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過去の記録
過去の記録 ～04/23｜本日 04/24 | 今後の予定 04/25～
2016年11月02日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Yves André 氏 (CNRS, Institut de Mathématiques de Jussieu)
Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)
Yves André 氏 (CNRS, Institut de Mathématiques de Jussieu)
Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)
[ 講演概要 ]
According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理,
Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理,
Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
2016年11月01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
大場 貴裕 氏 (東京工業大学)
Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)
Tea: Common Room 16:30-17:00
大場 貴裕 氏 (東京工業大学)
Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)
[ 講演概要 ]
A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.
Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.
A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.
Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.
FMSPレクチャーズ
10:30-11:30 数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (1) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (1) (ENGLISH)
[ 講演概要 ]
https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照
[ 参考URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf
FMSPレクチャーズ
13:15-14:15 数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (2) (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (2) (ENGLISH)
[ 講演概要 ]
https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照
[ 参考URL ]https://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf を参照
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf
統計数学セミナー
10:40-11:30 数理科学研究科棟(駒場) 123号室
Yuta Koike 氏 (Tokyo Metropolitan University, JST CREST)
Wavelet-based methods for high-frequency lead-lag analysis
Yuta Koike 氏 (Tokyo Metropolitan University, JST CREST)
Wavelet-based methods for high-frequency lead-lag analysis
[ 講演概要 ]
We propose a novel framework to investigate the lead-lag effect between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. This talk is based on a joint work of Prof. Takaki Hayashi (Keio University).
We propose a novel framework to investigate the lead-lag effect between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. This talk is based on a joint work of Prof. Takaki Hayashi (Keio University).
統計数学セミナー
11:30-12:30 数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (University du Luxembourg)
Second order fluctuations for zeros of arithmetic random waves
Giovanni Peccati 氏 (University du Luxembourg)
Second order fluctuations for zeros of arithmetic random waves
[ 講演概要 ]
Originally introduced by Rudnick and Wigman (2007), arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the high-energy behaviour of the so-called « nodal length » (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. I will also discuss the connected problem of counting the number of intersections points of independent nodal sets (equivalent to « phase singularities » for complex waves) in the high-energy regime. Both issues are tightly connected to the arithmetic study of lattice points on circles. One key concept in our presentation is that of ‘Berry cancellation phenomenon’ (see M.V. Berry, 2002), for which an explanation in terms of chaos expansions and integration by parts (Green formula) will be provided. Based on joint works (GAFA 2016 & Preprint 2016) with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King’s College, London), and with F. Dalmao (University of Uruguay), I. Nourdin (Luxembourg) and M. Rossi (Luxembourg).
Originally introduced by Rudnick and Wigman (2007), arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the high-energy behaviour of the so-called « nodal length » (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. I will also discuss the connected problem of counting the number of intersections points of independent nodal sets (equivalent to « phase singularities » for complex waves) in the high-energy regime. Both issues are tightly connected to the arithmetic study of lattice points on circles. One key concept in our presentation is that of ‘Berry cancellation phenomenon’ (see M.V. Berry, 2002), for which an explanation in terms of chaos expansions and integration by parts (Green formula) will be provided. Based on joint works (GAFA 2016 & Preprint 2016) with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King’s College, London), and with F. Dalmao (University of Uruguay), I. Nourdin (Luxembourg) and M. Rossi (Luxembourg).
