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過去の記録
過去の記録 ～04/25｜本日 04/26 | 今後の予定 04/27～
古典解析セミナー
16:00-17:00 数理科学研究科棟(駒場) 122号室
Claude Mitschi 氏 (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
Claude Mitschi 氏 (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
[ 講演概要 ]
Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.
Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.
2010年04月14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
Gerard Laumon 氏 (CNRS, Universite Paris XI - Orsay)
The cohomological weighted fundamental lemma
Gerard Laumon 氏 (CNRS, Universite Paris XI - Orsay)
The cohomological weighted fundamental lemma
[ 講演概要 ]
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.
(本講演は「東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とIHESとの双方向同時中継で行います。)
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.
(本講演は「東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とIHESとの双方向同時中継で行います。)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)までの情報が掲載されております。
横山悦郎 氏 (学習院大学計算機センター)
国際宇宙ステーション「きぼう」における「氷の結晶成長における形態不安定化」実験解析ー氷の底面及び樹枝先端の成長速度解析とその理論的考察 (JAPANESE)
北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)までの情報が掲載されております。
横山悦郎 氏 (学習院大学計算機センター)
国際宇宙ステーション「きぼう」における「氷の結晶成長における形態不安定化」実験解析ー氷の底面及び樹枝先端の成長速度解析とその理論的考察 (JAPANESE)
[ 講演概要 ]
2008年12月から2009年2月にかけて国際宇宙ステーション「きぼう」において「氷の結晶成長における形態不安定化」という実験が実施された(研究代表者・北大研・古川義純)。そこでは、微小重力下において重水から成長する氷単結晶のその場観察が130回以上行うことができた。得られた明視野及び干渉縞の動画像の記録を解析し、次の2つの結果を得た。1)氷の底面の成長速度(c軸方向の速度)は、成長が測定できる臨界過冷却度(約0.1K)が存在し、臨界過冷却度以上では成長速度は過冷却度の2乗に比例する。2)樹枝先端の成長速度(a軸方向の速度)は、0.2K以上で過冷却度の2.5乗に比例する。このセミナーでは、得られた結果が理論モデルと一致することについて解説する。
2008年12月から2009年2月にかけて国際宇宙ステーション「きぼう」において「氷の結晶成長における形態不安定化」という実験が実施された(研究代表者・北大研・古川義純)。そこでは、微小重力下において重水から成長する氷単結晶のその場観察が130回以上行うことができた。得られた明視野及び干渉縞の動画像の記録を解析し、次の2つの結果を得た。1)氷の底面の成長速度(c軸方向の速度)は、成長が測定できる臨界過冷却度(約0.1K)が存在し、臨界過冷却度以上では成長速度は過冷却度の2乗に比例する。2)樹枝先端の成長速度(a軸方向の速度)は、0.2K以上で過冷却度の2.5乗に比例する。このセミナーでは、得られた結果が理論モデルと一致することについて解説する。
2010年04月13日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Christian Kassel 氏 (CNRS, Univ. de Strasbourg)
Torsors in non-commutative geometry (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Christian Kassel 氏 (CNRS, Univ. de Strasbourg)
Torsors in non-commutative geometry (ENGLISH)
[ 講演概要 ]
G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.
G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Jean-Marc Bouclet 氏 (トゥールーズ大学,フランス)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
Jean-Marc Bouclet 氏 (トゥールーズ大学,フランス)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)
2010年04月12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
千葉 優作 氏 (東大数理)
Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space
[ 参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html
千葉 優作 氏 (東大数理)
Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space
[ 参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html
2010年04月06日(火)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
加藤周 氏 (京都大学)
On the characters of tempered modules of affine Hecke
algebras of classical type
加藤周 氏 (京都大学)
On the characters of tempered modules of affine Hecke
algebras of classical type
[ 講演概要 ]
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.
Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.
This is a joint work with Dan Ciubotaru at Utah.
