本文印刷
全画面プリント
過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
2017年08月30日(水)
博士論文発表会
10:00-11:15 数理科学研究科棟(駒場) 128号室
佐藤 僚 氏 (東京大学大学院数理科学研究科)
Modular invariant representations over the N=2 superconformal algebra
（モジュラー不変性をもつN=2 超共形代数の表現について） (JAPANESE)
佐藤 僚 氏 (東京大学大学院数理科学研究科)
Modular invariant representations over the N=2 superconformal algebra
（モジュラー不変性をもつN=2 超共形代数の表現について） (JAPANESE)
2017年08月25日(金)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 128号室
CLINET, Simon 氏 (東京大学大学院数理科学研究科)
Statistical inference for point processes and application to Limit Order Book
（点過程に対する統計的推測及びリミットオーダーブックへの応用） (ENGLISH)
CLINET, Simon 氏 (東京大学大学院数理科学研究科)
Statistical inference for point processes and application to Limit Order Book
（点過程に対する統計的推測及びリミットオーダーブックへの応用） (ENGLISH)
2017年08月23日(水)
統計数学セミナー
13:30-14:40 数理科学研究科棟(駒場) 052号室
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
Sebastian Holtz 氏 (Humboldt University of Berlin)
Covariation estimation from noisy Gaussian observations:equivalence, efficiency and estimation
[ 講演概要 ]
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
In this work the estimation of functionals of the quadratic covariation matrix from a discretely observed Gaussian path on [0,1] under noise is discussed and analysed on a large scale. At first asymptotic equivalence in Le Cam's sense is established to link the initial high-frequency model to its continuous counterpart. Then sharp asymptotic lower bounds for a general class of parametric basic case models, including the fractional Brownian motion, are derived. These bounds are generalised to the nonparametric and even random parameter setup for certain special cases, e.g. Itô processes. Finally, regular sequences of spectral estimators are constructed that obey the derived efficiency statements.
2017年07月28日(金)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
Benoit Collins 氏 (京大理)
Free orthogonal groups and quantum information (English)
Benoit Collins 氏 (京大理)
Free orthogonal groups and quantum information (English)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 128号室
江尻 祥 氏 (東京大学大学院数理科学研究科)
Studies on algebraic fiber spaces in positive characteristic
（正標数の代数的ファイバー空間に関する研究） (JAPANESE)
江尻 祥 氏 (東京大学大学院数理科学研究科)
Studies on algebraic fiber spaces in positive characteristic
（正標数の代数的ファイバー空間に関する研究） (JAPANESE)
博士論文発表会
15:45-17:00 数理科学研究科棟(駒場) 128号室
金光 秋博 氏 (東京大学大学院数理科学研究科)
Studies on Fano manifolds and vector bundles
（Fano多様体とベクトル束の研究） (JAPANESE)
金光 秋博 氏 (東京大学大学院数理科学研究科)
Studies on Fano manifolds and vector bundles
（Fano多様体とベクトル束の研究） (JAPANESE)
2017年07月25日(火)
博士論文発表会
15:00-16:15 数理科学研究科棟(駒場) 128号室
桑垣 樹 氏 (東京大学大学院数理科学研究科)
The nonequivariant coherent-constructible correspondence for toric stacks
(トーリックスタックにおける連接-構成可能対応) (JAPANESE)
桑垣 樹 氏 (東京大学大学院数理科学研究科)
The nonequivariant coherent-constructible correspondence for toric stacks
(トーリックスタックにおける連接-構成可能対応) (JAPANESE)
2017年07月21日(金)
社会数理コロキウム
16:30-17:30 数理科学研究科棟(駒場) 123号室
17:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
数理科学を原理とする第4次産業革命 (JAPANESE)
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20170721.pdf
17:30から 2階コモンルームで講演者を囲んで情報交換会を予定しております。
藤原 洋 氏 (株式会社ブロードバンドタワー 代表取締役会長兼社長CEO)
数理科学を原理とする第4次産業革命 (JAPANESE)
[ 講演概要 ]