2016年10月31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
石井 豊 氏 (九州大学)
Henon 写像族のパラメータ空間におけるホースシュー領域について (JAPANESE)
石井 豊 氏 (九州大学)
Henon 写像族のパラメータ空間におけるホースシュー領域について (JAPANESE)
[ 講演概要 ]
パラメータ $(a, b)$ を持つ平面からそれ自身への多項式写像の族 $f_{a, b} : (x, y)\rightarrow (x^2-a-by, x)$ は Henon 写像族と呼ばれ、非線形力学系の最も基本的なクラスとして多くの数学者や物理学者によって研究されてきた。この写像がなす力学系はパラメータ $(a, b)$ の取り方に大きく依存するが、ある部分パラメータ領域から $(a, b)$ を選ぶと、対応する Henon 写像は「ホースシュー」と呼ばれるカオス力学系の典型的なモデルになることが知られている。今からおよそ３５年前に宇敷重広や Christian Mira らは、Henon 写像がホースシューになるようなパラメータ領域の境界がある滑らかな曲線で特徴付けられることを数値的に観察した。今回の講演では、この数値的観察に対する数学的に厳密な証明について説明する。その証明は、Henon 写像の相空間とパラメータ空間を共に複素拡張し、複素力学系や複素幾何のテクニックを精度保証計算と組み合わせることによって得られる。
パラメータ $(a, b)$ を持つ平面からそれ自身への多項式写像の族 $f_{a, b} : (x, y)\rightarrow (x^2-a-by, x)$ は Henon 写像族と呼ばれ、非線形力学系の最も基本的なクラスとして多くの数学者や物理学者によって研究されてきた。この写像がなす力学系はパラメータ $(a, b)$ の取り方に大きく依存するが、ある部分パラメータ領域から $(a, b)$ を選ぶと、対応する Henon 写像は「ホースシュー」と呼ばれるカオス力学系の典型的なモデルになることが知られている。今からおよそ３５年前に宇敷重広や Christian Mira らは、Henon 写像がホースシューになるようなパラメータ領域の境界がある滑らかな曲線で特徴付けられることを数値的に観察した。今回の講演では、この数値的観察に対する数学的に厳密な証明について説明する。その証明は、Henon 写像の相空間とパラメータ空間を共に複素拡張し、複素力学系や複素幾何のテクニックを精度保証計算と組み合わせることによって得られる。
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
鍾菁廣 氏 (大阪大学サイバーメディアセンター)
半導体における量子流体方程式系の数値解法 (日本語)
鍾菁廣 氏 (大阪大学サイバーメディアセンター)
半導体における量子流体方程式系の数値解法 (日本語)
[ 講演概要 ]
本講演では, Wigner-Boltzmann方程式から階層的に導出される量子流体方程式とその数値スキームについて述べる. 量子流体方程式から階層モデルの一つである放物-楕円型の量子エネルギー輸送方程式(4モーメントQETモデル)が導出される. 運動量保存式とエネルギー保存式が同一形式に書けることに着目し, 有限体積法を基にした高精度保存スキームを開発した. さらに減速緩和法による反復解法を開発し, これにより量子効果とホットキャリア効果を伴った半導体内の電子輸送のシミュレーションを実現した. 本講演では, さらに半導体デバイスの現実問題に対する対応についても述べる.
本講演では, Wigner-Boltzmann方程式から階層的に導出される量子流体方程式とその数値スキームについて述べる. 量子流体方程式から階層モデルの一つである放物-楕円型の量子エネルギー輸送方程式(4モーメントQETモデル)が導出される. 運動量保存式とエネルギー保存式が同一形式に書けることに着目し, 有限体積法を基にした高精度保存スキームを開発した. さらに減速緩和法による反復解法を開発し, これにより量子効果とホットキャリア効果を伴った半導体内の電子輸送のシミュレーションを実現した. 本講演では, さらに半導体デバイスの現実問題に対する対応についても述べる.
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
Sergey Neshveyev 氏 (Univ. Oslo)
Dual cocycles and equivariant deformation quantization (English)
Sergey Neshveyev 氏 (Univ. Oslo)
Dual cocycles and equivariant deformation quantization (English)
統計数学セミナー
10:40-11:30 数理科学研究科棟(駒場) 123号室
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Martingale expansion revisited
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Martingale expansion revisited
[ 講演概要 ]
The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).
The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).