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.
Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.
This is a joint work with Dan Ciubotaru at Utah.
2010年04月05日(月)
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
Alexandru Dimca 氏 (Université Nice-Sophia Antipolis)
From Lang's Conjecture to finiteness properties of Torelli groups
Alexandru Dimca 氏 (Université Nice-Sophia Antipolis)
From Lang's Conjecture to finiteness properties of Torelli groups
[ 講演概要 ]
First we recall one of Lang's conjectures in diophantine geometry
on the interplay between subvarieties and translated subgroups in a
commutative algebraic group
(proved by M. Laurent in the case of affine tori in 1984).
Then we present the technique of resonance and characteristic varieties,
a powerful tool in the study of fundamental groups of algebraic varieties.
Finally, using the two ingredients above, we show that the Torelli
groups $T_g$
have some surprising finiteness properties for $g>3$.
In particular, we show that for any subgroup $N$ in $T_g$ containing
the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$
is finite dimensional.
All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.
First we recall one of Lang's conjectures in diophantine geometry
on the interplay between subvarieties and translated subgroups in a
commutative algebraic group
(proved by M. Laurent in the case of affine tori in 1984).
Then we present the technique of resonance and characteristic varieties,
a powerful tool in the study of fundamental groups of algebraic varieties.
Finally, using the two ingredients above, we show that the Torelli
groups $T_g$
have some surprising finiteness properties for $g>3$.
In particular, we show that for any subgroup $N$ in $T_g$ containing
the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$
is finite dimensional.
All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.
2010年03月30日(火)
GCOEセミナー
10:00-15:00 数理科学研究科棟(駒場) 122号室
山本 昌宏 氏 (東大数理) 10:00-10:50
産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)
中村 周 氏 (東大数理) 11:00-11:50
量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)
伊東 一文 氏 (東大数理、ノースカロライナ州立大学) 13:20-14:10
Semismooth Newton法の理論、及び応用 (JAPANESE)
ゲオク・ヴァイス 氏 (東大数理) 14:10-15:00
未定 (JAPANESE)
山本 昌宏 氏 (東大数理) 10:00-10:50
産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)
中村 周 氏 (東大数理) 11:00-11:50
量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)
伊東 一文 氏 (東大数理、ノースカロライナ州立大学) 13:20-14:10
Semismooth Newton法の理論、及び応用 (JAPANESE)
ゲオク・ヴァイス 氏 (東大数理) 14:10-15:00
未定 (JAPANESE)
2010年03月29日(月)
統計数学セミナー
13:00-14:10 数理科学研究科棟(駒場) 002号室
Catherine Laredo 氏 (MIA, INRA)
Inference for partially observed Markov processes and applications
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html
Catherine Laredo 氏 (MIA, INRA)
Inference for partially observed Markov processes and applications
[ 講演概要 ]
We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.
We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.
[ 参考URL ]We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.
We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html
2010年03月25日(木)
講演会
17:00-18:00 数理科学研究科棟(駒場) 370号室
Dr Bangti Jin 氏 (Center for Industrial Mathematics University of Bremen, Germany)
Heuristic Choice Rules for Convex Variational Regularization
Dr Bangti Jin 氏 (Center for Industrial Mathematics University of Bremen, Germany)
Heuristic Choice Rules for Convex Variational Regularization
[ 講演概要 ]
In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.
In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.
講演会
16:00-17:00 数理科学研究科棟(駒場) 370号室
M.M. Lavrentiev, Jr. 氏 (Sobolev Institute of Mathematics, Novosibirsk, Russia)
Modern computer architectures for tsunami simulation
M.M. Lavrentiev, Jr. 氏 (Sobolev Institute of Mathematics, Novosibirsk, Russia)
Modern computer architectures for tsunami simulation
[ 講演概要 ]
Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.
Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.
