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過去の記録 ～12/05｜本日 12/06 | 今後の予定 12/07～
2014年03月11日(火)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 118号室
Lucie Baudouin 氏 (LAAS-CNRS, equipe MAC)
Inverse problem for the waves : stability and convergence matters (ENGLISH)
Lucie Baudouin 氏 (LAAS-CNRS, equipe MAC)
Inverse problem for the waves : stability and convergence matters (ENGLISH)
[ 講演概要 ]
This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.
This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.
2014年03月10日(月)
GCOEセミナー
13:30-15:00 数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich)
The two-dimensional random walk in an isotropic random environment (ENGLISH)
Erwin Bolthausen 氏 (University of Zurich)
The two-dimensional random walk in an isotropic random environment (ENGLISH)
講演会
15:15-16:45 数理科学研究科棟(駒場) 123号室
Marielle Simon 氏 (ENS Lyon, UMPA)
Energy fluctuations in the disordered harmonic chain (ENGLISH)
Marielle Simon 氏 (ENS Lyon, UMPA)
Energy fluctuations in the disordered harmonic chain (ENGLISH)
[ 講演概要 ]
We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.
We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 118号室
Bernadette Miara 氏 (Univ. Paris-Est)
ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf
Bernadette Miara 氏 (Univ. Paris-Est)
ELASTIC WAVES IN STRONGLY HETEROGENEOUS PLATES (ENGLISH)
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/bm01.pdf
2014年03月06日(木)
GCOEセミナー
10:10-11:00 数理科学研究科棟(駒場) 002号室
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
J. Cheng 氏 (Fudan Univ.)
The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
J. Cheng 氏 (Fudan Univ.)
The Mathematical Model for the Contamination Problems and Related Inverse Problems (ENGLISH)
[ 講演概要 ]
In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.
In this talk, we discuss the motivation for the study of the abnormal diffusion models for the contamination problems. From the practical point of view, several inverse problems proposed and studied Theoretic results, for example, the uniqueness and stability are shown. The possibility of the application of these studies is mentioned.
GCOEセミナー
11:10-12:00 数理科学研究科棟(駒場) 002号室
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
W. Rundell 氏 (Texas A&M Univ.)
Inverse problems with fractional derivatives in the space variable (ENGLISH)
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
W. Rundell 氏 (Texas A&M Univ.)
Inverse problems with fractional derivatives in the space variable (ENGLISH)
[ 講演概要 ]
This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.
This talk will look at some classical inverse problems where the highest order term in the spatial direction is replaced by a fractional derivative. There are again some surprising results over what is known in the usual case of integer order derivatives but also quite different from the case of fractional diffusion in the time variable. The talk will give some answers, but pose many more open problems.
GCOEセミナー
14:30-15:20 数理科学研究科棟(駒場) 002号室
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
Y. Luchko 氏 (Beuth Technical University of Applied Sciences)
Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
Y. Luchko 氏 (Beuth Technical University of Applied Sciences)
Neutral-fractional diffusion-wave equation and some properties of its fundamental solution (ENGLISH)
[ 講演概要 ]
Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.
In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.
In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.
Recently, the so called neutral-fractional diffusion-wave equation was introduced and analysed in the case of one spatial variable. In contrast to the fractional diffusion of diffusion-wave equations, the neutral-fractional diffusion-wave equation contains fractional derivatives of the same order both in space and in time. The fundamental solution of the neutral-fractional diffusion-wave equation was shown to exhibit properties of both the solutions of the diffusion equation and those of the wave equation.
In the one-dimensional case, the fundamental solution of the neutral-fractional diffusion-wave equation can be interpreted as a spatial probability density function evolving in time. At the same time, it can be treated as a damped wave whose amplitude maximum and the gravity and mass centres propagate with the constant velocities that depend just on the equation order.
In this talk, the problems mentioned above are considered for the multi- dimensional neutral-fractional diffusion-wave equation. To illustrate analytical findings, some results of numerical calculations and plots are presented.
GCOEセミナー
16:20-17:10 数理科学研究科棟(駒場) 002号室
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
M. Cristofol 氏 (Aix-Marseille Univ.)
New kind of observations in an inverse parabolic problem (ENGLISH)
このセミナーは 研究集会「異常拡散の数理とシミュレーション手法ならびに関連する課題」(主催・共催:数物フロンティア・リーディング大学院プログラム、卓越した大学院拠点形成支援補
M. Cristofol 氏 (Aix-Marseille Univ.)
New kind of observations in an inverse parabolic problem (ENGLISH)
[ 講演概要 ]
In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.
