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過去の記録
過去の記録 ～11/11｜本日 11/12 | 今後の予定 11/13～
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials
[ 講演概要 ]
多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．
このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが
原点からある点へ移動するために必要とするコスト(到達コスト)を考える．
到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，
到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．
多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．
このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが
原点からある点へ移動するために必要とするコスト(到達コスト)を考える．
到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，
到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．
2015年10月30日(金)
FMSPレクチャーズ
15:00-16:15 数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
[ 講演参考URL ]In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf
FMSPレクチャーズ
16:30-17:45 数理科学研究科棟(駒場) 128号室
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
[ 講演概要 ]
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
[ 講演参考URL ]Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf
2015年10月28日(水)
数理人口学・数理生物学セミナー
14:55-16:40 数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
[ 講演概要 ]
r/K 選択説が提唱されてから半世紀になろうとしている．この仮説は生物の生活
史戦略の中で現れる、短命多産多死、長寿少産少死の戦略を持つ種の違いをロジ
スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて
種がその人口規模に応じてどちらか一方のパラメータを最大化させる戦略の違い
であると論じたものである．この説は発表当初から賛否両論を巻き起こしてきた．
特に論争の的となったのは人口密度が環境収容力付近にある場合に、生活史進化
が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である．実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた．2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か？”
という疑問を残したまま停滞している．そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この
問題に適用した．その結果、密度効果と確率制御理論の持つ生活史ノイズを組み
合わせることによって、飽和人口における最適戦略は従来のr/K選択説よりも多
様である事が示せた．本講演では、その結果を紹介したい．
r/K 選択説が提唱されてから半世紀になろうとしている．この仮説は生物の生活
史戦略の中で現れる、短命多産多死、長寿少産少死の戦略を持つ種の違いをロジ
スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて
種がその人口規模に応じてどちらか一方のパラメータを最大化させる戦略の違い
であると論じたものである．この説は発表当初から賛否両論を巻き起こしてきた．
特に論争の的となったのは人口密度が環境収容力付近にある場合に、生活史進化
が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である．実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた．2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か？”
という疑問を残したまま停滞している．そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この
問題に適用した．その結果、密度効果と確率制御理論の持つ生活史ノイズを組み
合わせることによって、飽和人口における最適戦略は従来のr/K選択説よりも多
様である事が示せた．本講演では、その結果を紹介したい．
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions
2015年10月27日(火)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
[ 講演概要 ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
(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.)
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
(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.)
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
Yuanyuan Bao 氏 (東京大学大学院数理科学研究科)
Heegaard Floer homology for graphs (JAPANESE)
Tea : Common Room 16:30 -- 17:00
Yuanyuan Bao 氏 (東京大学大学院数理科学研究科)
Heegaard Floer homology for graphs (JAPANESE)
[ 講演概要 ]
Ozsváth and Szabó defined the Heegaard Floer homology (HF) for a closed oriented 3-manifold. The definition was then generalized to links embedded in a 3-manifold and the manifolds with boundary (sutured and bordered manifolds). In the case of links, there is a beautiful combinatorial way to rewrite the original definition of HF, which was defined on a Heegaard diagram of the given link, by using grid diagram. For a balanced bipartite graph, we defined its Heegaard diagram and the HF for it. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods.
Ozsváth and Szabó defined the Heegaard Floer homology (HF) for a closed oriented 3-manifold. The definition was then generalized to links embedded in a 3-manifold and the manifolds with boundary (sutured and bordered manifolds). In the case of links, there is a beautiful combinatorial way to rewrite the original definition of HF, which was defined on a Heegaard diagram of the given link, by using grid diagram. For a balanced bipartite graph, we defined its Heegaard diagram and the HF for it. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods.
トポロジー火曜セミナー
15:00-16:30 数理科学研究科棟(駒場) 056号室
Jianfeng Lin 氏 (UCLA)
The unfolded Seiberg-Witten-Floer spectrum and its applications
(ENGLISH)
Jianfeng Lin 氏 (UCLA)
The unfolded Seiberg-Witten-Floer spectrum and its applications
(ENGLISH)
[ 講演概要 ]
Following Furuta's idea of finite dimensional approximation in
the Seiberg-Witten theory, Manolescu defined the Seiberg-Witten-Floer
stable homotopy type for rational homology three-spheres in 2003. In
this talk, I will explain how to construct similar invariants for a
general three-manifold and discuss some applications of these new
invariants. This is a joint work with Tirasan Khandhawit and Hirofumi
Sasahira.
Following Furuta's idea of finite dimensional approximation in
the Seiberg-Witten theory, Manolescu defined the Seiberg-Witten-Floer
stable homotopy type for rational homology three-spheres in 2003. In
this talk, I will explain how to construct similar invariants for a
general three-manifold and discuss some applications of these new
invariants. This is a joint work with Tirasan Khandhawit and Hirofumi
Sasahira.
