考えてみたい。
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.
Infinite Analysis Seminar Tokyo
13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
岩尾慎介 (東大数理)
離散周期戸田方程式の解の超離散化による周期箱玉系の初期値問題の解法
岩尾慎介 (東大数理)
離散周期戸田方程式の解の超離散化による周期箱玉系の初期値問題の解法
[ Abstract ]
周期境界条件をもつ箱玉系の初期値問題の解は、周期境界条件を持つ離散方程式の解を超離散化することによって得られる。離散方程式の解は、あるリーマン面上のアーベル積分を用いて表現される。このリーマン面の周期行列を直接超離散化することによって、任意の初期状態の箱玉系の基本周期を得ることができる。
周期境界条件をもつ箱玉系の初期値問題の解は、周期境界条件を持つ離散方程式の解を超離散化することによって得られる。離散方程式の解は、あるリーマン面上のアーベル積分を用いて表現される。このリーマン面の周期行列を直接超離散化することによって、任意の初期状態の箱玉系の基本周期を得ることができる。
Infinite Analysis Seminar Tokyo
15:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
土谷洋平 (東大数理)
積分変換の項を持つソリトン方程式とその解の構造について
土谷洋平 (東大数理)
積分変換の項を持つソリトン方程式とその解の構造について
[ Abstract ]
ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。
ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。
2006/11/17
Seminar on Probability and Statistics
15:00-16:10 Room #118 (Graduate School of Math. Sci. Bldg.)
清水 泰隆 (大阪大学大学院基礎工学研究科)
Functional estimation of L'evy measure for jump-type processes
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
清水 泰隆 (大阪大学大学院基礎工学研究科)
Functional estimation of L'evy measure for jump-type processes
[ Abstract ]
Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.
[ Reference URL ]Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
2006/11/16
Lectures
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Applied Analysis
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
奈良 光紀 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
奈良 光紀 (東京工業大学)
The large time behavior of graphical surfaces in the mean curvature flow
[ Abstract ]
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
戸松玲治 (東大数理)
商型右余イデアルの特徴づけとポワソン境界の分類
戸松玲治 (東大数理)
商型右余イデアルの特徴づけとポワソン境界の分類
2006/11/15
Lectures
16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules
Mathematical Finance
17:30-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)
塚原 英敦 (成城大)
歪みリスク尺度の1-パラメータ族とその応用
塚原 英敦 (成城大)
歪みリスク尺度の1-パラメータ族とその応用
2006/11/14
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
高瀬将道 (信州大学理学部)
High-codimensional knots spun about manifolds
高瀬将道 (信州大学理学部)
High-codimensional knots spun about manifolds
[ Abstract ]
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.
2006/11/13
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
小野 肇 (東京工業大学)
Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds
小野 肇 (東京工業大学)
Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds
Algebraic Geometry Seminar
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
青木昌雄 (京大数理研)
Hom stacks and Picard stacks
青木昌雄 (京大数理研)
Hom stacks and Picard stacks
2006/11/10
Geometry Seminar
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
中島啓 (京都大学大学院理学研究科)
箙多様体のベッチ数の計算
中島啓 (京都大学大学院理学研究科)
箙多様体のベッチ数の計算
[ Abstract ]
箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.
箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.
Tuesday Seminar on Topology
17:40-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)
樋上和弘 (東京大学大学院理学系研究科 物理)
WRT invariant for Seifert manifolds and modular forms
樋上和弘 (東京大学大学院理学系研究科 物理)
WRT invariant for Seifert manifolds and modular forms
[ Abstract ]
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.
2006/11/09
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
2006/11/08
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Fredric Flin (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Fredric Flin (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
[ Abstract ]
Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
[ Reference URL ]Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
Geometry Seminar
14:40-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
梶原 健 (横浜国立大学大学院工学研究院応用数学) 14:40-16:10
代数多様体の退化とトロピカル幾何
Counting problem in tropical geometry
梶原 健 (横浜国立大学大学院工学研究院応用数学) 14:40-16:10
代数多様体の退化とトロピカル幾何
[ Abstract ]
トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.
西納 武男 (京都大学理学研究科数学教室) 16:30-18:00トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.
Counting problem in tropical geometry
[ Abstract ]
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
蛭川 潤一 (早稲田大学)
LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
蛭川 潤一 (早稲田大学)
LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses
[ Abstract ]
This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
[ Reference URL ]This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
2006/11/07
Lectures
16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
S. Bloch (シカゴ大学)
<連続講演> Graphs and motives
2006/11/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Mihai Paun (Université Henri Poincaré Nancy)
On the extension of twisted pluricanonical forms
Mihai Paun (Université Henri Poincaré Nancy)
On the extension of twisted pluricanonical forms
2006/11/02
Operator Algebra Seminars
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)
水田有一 (東大数理)
Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)
Applied Analysis
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
Messoud Efendiev (ミュンヘン工科大学)
On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy
[ Abstract ]
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
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