統計数学セミナー
11:30-12:20 数理科学研究科棟(駒場) 123号室
Nobuaki Naganuma 氏 (Osaka University)
Error analysis for approximations to one-dimensional SDEs via perturbation method
Nobuaki Naganuma 氏 (Osaka University)
Error analysis for approximations to one-dimensional SDEs via perturbation method
[ 講演概要 ]
We consider one-dimensional stochastic differential equations driven by fractional Brownian motions and adopt the Euler scheme, the Milstein type scheme and the Crank-Nicholson scheme to approximate solutions to the equations. We introduce perturbation method in order to analyze errors of the schemes. By using this method, we can express the errors in terms of directional derivatives of the solutions explicitly. We obtain asymptotic error distributions of the three schemes by combining the expression of the errors and the fourth moment theorem. This talk is based on a joint work with Prof. Shigeki Aida (Tohoku University).
We consider one-dimensional stochastic differential equations driven by fractional Brownian motions and adopt the Euler scheme, the Milstein type scheme and the Crank-Nicholson scheme to approximate solutions to the equations. We introduce perturbation method in order to analyze errors of the schemes. By using this method, we can express the errors in terms of directional derivatives of the solutions explicitly. We obtain asymptotic error distributions of the three schemes by combining the expression of the errors and the fourth moment theorem. This talk is based on a joint work with Prof. Shigeki Aida (Tohoku University).
統計数学セミナー
13:50-14:40 数理科学研究科棟(駒場) 123号室
Seiichiro Kusuoka 氏 (Okayama University)
Characterization of the convergence in total variation by Stein's method and Malliavin calculus
Seiichiro Kusuoka 氏 (Okayama University)
Characterization of the convergence in total variation by Stein's method and Malliavin calculus
[ 講演概要 ]
Recently, convergence in distributions and estimates of distances between distributions are studied by means of Stein's equation and Malliavin calculus. However, in known results, the target distributions of the convergence were some specific distributions. In this talk, we extend the target distributions to invariant probability measures of diffusion processes. Precisely speaking, we prepare Stein's equation with respect to invariant measures of diffusion processes and consider the characterization of the convergence to the invariant measure in total variation by applying Malliavin calculus. This is a joint work with Ciprian Tudor.
Recently, convergence in distributions and estimates of distances between distributions are studied by means of Stein's equation and Malliavin calculus. However, in known results, the target distributions of the convergence were some specific distributions. In this talk, we extend the target distributions to invariant probability measures of diffusion processes. Precisely speaking, we prepare Stein's equation with respect to invariant measures of diffusion processes and consider the characterization of the convergence to the invariant measure in total variation by applying Malliavin calculus. This is a joint work with Ciprian Tudor.
統計数学セミナー
14:50-15:40 数理科学研究科棟(駒場) 123号室
Teppei Ogihara 氏 (The Institute of Statistical Mathematics, JST PRESTO, JST CREST)
Parameter estimation for diffusion processes with high-frequency observations
Teppei Ogihara 氏 (The Institute of Statistical Mathematics, JST PRESTO, JST CREST)
Parameter estimation for diffusion processes with high-frequency observations
[ 講演概要 ]
We study statistical inference for security prices modeled by diffusion processes with high-frequency observations. In particular, we focus on two specific problems on analysis of high-frequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We construct a maximum-likelihood-type estimator of parameters, and study their asymptotic mixed normality. We also discuss on asymptotic efficiency of estimators.
We study statistical inference for security prices modeled by diffusion processes with high-frequency observations. In particular, we focus on two specific problems on analysis of high-frequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We construct a maximum-likelihood-type estimator of parameters, and study their asymptotic mixed normality. We also discuss on asymptotic efficiency of estimators.
統計数学セミナー
15:40-16:30 数理科学研究科棟(駒場) 123号室
Kengo Kamatani 氏 (Osaka University, JST CREST)
Markov chain Monte Carlo for high-dimensional target distribution
Kengo Kamatani 氏 (Osaka University, JST CREST)
Markov chain Monte Carlo for high-dimensional target distribution
[ 講演概要 ]
The Markov chain Monte Carlo (MCMC) algorithms are widely used to evaluate complicated integrals in Bayesian Statistics. Since the method is not free from the curse of dimensionality, it is important to quantify the effect of the dimensionality and establish an optimal MCMC strategy in high-dimension. In this talk, I will review some high-dimensional asymptotics of MCMC initiated by Roberts et. al. 97, and explain some asymptotic properties of the MpCN algorithm. I will also mention some connection to Stein-Malliavin techniques.