In this talk, I analyze the inverse problem of determining the reaction term f(x,u) in reaction-diffusion equations of the form ¥partial_t u-D¥partial_{xx}u = f(x,u), where f is assumed to be periodic with respect to x in R. Starting from a family of exponentially decaying initial conditions u_{0,¥lambda}, I will show that the solutions u_¥lambda of this equation propagate with constant asymptotic spreading speeds w_¥lambda. The main result shows that the linearization of f around the steady state 0,¥partial_u f(x,0), is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds w_¥lambda.
2014年02月28日(金)
GCOEセミナー
13:00-14:00 数理科学研究科棟(駒場) 002号室
Patricia Gaitan 氏 (Aix-Marseille University)
Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)
Patricia Gaitan 氏 (Aix-Marseille University)
Probing for inclusions for heat conductive bodies. Time independent and time dependent cases (ENGLISH)
[ 講演概要 ]
This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.
For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).
This work deals with an inverse boundary value problem arising from the equation of heat conduction. Mathematical theory and algorithm is described in dimensions 1{3 for probing the discontinuous part of the conductivity from local temperature and heat ow measurements at the boundary. The ap- proach is based on the use of complex spherical waves, and no knowledge is needed about the initial temperature distribution. In dimension two we show how conformal transformations can be used for probing deeper than is pos- sible with discs. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method is capable of recovering loca- tions of discontinuities approximately from noisy data.
For moving inclusions, we consider an inverse boundary value problem for the heat equation on the interval (0; 1), where the heat conductivity (t; x) is piecewise constant and the point of discontinuity depends on time : (t; x) = k2 (0 < x < s(t)), (t; x) = 1 (s(t) < x < 1). Firstly we show that k and s(t) on the time interval [0; T] are determined from the partial Dirichlet- to-Neumann map : u(t; 1) ! @xu(t; 1); 0 < t < T, u(t; x) being the solu- tion to the heat equation such that u(t; 0) = 0, independently of the initial data u(0; x). Secondly we show that the partial Dirichlet-to-Neumann map u(t; 0) ! @xu(t; 1); 0 < t < T, u(t; x) being the solution to the heat equation such that u(t; 1) = 0, determines at most two couples (k; s(t)) on the time interval [0; T], independently of the initial data u(0; x).
GCOEセミナー
11:00-12:00 数理科学研究科棟(駒場) 002号室
Assia Benabdallah 氏 (Aix-Marseille University)
Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)
Assia Benabdallah 氏 (Aix-Marseille University)
Minimal time for the null controllability of parabolic systems: the effect of the index of condensation of complex sequences (ENGLISH)
2014年02月27日(木)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 370号室
Yves Dermenjian 氏 (Univ. of Marseille)
A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)
Yves Dermenjian 氏 (Univ. of Marseille)
A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part II: for a an anisotropic elliptic operator. (ENGLISH)
2014年02月18日(火)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 370号室
Yves Dermenjian 氏 (Univ. of Marseille)
A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)
Yves Dermenjian 氏 (Univ. of Marseille)
A Carleman estimate with discontinuous coefficients through an interface crossing the boundary, Part I: for a stratified parabolic operator. (ENGLISH)
2014年02月17日(月)
講演会
16:30-17:30 数理科学研究科棟(駒場) 002号室
Canceled!! (本人の都合により,講演は取りやめとなりました.)
Ratnasingham Shivaji 氏 (The University of North Carolina at Greensboro)
Canceled!! (ENGLISH)
Canceled!! (本人の都合により,講演は取りやめとなりました.)
Ratnasingham Shivaji 氏 (The University of North Carolina at Greensboro)
Canceled!! (ENGLISH)
[ 講演概要 ]
Canceled!!
Canceled!!
2014年02月15日(土)
調和解析駒場セミナー
13:00-18:00 数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
Batbold Tserendorj 氏 (National University of Mongolia) 13:30-15:00
Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)
弱空間に於ける条件付き平均作用素の一様有界性とその応用 (JAPANESE)
このセミナーは,月に1度程度,不定期に開催されます.