2015年10月26日(月)
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
Lawrence Ein 氏 (University of Illinois at Chicago)
Asymptotic syzygies and the gonality conjecture (English)
Lawrence Ein 氏 (University of Illinois at Chicago)
Asymptotic syzygies and the gonality conjecture (English)
[ 講演概要 ]
We'll discuss my joint work with Lazarsfeld on the gonality conjecture about the syzygies of a smooth projective curve when it is embedded into the projective space by the complete linear system of a sufficiently very ample line bundles. We'll also discuss some results about the asymptotic syzygies f higher dimensional varieties.
We'll discuss my joint work with Lazarsfeld on the gonality conjecture about the syzygies of a smooth projective curve when it is embedded into the projective space by the complete linear system of a sufficiently very ample line bundles. We'll also discuss some results about the asymptotic syzygies f higher dimensional varieties.
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
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
[ 講演概要 ]
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Fredrik Lindgren 氏 (大阪大学)
Numerical approximation of spinodal decomposition in the presence of noise (English)
Fredrik Lindgren 氏 (大阪大学)
Numerical approximation of spinodal decomposition in the presence of noise (English)
[ 講演概要 ]
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.
In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.
We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.
If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.
This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.
In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.
We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.
If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.
This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).
2015年10月23日(金)
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 126号室
大鳥羽 暢彦 氏 (慶應義塾大学)
球面束上のスカラー曲率一定計量 (Japanese)
大鳥羽 暢彦 氏 (慶應義塾大学)
球面束上のスカラー曲率一定計量 (Japanese)
[ 講演概要 ]
この講演は Jimmy Petean 氏との共同研究に基づく.
2つの Riemann 多様体の捻れ積 (より正確には, 全測地的ファイバーを持つ Riemann 沈め込みの全空間) の上で山辺 PDE を解析する我々の試みについて話す. 例として, それぞれ内積つきのベクトル束 $E$ と直線束 $L$ の Whitney 和の単位球面束 $U(E \oplus L)$ の上にスカラー曲率一定計量を構成し, この場合にはどのようにして山辺 PDE の解の個数を評価できるか説明する.
この講演は Jimmy Petean 氏との共同研究に基づく.
2つの Riemann 多様体の捻れ積 (より正確には, 全測地的ファイバーを持つ Riemann 沈め込みの全空間) の上で山辺 PDE を解析する我々の試みについて話す. 例として, それぞれ内積つきのベクトル束 $E$ と直線束 $L$ の Whitney 和の単位球面束 $U(E \oplus L)$ の上にスカラー曲率一定計量を構成し, この場合にはどのようにして山辺 PDE の解の個数を評価できるか説明する.
2015年10月22日(木)
FMSPレクチャーズ
16:00-16:50 数理科学研究科棟(駒場) 002号室
応用解析セミナーとの共催
Hans-Otto Walther 氏 (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
応用解析セミナーとの共催
Hans-Otto Walther 氏 (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
[ 講演概要 ]
The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
[ 講演参考URL ]The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
FMSPレクチャーズ
17:00-17:50 数理科学研究科棟(駒場) 002号室
応用解析セミナーとの共催
Hans-Otto Walther 氏 (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
応用解析セミナーとの共催
Hans-Otto Walther 氏 (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ 講演概要 ]
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[ 講演参考URL ]What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
応用解析セミナー
16:00-17:50 数理科学研究科棟(駒場) 002号室
2つ講演があります．
Hans-Otto Walther 氏 (ギーセン大学)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
2つ講演があります．
Hans-Otto Walther 氏 (ギーセン大学)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ 講演概要 ]
(Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.
The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
[ 講演参考URL ](Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.
The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
2015年10月21日(水)
数理人口学・数理生物学セミナー
14:55-16:40 数理科学研究科棟(駒場) 128演習室号室
大森亮介 氏 (北海道大学人獣共通感染症リサーチセンター バイオインフォマティクス部門)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html
大森亮介 氏 (北海道大学人獣共通感染症リサーチセンター バイオインフォマティクス部門)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
[ 講演概要 ]
Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
[ 講演参考URL ]Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html
2015年10月20日(火)
FMSPレクチャーズ
16:50-18:20 数理科学研究科棟(駒場) 128号室
解析学火曜セミナーと共催
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
解析学火曜セミナーと共催
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ 講演概要 ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ 講演参考URL ]We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
FMSPレクチャーズと共催／部屋が普段と異なりますのでご注意ください
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
FMSPレクチャーズと共催／部屋が普段と異なりますのでご注意ください
Danielle Hilhorst 氏 (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ 講演概要 ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ 講演参考URL ]We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
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
Bruno Scardua 氏 (Universidade Federal do Rio de Janeiro)
On the existence of stable compact leaves for
transversely holomorphic foliations (ENGLISH)
Tea : Common Room 17:00 -- 17:30
Bruno Scardua 氏 (Universidade Federal do Rio de Janeiro)
On the existence of stable compact leaves for
transversely holomorphic foliations (ENGLISH)
[ 講演概要 ]
One of the most important results in the theory of foliations is
the celebrated Local stability theorem of Reeb :
A compact leaf of a foliation having finite holonomy group is
stable, indeed, it admits a fundamental system of invariant
neighborhoods where each leaf is compact with finite holonomy
group. This result, together with the Global stability theorem of Reeb
(for codimension one real foliations), has many important consequences
and motivates several questions in the theory of foliations. In this talk
we show how to prove:
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable
leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
This is a joint work with Cesar Camacho.