The Markov chain Monte Carlo (MCMC) algorithms are widely used to evaluate complicated integrals in Bayesian Statistics. Since the method is not free from the curse of dimensionality, it is important to quantify the effect of the dimensionality and establish an optimal MCMC strategy in high-dimension. In this talk, I will review some high-dimensional asymptotics of MCMC initiated by Roberts et. al. 97, and explain some asymptotic properties of the MpCN algorithm. I will also mention some connection to Stein-Malliavin techniques.
統計数学セミナー
16:50-17:40 数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Universite du Luxembourg)
New Functionals inequalities via Stein's discrepancies
Giovanni Peccati 氏 (Universite du Luxembourg)
New Functionals inequalities via Stein's discrepancies
[ 講演概要 ]
I will present a new set of functional inequalities involving the following four parameters associated with a given multidimensional distribution: the relative entropy, the relative Fisher information, the 2-Wasserstein distance, and the Stein discrepancy (which is a natural object arising in the framework of the Malliavin-Stein method on a Gaussian space). Our results improve the classical log-Sobolev inequality, as well Talagrand's transport inequality, and allow one to deduce new quantitative entropic limit theorems on Gaussian spaces. Joint works (JFA 2014 and GAFA 2015) with M. Ledoux (Toulouse), I. Nourdin (Luxembourg) and Y. Swan (Liège).
I will present a new set of functional inequalities involving the following four parameters associated with a given multidimensional distribution: the relative entropy, the relative Fisher information, the 2-Wasserstein distance, and the Stein discrepancy (which is a natural object arising in the framework of the Malliavin-Stein method on a Gaussian space). Our results improve the classical log-Sobolev inequality, as well Talagrand's transport inequality, and allow one to deduce new quantitative entropic limit theorems on Gaussian spaces. Joint works (JFA 2014 and GAFA 2015) with M. Ledoux (Toulouse), I. Nourdin (Luxembourg) and Y. Swan (Liège).
統計数学セミナー
17:40-18:30 数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Université du Luxembourg)
Stochastic geometry and Malliavin calculus on configuration spaces
Giovanni Peccati 氏 (Université du Luxembourg)
Stochastic geometry and Malliavin calculus on configuration spaces
[ 講演概要 ]
I will present some recent advances in the domain of quantitative limit theorems for geometric Poisson functionals, associated e.g. with random geometric graphs and random tessellations, obtained by means of Malliavin calculus techniques. One of our main results consists in a general (optimal) Berry-Esseen bound for stabilizing functionals, based on Stein’s method, iterated Poincaré inequalities and a variant of Mehler’s formula. Based on several joint works with S. Bourguin, R. Lachièze-Rey, G. Last and M. Schulte, as well as on the recent monograph that I co-edited with M. Reitzner.
I will present some recent advances in the domain of quantitative limit theorems for geometric Poisson functionals, associated e.g. with random geometric graphs and random tessellations, obtained by means of Malliavin calculus techniques. One of our main results consists in a general (optimal) Berry-Esseen bound for stabilizing functionals, based on Stein’s method, iterated Poincaré inequalities and a variant of Mehler’s formula. Based on several joint works with S. Bourguin, R. Lachièze-Rey, G. Last and M. Schulte, as well as on the recent monograph that I co-edited with M. Reitzner.
2016年10月28日(金)
数理人口学・数理生物学セミナー
13:30-14:30 数理科学研究科棟(駒場) 126号室
原 朱音 氏 (九州大学システム生命科学府)
When is the allergen immunotherapy effective? (JAPANESE)
原 朱音 氏 (九州大学システム生命科学府)
When is the allergen immunotherapy effective? (JAPANESE)
[ 講演概要 ]
Allergen immunotherapy is a method to treat allergic symptoms, for example rhinitis and sneezing in Japanese cedar pollen allergy (JCPA). In the immunotherapy of JCPA, patients take in a small amount of pollen over several years, which suppress severe allergic symptoms when exposed to a large amount of environmental pollen after the therapy. We develop a simple mathematical model to identify the condition for successful therapy. We consider the dynamics of type 2 T helper cells (Th2) and regulatory T cells (Treg) and both of them are differentiated from naive T cells. We assume that Treg cells have a much longer lifespan than Th2 cells, which makes Treg cells accumulate over many years during the therapy.