第1次産業革命は、力学を原理としてイギリスで生まれた紡績機械・蒸気機関・石炭製鉄の発明で、海運業・鉄道業というサービス産業を産み出した。第2次産業革命は、化学反応を原理として、ドイツで生まれた物質科学による内燃機関の発明によってアメリカで発展したもので、自動車物流・電力供給というサービス産業を産み出した。第3次産業革命は、量子物理学を原理として、アメリカで生まれた通信・コンピュータ・半導体の発明によって金融・流通というサービス産業を革新的に発展させた。このように、産業革命とは、ものづくりがサービスと連携することにその本質がある。すなわち、第2次産業と第3次産業との連携にその本質がある。
そこで、第4次産業革命を数理科学を原理とする「デジタル・トランスフォーメーション革命」と捉え、従来成立しているあらゆる産業をデジタル化すること、すなわちビジネスモデルを転換する新たな産業革命であると考えることが重要である。
本講義では、この新たな産業革命は、IoT/ビッグデータ/AI（人工知能）とこれを支える数理科学の役割について述べることとする。
[ 参考URL ]第1次産業革命は、力学を原理としてイギリスで生まれた紡績機械・蒸気機関・石炭製鉄の発明で、海運業・鉄道業というサービス産業を産み出した。第2次産業革命は、化学反応を原理として、ドイツで生まれた物質科学による内燃機関の発明によってアメリカで発展したもので、自動車物流・電力供給というサービス産業を産み出した。第3次産業革命は、量子物理学を原理として、アメリカで生まれた通信・コンピュータ・半導体の発明によって金融・流通というサービス産業を革新的に発展させた。このように、産業革命とは、ものづくりがサービスと連携することにその本質がある。すなわち、第2次産業と第3次産業との連携にその本質がある。
そこで、第4次産業革命を数理科学を原理とする「デジタル・トランスフォーメーション革命」と捉え、従来成立しているあらゆる産業をデジタル化すること、すなわちビジネスモデルを転換する新たな産業革命であると考えることが重要である。
本講義では、この新たな産業革命は、IoT/ビッグデータ/AI（人工知能）とこれを支える数理科学の役割について述べることとする。
http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20170721.pdf
2017年07月18日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
呼子 笛太郎 氏 (東北大理)
On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)
呼子 笛太郎 氏 (東北大理)
On a generalization of Frobenius-splitting and a lifting problem of Calabi-Yau varieties (JAPANESE)
[ 講演概要 ]
In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.
In this talk, we introduce a notion of Frobenius-splitting height which quantifies Frobenius-splitting varieties and show that a Calabi-Yau variety of finite height over an algebraically closed field of positive characteristic admits a flat lifting to the ring of Witt vectors of length two.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
米田 剛 氏 (東京大学)
軸対称非圧縮Euler方程式の或る瞬間爆発について (日本語)
米田 剛 氏 (東京大学)
軸対称非圧縮Euler方程式の或る瞬間爆発について (日本語)
[ 講演概要 ]
本講演では、軸対称非圧縮Euler方程式の瞬間爆発についての結果を報告する。より具体的には、$C^{2,\alpha}$ ($0<\alpha<1$)に入る初期速度場に対応する解が、任意の$T$における$C^1([0,T):C^2)$には入らないという定理を紹介する。定理の証明には、特異積分作用素の$L^\infty$-非有界性は一切使わず、代わりにFrenet-Serret formulasやorthonormal moving frameといった幾何学的概念を本質的に使う。時間があれば、この洞察の物理的背景も紹介したい。
本講演では、軸対称非圧縮Euler方程式の瞬間爆発についての結果を報告する。より具体的には、$C^{2,\alpha}$ ($0<\alpha<1$)に入る初期速度場に対応する解が、任意の$T$における$C^1([0,T):C^2)$には入らないという定理を紹介する。定理の証明には、特異積分作用素の$L^\infty$-非有界性は一切使わず、代わりにFrenet-Serret formulasやorthonormal moving frameといった幾何学的概念を本質的に使う。時間があれば、この洞察の物理的背景も紹介したい。
2017年07月13日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 122号室
下條昌彦 氏 (岡山理科大学)
Behaviors of solutions for a singular prey-predator model and its shadow system
(JAPANESE)
下條昌彦 氏 (岡山理科大学)
Behaviors of solutions for a singular prey-predator model and its shadow system
(JAPANESE)
[ 講演概要 ]
We study the asymptotic behavior and quenching of solutions for a two-component system of reaction diffusion equations modeling prey-predator interactions in an insular environment. First, we give the global existence of solutions to the corresponding shadow system. Then, by constructing some suitable Lyapunov functionals, we characterize the asymptotic behaviors of global solutions to the shadow system. Also, we give a quenching result for the shadow system. Finally, some global existence results and the asymptotic behavior for the original reaction diffusion system are given.