2010年03月23日(火)
GCOEセミナー
15:00-17:15 数理科学研究科棟(駒場) 370号室
Mourad Bellassoued 氏 (Univ. of Bizerte) 15:00-16:00
Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map
On uniqueness in inverse elastic obstacle scattering
Mourad Bellassoued 氏 (Univ. of Bizerte) 15:00-16:00
Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map
[ 講演概要 ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
Johannes Elschner 氏 (Weierstrass Institute Berlin, Germany) 16:15-17:15In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
On uniqueness in inverse elastic obstacle scattering
[ 講演概要 ]
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.
2010年03月19日(金)
講演会
11:00-12:00 数理科学研究科棟(駒場) 366号室
竹内 知哉 氏 (North Carolina State University, USA)
A Regularization Parameter for Nonsmooth Tikhonov Regularization
竹内 知哉 氏 (North Carolina State University, USA)
A Regularization Parameter for Nonsmooth Tikhonov Regularization
[ 講演概要 ]
We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.
We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.
2010年03月17日(水)
講演会
16:30-17:30 数理科学研究科棟(駒場) 128号室
三角 淳 氏 (東大数理)
方向依存性を持つ長距離パーコレーションの臨界曲線
三角 淳 氏 (東大数理)
方向依存性を持つ長距離パーコレーションの臨界曲線
2010年03月15日(月)
統計数学セミナー
15:00-16:00 数理科学研究科棟(駒場) 002号室
Cecilia Mancini 氏 (University of Florence)
BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html
Cecilia Mancini 氏 (University of Florence)
BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION
[ 講演概要 ]
We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.
Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.
Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.
The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.
This talk is based on Mancini and Gobbi (2009), and Mancini (2010).
[ 参考URL ]We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.
Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.
Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.
The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.
This talk is based on Mancini and Gobbi (2009), and Mancini (2010).
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html
統計数学セミナー
14:00-15:00 数理科学研究科棟(駒場) 002号室
Alexandre Brouste 氏 (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
Alexandre Brouste 氏 (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
[ 講演概要 ]
In various fields, the {\\it signal} process, whose law depends on an unknown parameter $ artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $ artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.
[ 参考URL ]In various fields, the {\\it signal} process, whose law depends on an unknown parameter $ artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $ artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
2010年03月12日(金)
談話会・数理科学講演会
15:00-17:30 数理科学研究科棟(駒場) 050号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
岡本和夫 氏 (東京大学大学院数理科学研究科) 15:00-16:00
ガルニエ系の数理
特性類と不変量を巡る旅
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
岡本和夫 氏 (東京大学大学院数理科学研究科) 15:00-16:00
ガルニエ系の数理
[ 講演概要 ]
ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。
森田茂之 氏 (東京大学大学院数理科学研究科) 16:30-17:30ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。
特性類と不変量を巡る旅
[ 講演概要 ]
40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.
40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.
2010年03月09日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 123号室
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Joachim Escher 氏 (Leibniz University of Hanover)
Shallow water waves with singularities
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Joachim Escher 氏 (Leibniz University of Hanover)
Shallow water waves with singularities
[ 講演概要 ]
The Degasperis-Procesi equation is a recently derived shallow water wave equation, which is - similar as the Camassa-Holm equation - embedded in a family of spatially periodic third order dispersive conservation laws.
The coexistence of globally in time defined classical solutions, wave breaking solutions, and spatially periodic peakons and shock waves is evidenced in the talk, and the precise blow-up scenario, including blow-up rates and blow-up sets, is discussed in detail. Finally several conditions on the initial profile are presented, which ensure the occurence of a breaking wave.
The Degasperis-Procesi equation is a recently derived shallow water wave equation, which is - similar as the Camassa-Holm equation - embedded in a family of spatially periodic third order dispersive conservation laws.