We regard that the therapy is successful if (1) without therapy the patient develops allergic symptoms upon exposure to the environmental pollen, (2) the patient does not develop allergic symptoms caused by the therapy itself, and (3) with therapy the patient does not develop symptoms upon exposure. We find the conditions of each parameter for successful therapy. We also find that the therapy of linearly increasing dose is able to reduce the risk of allergic symptoms caused by the therapy itself, rather than constant dose. We would like to consider application of this model to other kind of allergy, such as food allergy.
Allergen immunotherapy is a method to treat allergic symptoms, for example rhinitis and sneezing in Japanese cedar pollen allergy (JCPA). In the immunotherapy of JCPA, patients take in a small amount of pollen over several years, which suppress severe allergic symptoms when exposed to a large amount of environmental pollen after the therapy. We develop a simple mathematical model to identify the condition for successful therapy. We consider the dynamics of type 2 T helper cells (Th2) and regulatory T cells (Treg) and both of them are differentiated from naive T cells. We assume that Treg cells have a much longer lifespan than Th2 cells, which makes Treg cells accumulate over many years during the therapy.
We regard that the therapy is successful if (1) without therapy the patient develops allergic symptoms upon exposure to the environmental pollen, (2) the patient does not develop allergic symptoms caused by the therapy itself, and (3) with therapy the patient does not develop symptoms upon exposure. We find the conditions of each parameter for successful therapy. We also find that the therapy of linearly increasing dose is able to reduce the risk of allergic symptoms caused by the therapy itself, rather than constant dose. We would like to consider application of this model to other kind of allergy, such as food allergy.
2016年10月27日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
Fred Weissler 氏 (パリ第13大学)
Sign-changing solutions of the nonlinear heat equation with positive initial value
(ENGLISH)
Fred Weissler 氏 (パリ第13大学)
Sign-changing solutions of the nonlinear heat equation with positive initial value
(ENGLISH)
[ 講演概要 ]
We consider the nonlinear heat equation with a power nonlinear source term on all of N-dimensional space. It is well known that the associated Cauchy problem is locally well-posed in a variety of function spaces, including certain Lebesgue spaces, depending on the power. In other Lebesgue spaces, it can happen that the Cauchy problem is not well-posed. In particular, there exist non-negative initial values for which no local (in time) non-negative solution exists. This can happen also for some homogeneous functions, where the homogeneity is linked to the scaling properties of the equation.
I will discuss recent work, in collaboration with T. Cazenave, F. Dickstein and I. Naumkin. We show that for a certain class of non-negative initial values which, as mentioned above, do not admit local non-negative solutions, there exist in fact local (or global) solutions which change sign. In particular, in the case of non-negative homogeneous initial data which do not admit non-negative solutions, we construct sign-changing self-similar solutions with the given initial data.
https://www.ms.u-tokyo.ac.jp/~miyamoto/Weissler-abstract.pdf
数式を含むアブストラクト(英語)は，上記のURLからダウンロードできます．
We consider the nonlinear heat equation with a power nonlinear source term on all of N-dimensional space. It is well known that the associated Cauchy problem is locally well-posed in a variety of function spaces, including certain Lebesgue spaces, depending on the power. In other Lebesgue spaces, it can happen that the Cauchy problem is not well-posed. In particular, there exist non-negative initial values for which no local (in time) non-negative solution exists. This can happen also for some homogeneous functions, where the homogeneity is linked to the scaling properties of the equation.