One of the most important results in the theory of foliations is
the celebrated Local stability theorem of Reeb :
A compact leaf of a foliation having finite holonomy group is
stable, indeed, it admits a fundamental system of invariant
neighborhoods where each leaf is compact with finite holonomy
group. This result, together with the Global stability theorem of Reeb
(for codimension one real foliations), has many important consequences
and motivates several questions in the theory of foliations. In this talk
we show how to prove:
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable
leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
This is a joint work with Cesar Camacho.
2015年10月19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
森脇 淳 氏 (京都大学)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
森脇 淳 氏 (京都大学)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
[ 講演概要 ]
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
Stefano Olla 氏 (University of Paris-Dauphine)
Entropy and hypo-coercive methods in hydrodynamic limits
Stefano Olla 氏 (University of Paris-Dauphine)
Entropy and hypo-coercive methods in hydrodynamic limits
[ 講演概要 ]
Relative Entropy and entropy production have been main tools
in obtaining hydrodynamic limits Entropic hypo-coercivity can be used to
extend this method to dynamics with highly degenerate noise. I will
apply it to a chain of anharmonic oscillators immersed in a temperature
gradient. Stationary states of these dynamics are of ’non equilibrium’,
and their entropy production does not allow the application of previous
techniques. These dynamics model microscopically an isothermal
thermodynamic transformation between non-equilibrium stationary states.
Ref: http://arxiv.org/abs/1505.05002
Relative Entropy and entropy production have been main tools
in obtaining hydrodynamic limits Entropic hypo-coercivity can be used to
extend this method to dynamics with highly degenerate noise. I will
apply it to a chain of anharmonic oscillators immersed in a temperature
gradient. Stationary states of these dynamics are of ’non equilibrium’,
and their entropy production does not allow the application of previous
techniques. These dynamics model microscopically an isothermal
thermodynamic transformation between non-equilibrium stationary states.
Ref: http://arxiv.org/abs/1505.05002
統計数学セミナー
13:00-16:40 数理科学研究科棟(駒場) 052号室
水田 正弘 氏 (北海道大学 情報基盤センター)
ビッグデータブームと統計学
水田 正弘 氏 (北海道大学 情報基盤センター)
ビッグデータブームと統計学
[ 講演概要 ]
ビッグデータおよび関連する事項について扱います。
以下の内容を予定しております。
１．ビッグデータの定義と特徴
２．ビッグデータブーム・・・？
３．統計学の流れ
４．ビッグデータの解析に使える統計学
５．可視化は有効か？
６．ミニデータ
７．SDAとFDA
８．その他
ビッグデータおよび関連する事項について扱います。
以下の内容を予定しております。
１．ビッグデータの定義と特徴
２．ビッグデータブーム・・・？
３．統計学の流れ
４．ビッグデータの解析に使える統計学
５．可視化は有効か？
６．ミニデータ
７．SDAとFDA
８．その他
2015年10月16日(金)
FMSPレクチャーズ
15:00-17:30 数理科学研究科棟(駒場) 056号室
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization IV (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization IV (ENGLISH)
[ 講演概要 ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ 講演参考URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 126号室
山川大亮 氏 (東京工業大学)
射影直線上の有理型接続と箙多様体 (Japanese)
山川大亮 氏 (東京工業大学)
射影直線上の有理型接続と箙多様体 (Japanese)
[ 講演概要 ]
Crawley-Boevey によって，射影直線上のある種の対数型接続のモジュライ空間が複素シンプレクティック多様体として中島箙多様体と同型である事が示された．この講演では，Boalch によって予想され廣惠一希との共同研究によって正当化された彼の結果の一般化について紹介し，またそれと関連して有理型接続のモノドロミー保存変形のワイル群対称性についても述べる．
Crawley-Boevey によって，射影直線上のある種の対数型接続のモジュライ空間が複素シンプレクティック多様体として中島箙多様体と同型である事が示された．この講演では，Boalch によって予想され廣惠一希との共同研究によって正当化された彼の結果の一般化について紹介し，またそれと関連して有理型接続のモノドロミー保存変形のワイル群対称性についても述べる．
2015年10月15日(木)
FMSPレクチャーズ
15:00-18:00 数理科学研究科棟(駒場) 126号室
David Sauzin 氏 (CNRS - Centro di Ricerca Matematica Ennio De Giorgi Scuola Normale Superiore di Pisa)
Introduction to 1-summability and resurgence (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf
David Sauzin 氏 (CNRS - Centro di Ricerca Matematica Ennio De Giorgi Scuola Normale Superiore di Pisa)
Introduction to 1-summability and resurgence (ENGLISH)
[ 講演概要 ]
The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.
[ 講演参考URL ]The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf
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