This is joint work with Jong-Shenq Guo (Tamkang Univ.) and Arnaud Ducrot (Univ. Bordeaux).
We study the asymptotic behavior and quenching of solutions for a two-component system of reaction diffusion equations modeling prey-predator interactions in an insular environment. First, we give the global existence of solutions to the corresponding shadow system. Then, by constructing some suitable Lyapunov functionals, we characterize the asymptotic behaviors of global solutions to the shadow system. Also, we give a quenching result for the shadow system. Finally, some global existence results and the asymptotic behavior for the original reaction diffusion system are given.
This is joint work with Jong-Shenq Guo (Tamkang Univ.) and Arnaud Ducrot (Univ. Bordeaux).
2017年07月11日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
松澤 陽介 氏 (東大数理)
Arithmetic and dynamical degrees of self-maps of algebraic varieties (English or Japanese)
松澤 陽介 氏 (東大数理)
Arithmetic and dynamical degrees of self-maps of algebraic varieties (English or Japanese)
[ 講演概要 ]
The first dynamical degree is an important birational invariant which measures the geometric complexity of dominant rational self-maps of algebraic varieties. On the other hand, when the variety is defined over a number field, one can associate to an orbit an invariant using Weil height function, called arithmetic degree, which measures the arithmetic complexity of the orbit. It is conjectured that the arithmetic degree of a Zariski dense orbit is equal to the first dynamical degree (Kawaguchi-Silverman). I will explain several results related to this conjecture. I will also explain applications to proofs of purely geometric statements.
The first dynamical degree is an important birational invariant which measures the geometric complexity of dominant rational self-maps of algebraic varieties. On the other hand, when the variety is defined over a number field, one can associate to an orbit an invariant using Weil height function, called arithmetic degree, which measures the arithmetic complexity of the orbit. It is conjectured that the arithmetic degree of a Zariski dense orbit is equal to the first dynamical degree (Kawaguchi-Silverman). I will explain several results related to this conjecture. I will also explain applications to proofs of purely geometric statements.
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
Celeste Damiani 氏 (JSPS, 大阪市立大学)
Some remarkable quotients of virtual braid groups (ENGLISH)
Tea: Common Room 16:30-17:00
Celeste Damiani 氏 (JSPS, 大阪市立大学)
Some remarkable quotients of virtual braid groups (ENGLISH)
[ 講演概要 ]
Virtual braid groups are one of the most famous generalizations of braid groups. We introduce a family of quotients of virtual braid groups, called loop braid groups. These groups have been an object of interest in different domains of mathematics and mathematical physics, and can be found in the literature also by names such as groups of permutation-conjugacy automorphisms, braid- permutation groups, welded braid groups, weakly virtual braid groups, untwisted ring groups, and others. We show that they share with braid groups the property of admitting many different definitions. After that we consider a further family of quotients called unrestricted virtual braids, describe their structure and explore their relations with fused links.
Virtual braid groups are one of the most famous generalizations of braid groups. We introduce a family of quotients of virtual braid groups, called loop braid groups. These groups have been an object of interest in different domains of mathematics and mathematical physics, and can be found in the literature also by names such as groups of permutation-conjugacy automorphisms, braid- permutation groups, welded braid groups, weakly virtual braid groups, untwisted ring groups, and others. We show that they share with braid groups the property of admitting many different definitions. After that we consider a further family of quotients called unrestricted virtual braids, describe their structure and explore their relations with fused links.