The coexistence of globally in time defined classical solutions, wave breaking solutions, and spatially periodic peakons and shock waves is evidenced in the talk, and the precise blow-up scenario, including blow-up rates and blow-up sets, is discussed in detail. Finally several conditions on the initial profile are presented, which ensure the occurence of a breaking wave.
2010年02月24日(水)
講演会
15:00-16:30 数理科学研究科棟(駒場) 370号室
Robert Penner 氏 (Aarhus University / University of Southern California)
Protein Moduli Space
Robert Penner 氏 (Aarhus University / University of Southern California)
Protein Moduli Space
[ 講演概要 ]
Recent joint works with J. E. Andersen and others
provide explicit discrete and continuous models
of protein geometry. These models are inspired
by corresponding constructions in the study of moduli
spaces of flat G-connections on surfaces, in particular,
for G=PSL(2,R) and G=SO(3). These models can be used
for protein classification as well as for folding prediction,
and computer experiments towards these ends will
be discussed.
Recent joint works with J. E. Andersen and others
provide explicit discrete and continuous models
of protein geometry. These models are inspired
by corresponding constructions in the study of moduli
spaces of flat G-connections on surfaces, in particular,
for G=PSL(2,R) and G=SO(3). These models can be used
for protein classification as well as for folding prediction,
and computer experiments towards these ends will
be discussed.
2010年02月23日(火)
講演会
14:00-15:00 数理科学研究科棟(駒場) 122号室
Bendong LOU 氏 (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
Bendong LOU 氏 (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
[ 講演概要 ]
We consider the Allen-Cahn equation in a cylinder with periodic undulating boundaries in the plane. Our problem involves two small parameters $\\delta$ and $\\epsilon$, where $\\delta$ appears in the equation to denote the scale of the singular limit and $\\epsilon$ appears in the boundary conditions to denote the scale of the homogenization limit. We consider the following two limiting processes:
(I): taking homogenization limit first and then taking singular limit;
(II) taking singular limit first and then taking homogenization limit.
We formally show that they both result in the same mean curvature flow equation, but with different boundary conditions.
We consider the Allen-Cahn equation in a cylinder with periodic undulating boundaries in the plane. Our problem involves two small parameters $\\delta$ and $\\epsilon$, where $\\delta$ appears in the equation to denote the scale of the singular limit and $\\epsilon$ appears in the boundary conditions to denote the scale of the homogenization limit. We consider the following two limiting processes:
(I): taking homogenization limit first and then taking singular limit;
(II) taking singular limit first and then taking homogenization limit.
We formally show that they both result in the same mean curvature flow equation, but with different boundary conditions.
2010年02月19日(金)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
[ 講演概要 ]
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
2010年02月18日(木)
GCOEレクチャーズ
10:30-17:00 数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
Discrete groups acting on homogeneous spaces IV
Yves Benoist 氏 (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ 講演概要 ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist 氏 (Paris Sud) 15:00-16:00In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Discrete groups acting on homogeneous spaces IV
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Roberto Longo 氏 (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory
Roberto Longo 氏 (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 002号室
Bendong LOU 氏 (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
Bendong LOU 氏 (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
[ 講演概要 ]
We consider a quasilinear parabolic equation with the following nonlinear Neumann boundary condition:
"the slope of the solution on the boundary is a function $g$ of the value of the solution". Here $g$ takes values near its supremum with the frequency of $\\epsilon$. We show that the homogenization limit of the solution, as $\\epsilon$ tends to 0, is the solution satisfying the linear Neumann boundary condition: "the slope of the solution on the boundary is the supremum of $g$".
We consider a quasilinear parabolic equation with the following nonlinear Neumann boundary condition:
"the slope of the solution on the boundary is a function $g$ of the value of the solution". Here $g$ takes values near its supremum with the frequency of $\\epsilon$. We show that the homogenization limit of the solution, as $\\epsilon$ tends to 0, is the solution satisfying the linear Neumann boundary condition: "the slope of the solution on the boundary is the supremum of $g$".
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