Batbold Tserendorj 氏 (National University of Mongolia) 13:30-15:00
Some Hilbert-type inequalities involving the Hardy operator (ENGLISH)
[ 講演概要 ]
In this talk,
we give some new Hilbert-type inequalities with a homogeneous kernel,
involving the Hardy operator. As an application,
we define related Hilbert-type integral operator
and consider its norm.
The problem of determining the norm of such operator is equivalent to
the problem of the best possible constant factor
involved in the right-hand side of related inequality.
In such a way,
we obtain the norm and the best possible constant factor in some general
settings
with conjugate exponents. In particular,
we obtain generalizations of some recent results,
from the literature.
菊池 万里 氏 (富山大学) 15:30-17:00In this talk,
we give some new Hilbert-type inequalities with a homogeneous kernel,
involving the Hardy operator. As an application,
we define related Hilbert-type integral operator
and consider its norm.
The problem of determining the norm of such operator is equivalent to
the problem of the best possible constant factor
involved in the right-hand side of related inequality.
In such a way,
we obtain the norm and the best possible constant factor in some general
settings
with conjugate exponents. In particular,
we obtain generalizations of some recent results,
from the literature.
弱空間に於ける条件付き平均作用素の一様有界性とその応用 (JAPANESE)
[ 講演概要 ]
Fatou property を持つ確率変数(可測関数)の Banach lattice を
Banach 関数空間と呼ぶ.Banach 関数空間 X から自然な方法で弱空間
w-X を定義するとき,あらゆる条件付き平均作用素が X から w-X への
作用素として一様有界になるための必要十分条件を紹介し,その応用
として,Doob の弱型不等式が成立する為の必要十分条件を導く.また,
時間が許せば,他の型のマルチンゲール不等式にも言及したい.
Fatou property を持つ確率変数(可測関数)の Banach lattice を
Banach 関数空間と呼ぶ.Banach 関数空間 X から自然な方法で弱空間
w-X を定義するとき,あらゆる条件付き平均作用素が X から w-X への
作用素として一様有界になるための必要十分条件を紹介し,その応用
として,Doob の弱型不等式が成立する為の必要十分条件を導く.また,
時間が許せば,他の型のマルチンゲール不等式にも言及したい.
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
大西良博 氏 (山梨大学教育人間科学部) 13:30-14:30
大雪の為、中止:Coble\\'s hypersurface and defining equation of Kummer varieties (JAPANESE)
漕江厚子 氏 (富山大学大学院理工学教育部) 15:00-16:00
大雪の為、中止:準アーベル多様体へのワイエルシュトラスのペー関数の一般化 (JAPANESE)
大西良博 氏 (山梨大学教育人間科学部) 13:30-14:30
大雪の為、中止:Coble\\'s hypersurface and defining equation of Kummer varieties (JAPANESE)
漕江厚子 氏 (富山大学大学院理工学教育部) 15:00-16:00
大雪の為、中止:準アーベル多様体へのワイエルシュトラスのペー関数の一般化 (JAPANESE)
2014年02月13日(木)
数値解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
いつもと,開催曜日,開催時刻,教室が異なっております.ご注意ください.
Mitchell Luskin 氏 (University of Minnesota)
Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)
http://www.infsup.jp/utnas/
いつもと,開催曜日,開催時刻,教室が異なっております.ご注意ください.
Mitchell Luskin 氏 (University of Minnesota)
Numerical analysis of atomistic-to-continuum coupling methods (ENGLISH)
[ 講演概要 ]
The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.
Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.
[ 参考URL ]The building blocks of micromechanics are the nucleation and movement of point, line, and surface defects and their long-range elastic interactions. Computational micromechanics has begun to extend the predictive scope of theoretical micromechanics, but mathematical theory able to assess the accuracy and efficiency of multiscale methods is needed for computational micromechanics to reach its full potential.
Many materials problems require the accuracy of atomistic modeling in small regions, such as the neighborhood of a crack tip. However, these localized defects typically interact through long range elastic fields with a much larger region that cannot be computed atomistically. Materials scientists have proposed many methods to compute solutions to these multiscale problems by coupling atomistic models near a localized defect with continuum models where the deformation is nearly uniform on the atomistic scale. During the past several years, a mathematical structure has been given to the description and formulation of atomistic-to-continuum coupling methods, and corresponding numerical analysis and benchmark computational experiments have clarified the relation between the various methods and their sources of error. Our numerical analysis has enabled the development of more accurate and efficient coupling methods.
http://www.infsup.jp/utnas/
2014年02月12日(水)
代数幾何学セミナー
14:00-17:30 数理科学研究科棟(駒場) 122号室
いつもと曜日・時間が異なります
松村 慎一 氏 (鹿児島大学) 14:00-15:30
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)
Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)
いつもと曜日・時間が異なります
松村 慎一 氏 (鹿児島大学) 14:00-15:30
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)
[ 講演概要 ]
In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.