博士論文発表会
15:00-16:15 数理科学研究科棟(駒場) 128号室
三浦 達哉 氏 (東京大学大学院数理科学研究科)
On effects of curvatures of curves, surfaces and graphs （曲線、曲面およびグラフの曲率の効果について）
(ENGLISH)
三浦 達哉 氏 (東京大学大学院数理科学研究科)
On effects of curvatures of curves, surfaces and graphs （曲線、曲面およびグラフの曲率の効果について）
(ENGLISH)
2017年07月10日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
Mei Yin 氏 (University of Denver)
Phase transitions in exponential random graphs (ENGLISH)
Mei Yin 氏 (University of Denver)
Phase transitions in exponential random graphs (ENGLISH)
[ 講演概要 ]
Large networks have become increasingly popular over the last decades, and their modeling and investigation have led to interesting and new ways to apply statistical and analytical methods. The introduction of exponential random graphs has aided in this pursuit, as they are able to capture a wide variety of common network tendencies by representing a complex global structure through a set of tractable local features. This talk with focus on the phenomenon of phase transitions in large exponential random graphs. The main techniques that we use are variants of statistical physics but the exciting new theory of graph limits, which has rich ties to many parts of mathematics and beyond, also plays an important role in the interdisciplinary inquiry. Some open problems and conjectures will be presented.
Large networks have become increasingly popular over the last decades, and their modeling and investigation have led to interesting and new ways to apply statistical and analytical methods. The introduction of exponential random graphs has aided in this pursuit, as they are able to capture a wide variety of common network tendencies by representing a complex global structure through a set of tractable local features. This talk with focus on the phenomenon of phase transitions in large exponential random graphs. The main techniques that we use are variants of statistical physics but the exciting new theory of graph limits, which has rich ties to many parts of mathematics and beyond, also plays an important role in the interdisciplinary inquiry. Some open problems and conjectures will be presented.
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
荒野悠輝 氏 (京大理)
Rokhlin actions of fusion categories
荒野悠輝 氏 (京大理)
Rokhlin actions of fusion categories
2017年07月07日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 002号室
Richard Stanley 氏 (MIT/University of Miami)
Smith Normal Form and Combinatorics (English)
http://www-math.mit.edu/~rstan/
Richard Stanley 氏 (MIT/University of Miami)
Smith Normal Form and Combinatorics (English)
[ 講演概要 ]
Let $R$ be a commutative ring (with identity) and $A$ an $n \times n$ matrix over $R$. Suppose there exist $n \times n$ matrices $P,Q$ invertible over $R$ for which PAQ is a diagonal matrix $diag(e_1,...,e_r,0,...,0)$, where $e_i$ divides $e_{i+1}$ in $R$. We then call $PAQ$ a Smith normal form (SNF) of $A$. If $R$ is a PID then an SNF always exists and is unique up to multiplication by units. Moreover if $A$ is invertible then $\det A=ua_1\cdots a_n$, where $u$ is a unit, so SNF gives a
canonical factorization of $\det A$.
We will survey some connections between SNF and combinatorics. Topics will include (1) the general theory of SNF, (2) a close connection between SNF and chip firing in graphs, (3) the SNF of a random matrix of integers (joint work with Yinghui Wang), (4) SNF of special classes of matrices, including some arising in the theory of symmetric functions, hyperplane arrangements, and lattice paths.
[ 参考URL ]Let $R$ be a commutative ring (with identity) and $A$ an $n \times n$ matrix over $R$. Suppose there exist $n \times n$ matrices $P,Q$ invertible over $R$ for which PAQ is a diagonal matrix $diag(e_1,...,e_r,0,...,0)$, where $e_i$ divides $e_{i+1}$ in $R$. We then call $PAQ$ a Smith normal form (SNF) of $A$. If $R$ is a PID then an SNF always exists and is unique up to multiplication by units. Moreover if $A$ is invertible then $\det A=ua_1\cdots a_n$, where $u$ is a unit, so SNF gives a
canonical factorization of $\det A$.