I will discuss recent work, in collaboration with T. Cazenave, F. Dickstein and I. Naumkin. We show that for a certain class of non-negative initial values which, as mentioned above, do not admit local non-negative solutions, there exist in fact local (or global) solutions which change sign. In particular, in the case of non-negative homogeneous initial data which do not admit non-negative solutions, we construct sign-changing self-similar solutions with the given initial data.
https://www.ms.u-tokyo.ac.jp/~miyamoto/Weissler-abstract.pdf
数式を含むアブストラクト(英語)は，上記のURLからダウンロードできます．
東京無限可積分系セミナー
15:00-17:30 数理科学研究科棟(駒場) 002号室
佐藤 僚 氏 (東大数理)
Non-unitary highest-weight modules over the $N=2$ superconformal algebra (JAPANESE)
佐藤 僚 氏 (東大数理)
Non-unitary highest-weight modules over the $N=2$ superconformal algebra (JAPANESE)
[ 講演概要 ]
$N=2$超共形代数とは，超対称性をもつVirasoro代数の一般化
である．そのユニタリ最高ウェイト表現の形式指標は古典的なテータ関数を用い
て記述することができ，モジュラー不変性という著しい性質を持つ．一方，Kac-
WakimotoはW代数の手法を用いて，ある特別な非ユニタリ最高ウェイト表現の形
式指標がaffine ${sl}_{2|1}$に付随する擬テータ関数を用いて記述されること
を示した．彼らはZwegersによる擬テータ関数の修正項を用いて，それらの指標
を実解析的モジュラー形式と関連付けた．
このセミナーでは，W代数の手法とは異なるKazama-Suzukiコセット構成を用いて，
affine ${sl}_{2}$の表現から上記の非ユニタリ表現を構成する手法を解説する．
また，その構成を用いて得られる擬テータ関数と古典的なテータ関数との関係に
ついて述べる．
$N=2$超共形代数とは，超対称性をもつVirasoro代数の一般化
である．そのユニタリ最高ウェイト表現の形式指標は古典的なテータ関数を用い
て記述することができ，モジュラー不変性という著しい性質を持つ．一方，Kac-
WakimotoはW代数の手法を用いて，ある特別な非ユニタリ最高ウェイト表現の形
式指標がaffine ${sl}_{2|1}$に付随する擬テータ関数を用いて記述されること
を示した．彼らはZwegersによる擬テータ関数の修正項を用いて，それらの指標
を実解析的モジュラー形式と関連付けた．
このセミナーでは，W代数の手法とは異なるKazama-Suzukiコセット構成を用いて，
affine ${sl}_{2}$の表現から上記の非ユニタリ表現を構成する手法を解説する．
また，その構成を用いて得られる擬テータ関数と古典的なテータ関数との関係に
ついて述べる．
2016年10月25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
Yongnam Lee 氏 (KAIST/RIMS)
Q-Gorenstein deformation theory and it applications to algebraic surfaces (English)
Yongnam Lee 氏 (KAIST/RIMS)
Q-Gorenstein deformation theory and it applications to algebraic surfaces (English)
[ 講演概要 ]
The notion of Q-Gorenstein variety is important for the minimal model theory and the compact moduli theory of algebraic varieties in characteristic 0. Also Q-Gorenstein deformation theory can be applied to construct (simply connected) surfaces of general type with geometric genus 0 over the field of any characteristic. In this talk, some applications of Q-Gorenstein deformation theory to algebraic surfaces and some interesting examples related to Q-Gorenstein morphisms will be presented.
The notion of Q-Gorenstein variety is important for the minimal model theory and the compact moduli theory of algebraic varieties in characteristic 0. Also Q-Gorenstein deformation theory can be applied to construct (simply connected) surfaces of general type with geometric genus 0 over the field of any characteristic. In this talk, some applications of Q-Gorenstein deformation theory to algebraic surfaces and some interesting examples related to Q-Gorenstein morphisms will be presented.