This theorem is a powerful generalization of various injectivity and vanishing theorems.
The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.
To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.
Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.
As an application, we obtain a Nadel type vanishing theorem.
Junyan Cao 氏 (KIAS) 16:00-17:30In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.
This theorem is a powerful generalization of various injectivity and vanishing theorems.
The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.
To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.
Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.
As an application, we obtain a Nadel type vanishing theorem.
Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)
[ 講演概要 ]
In this talk, we first prove a version of the Ohsawa-Takegoshi
extension theorem valid for on arbitrary K\\"ahler manifolds, and for
holomorphic line bundles equipped with possibly singular metrics. As an
application, we generalise Berndtsson and Paun 's result about the
pseudo-effectivity of the relative canonical bundles to arbitrary
compact K\\"ahler families.
In this talk, we first prove a version of the Ohsawa-Takegoshi
extension theorem valid for on arbitrary K\\"ahler manifolds, and for
holomorphic line bundles equipped with possibly singular metrics. As an
application, we generalise Berndtsson and Paun 's result about the
pseudo-effectivity of the relative canonical bundles to arbitrary
compact K\\"ahler families.
博士論文発表会
09:30-10:45 数理科学研究科棟(駒場) 118号室
清水 達郎 氏 (東京大学大学院数理科学研究科)
A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)
清水 達郎 氏 (東京大学大学院数理科学研究科)
A construction of a universal finite type invariant of homology 3-spheres(ホモロジー3球面の普遍有限型不変量のひとつの構成) (JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
平野 雄一 氏 (東京大学大学院数理科学研究科)
Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)
平野 雄一 氏 (東京大学大学院数理科学研究科)
Congruences of Hilbert modular forms over real quadratic fields and the special values of L-functions(実2次体上のHilbert保型形式の合同式とL関数の特殊値) (JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 128号室
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)
粕谷 直彦 氏 (東京大学大学院数理科学研究科)
On contact submanifolds of the odd dimensional Euclidean space(奇数次元ユークリッド空間の接触部分多様体について) (JAPANESE)
博士論文発表会
15:00-16:15 数理科学研究科棟(駒場) 128号室
金子 勇治 氏 (東京大学大学院数理科学研究科)
特異値間隔分布によるセルオートマトンの分類 (JAPANESE)
金子 勇治 氏 (東京大学大学院数理科学研究科)
特異値間隔分布によるセルオートマトンの分類 (JAPANESE)
2014年02月10日(月)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
許 本源 氏 (東京大学大学院数理科学研究科)
Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)
(JAPANESE)
許 本源 氏 (東京大学大学院数理科学研究科)
Liouville type theorems for the Navier-Stokes equations andapplications(ナヴィエ・ストークス方程式に対するリウヴィル型定理とその応用)
(JAPANESE)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 118号室
柏原 崇人 氏 (東京大学大学院数理科学研究科)
Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)
柏原 崇人 氏 (東京大学大学院数理科学研究科)
Mathematical and numerical analysis for incompressible fluid equations under friction boundary conditions(摩擦型境界条件下での非圧縮流体の方程式に対する数学解析と数値解析) (JAPANESE)
博士論文発表会
08:00-09:15 数理科学研究科棟(駒場) 128号室
森 真樹 氏 (東京大学大学院数理科学研究科)
A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)
森 真樹 氏 (東京大学大学院数理科学研究科)
A cellular approach to the Hecke-Clifford superalgebra(セルラー代数の手法によるHecke-Clifford スーパー代数の研究) (JAPANESE)
博士論文発表会
09:30-10:45 数理科学研究科棟(駒場) 128号室
柗本 雄也 氏 (東京大学大学院数理科学研究科)
Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)
(JAPANESE)
柗本 雄也 氏 (東京大学大学院数理科学研究科)
Good reduction criterion for K3 surfaces(K3曲面の良い還元の判定法)
(JAPANESE)
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