We will survey some connections between SNF and combinatorics. Topics will include (1) the general theory of SNF, (2) a close connection between SNF and chip firing in graphs, (3) the SNF of a random matrix of integers (joint work with Yinghui Wang), (4) SNF of special classes of matrices, including some arising in the theory of symmetric functions, hyperplane arrangements, and lattice paths.
http://www-math.mit.edu/~rstan/
2017年07月04日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
谷本 祥 氏 (University of Copenhagen)
The space of rational curves and Manin's conjecture (English)
谷本 祥 氏 (University of Copenhagen)
The space of rational curves and Manin's conjecture (English)
[ 講演概要 ]
Manin's conjecture predicts the asymptotic formula for the counting function of rational points on a Fano variety after removing the exceptional thin set. There are many developments on birational geometry of exceptional sets using MMP, due to Lehmann, myself, Tschinkel, Hacon, and Jiang. Recently we found that the study of exceptional sets has applications to questions regarding the space of rational curves, i.e., its dimension and the number of components. I would like to explain these applications. This is joint work with Brian Lehmann.
Manin's conjecture predicts the asymptotic formula for the counting function of rational points on a Fano variety after removing the exceptional thin set. There are many developments on birational geometry of exceptional sets using MMP, due to Lehmann, myself, Tschinkel, Hacon, and Jiang. Recently we found that the study of exceptional sets has applications to questions regarding the space of rational curves, i.e., its dimension and the number of components. I would like to explain these applications. This is joint work with Brian Lehmann.
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 002号室
Ming-Cheng Shiue 氏 (National Chiao Tung University)
Boundary conditions for Limited-Area Models (English)
Ming-Cheng Shiue 氏 (National Chiao Tung University)
Boundary conditions for Limited-Area Models (English)
[ 講演概要 ]
The problem of boundary conditions in a limited domain is recognized an important problem in geophysical fluid dynamics. This is due to that boundary conditions are proposed to have high resolution over a region of interest. The challenges for proposing later boundary conditions are of two types: on the computational side, if the proposed boundary conditions are not appropriate, it is well-known that the error from the lateral boundary can propagate into the computational domain and make a major effect on the numerical solution; on the mathematical side, the negative result of Oliger and Sundstrom that these equations including the inviscid primitive equations and shallow water equations in the multilayer case are not well-posed for any set of local boundary conditions.
In this talk, three-dimensional inviscid primitive equations and (one-layer and two-layer) shallow water equations which have been used in the limited-area numerical weather prediction modelings are considered. Our goals of this work are two folds: one is to propose boundary conditions which are physically suitable. That is, they let waves move freely out of the domain without producing spurious waves; the other is to numerically implement these boundary conditions by proposing suitable numerical methods. Numerical experiments are presented to demonstrate that these proposed boundary conditions and numerical schemes are suitable.
The problem of boundary conditions in a limited domain is recognized an important problem in geophysical fluid dynamics. This is due to that boundary conditions are proposed to have high resolution over a region of interest. The challenges for proposing later boundary conditions are of two types: on the computational side, if the proposed boundary conditions are not appropriate, it is well-known that the error from the lateral boundary can propagate into the computational domain and make a major effect on the numerical solution; on the mathematical side, the negative result of Oliger and Sundstrom that these equations including the inviscid primitive equations and shallow water equations in the multilayer case are not well-posed for any set of local boundary conditions.
In this talk, three-dimensional inviscid primitive equations and (one-layer and two-layer) shallow water equations which have been used in the limited-area numerical weather prediction modelings are considered. Our goals of this work are two folds: one is to propose boundary conditions which are physically suitable. That is, they let waves move freely out of the domain without producing spurious waves; the other is to numerically implement these boundary conditions by proposing suitable numerical methods. Numerical experiments are presented to demonstrate that these proposed boundary conditions and numerical schemes are suitable.
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
Jean-Baptiste Meilhan 氏 (Université Grenoble Alpes)
On link-homotopy for knotted surfaces in 4-space (ENGLISH)
Tea: Common Room 16:30-17:00
Jean-Baptiste Meilhan 氏 (Université Grenoble Alpes)
On link-homotopy for knotted surfaces in 4-space (ENGLISH)
[ 講演概要 ]
The purpose of this talk is to show how combinatorial objects (welded objects, which is a natural quotient of virtual knot theory) can be used to study knotted surfaces in 4-space.