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
山根 英司 氏 (関西学院大学理工学部数理科学科)
可積分離散非線型シュレーディンガー方程式の漸近解析 (JAPANESE)
山根 英司 氏 (関西学院大学理工学部数理科学科)
可積分離散非線型シュレーディンガー方程式の漸近解析 (JAPANESE)
2016年10月24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
清水 悟 氏 (東北大学)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
清水 悟 氏 (東北大学)
Structure and equivalence of a class of tube domains with solvable groups of automorphisms (JAPANESE)
[ 講演概要 ]
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains $T_\Omega$, investigating certain solvable subalgebras of $\frak g(T_{\Omega})$ plays an important role, where $\frak g(T_{\Omega})$ is the Lie algebra of all complete polynomial vector fields on $T_\Omega$. Related to this theme, we discuss the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 117号室
磯野優介 氏 (京大数理研)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
磯野優介 氏 (京大数理研)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
2016年10月18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
橋本 義武 氏 (東京都市大学)
拡大W代数に対する共形場理論 (JAPANESE)
Tea: Common Room 17:00-17:30
橋本 義武 氏 (東京都市大学)
拡大W代数に対する共形場理論 (JAPANESE)
[ 講演概要 ]
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.
In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".
This talk is based on a joint work with A. Tsuchiya (Kavli IPMU) and T. Matsumoto (Nagoya Univ). In 2006 Feigin-Gainutdinov-Semikhatov-Tipunin introduced vertex operator algebras M called extended W-algebras. Tsuchiya-Wood developed representation theory of M by the method of
"infinitesimal deformation of parameter" and Jack symmetric polynomials.
In this talk I will discuss the following subjects:
1. "factorization" in conformal field theory,
2. tensor structure of the category of M-modules and "module-bimodule correspondence".
2016年10月17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
野村 隆昭 氏 (九州大学)
等質開凸錐の実現 (JAPANESE)
野村 隆昭 氏 (九州大学)
等質開凸錐の実現 (JAPANESE)
[ 講演概要 ]
等質開凸錐は等質ジーゲル領域の構成要素の一つである．その観点で，等質開凸錐の研究を，伊師英之，中島秀斗，山崎貴史等，若い研究者達と一緒にここ10年ほど続けてきて得られた成果のいくつかを紹介したい．中心となる話題は等質開凸錐の実現であり，これは山崎との共著論文として昨年の Kyushu J. Math.に出版されたもので，向き付けグラフを援用しながら，5次元の非対称等質開凸錐の記述にVinbergが用いたアイデア（露語オリジナルは1960年）が，そのままの形で一般の等質開凸錐の実現に通用することを示すものである．基本相対不変式における伊師等による成果を用いる証明を完全にブラックボックス化し，結果としては単に手続きを述べる形になっているので，非専門家にもアクセスが容易で，統計学等への応用も可能であると考えている．また，一般の非対称等質開凸錐に付随する管状領域の正則同型群やその構造の研究への応用も十分に見込める．さらに，Graczyk-Ishi による等質開凸錐の presentation (2014)の内で最小サイズのものも，上述の実現からやはり単なる手続き論で得られる．呈示される行列のサイズ等や零行列となるブロック・小ブロック等も，付随する向き付けグラフから読み取れる．
等質開凸錐は等質ジーゲル領域の構成要素の一つである．その観点で，等質開凸錐の研究を，伊師英之，中島秀斗，山崎貴史等，若い研究者達と一緒にここ10年ほど続けてきて得られた成果のいくつかを紹介したい．中心となる話題は等質開凸錐の実現であり，これは山崎との共著論文として昨年の Kyushu J. Math.に出版されたもので，向き付けグラフを援用しながら，5次元の非対称等質開凸錐の記述にVinbergが用いたアイデア（露語オリジナルは1960年）が，そのままの形で一般の等質開凸錐の実現に通用することを示すものである．基本相対不変式における伊師等による成果を用いる証明を完全にブラックボックス化し，結果としては単に手続きを述べる形になっているので，非専門家にもアクセスが容易で，統計学等への応用も可能であると考えている．また，一般の非対称等質開凸錐に付随する管状領域の正則同型群やその構造の研究への応用も十分に見込める．さらに，Graczyk-Ishi による等質開凸錐の presentation (2014)の内で最小サイズのものも，上述の実現からやはり単なる手続き論で得られる．呈示される行列のサイズ等や零行列となるブロック・小ブロック等も，付随する向き付けグラフから読み取れる．
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