We will first consider the case of 'ribbon' knotted surfaces, which are embedded surfaces bounding immersed 3-manifolds with only ribbon singularities. More precisely, we will consider ribbon knotted annuli ; these objects act naturally on the reduced free group, and we prove, using welded theory, that this action gives a classification up to link-homotopy, that is, up to continuous deformations leaving distinct component disjoint. This in turns implies a classification result for ribbon knotted tori.
Next, we will show how to extend this classification result beyond the ribbon case.
This is based on joint works with B. Audoux, P. Bellingeri and E. Wagner.
The purpose of this talk is to show how combinatorial objects (welded objects, which is a natural quotient of virtual knot theory) can be used to study knotted surfaces in 4-space.
We will first consider the case of 'ribbon' knotted surfaces, which are embedded surfaces bounding immersed 3-manifolds with only ribbon singularities. More precisely, we will consider ribbon knotted annuli ; these objects act naturally on the reduced free group, and we prove, using welded theory, that this action gives a classification up to link-homotopy, that is, up to continuous deformations leaving distinct component disjoint. This in turns implies a classification result for ribbon knotted tori.
Next, we will show how to extend this classification result beyond the ribbon case.
This is based on joint works with B. Audoux, P. Bellingeri and E. Wagner.
2017年07月03日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
徐 路 氏 (九州大学 大学院数理学研究院)
Equilibrium fluctuation for a chain of anharmonic oscillators (JAPANESE)
徐 路 氏 (九州大学 大学院数理学研究院)
Equilibrium fluctuation for a chain of anharmonic oscillators (JAPANESE)
[ 講演概要 ]
A chain of oscillators is a particle system whose microscopic time evolution is given by Hamilton equations with various kinds of conservative noises. Mathematicians and physicians are interested in its macroscopic behaviors (ε → 0) under different space-time scales: ballistic (hyperbolic) (εx, εt), diffusive (εx, ε^2t) and superdiffusive (εx, ε^αt) for 1 < α < 2. In this talk, we consider a 1-dimensional chain of anharmonic oscillators perturbed by noises preserving the total momentum as well as the total energy. We present a result about the hyperbolic scaling limit of its equilibrium fluctuation as well as some further discussions. (A joint work with S. Olla, Université Paris-Dauphine)
A chain of oscillators is a particle system whose microscopic time evolution is given by Hamilton equations with various kinds of conservative noises. Mathematicians and physicians are interested in its macroscopic behaviors (ε → 0) under different space-time scales: ballistic (hyperbolic) (εx, εt), diffusive (εx, ε^2t) and superdiffusive (εx, ε^αt) for 1 < α < 2. In this talk, we consider a 1-dimensional chain of anharmonic oscillators perturbed by noises preserving the total momentum as well as the total energy. We present a result about the hyperbolic scaling limit of its equilibrium fluctuation as well as some further discussions. (A joint work with S. Olla, Université Paris-Dauphine)
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
長友 康行 氏 (明治大学)
Holomorphic isometric embeddings into Grassmannians of rank $2$
長友 康行 氏 (明治大学)
Holomorphic isometric embeddings into Grassmannians of rank $2$
[ 講演概要 ]
We suppose that Grassmannians are equipped with the standard Kähler metrics of Fubini-Study type. This means that the ${\it universal \ quotient}$ bundles over Grassmannians are provided with not only fibre metrics but also connections. Such connections are called the ${\it canonical}$ connection.
First of all, we classify $\text{SU}(2)$ equivariant holomorphic embeddings of the complex projective line into complex Grassmannians of $2$-planes. To do so, we focus our attention on the pull-back connection of the canonical connection, which is an $\text{SU}(2)$ invariant connection by our hypothesis. We use ${\it extensions}$ of vector bundles to classify $\text{SU}(2)$ invariant connections on vector bundles of rank $2$ over the complex projective line. Since the extensions are in one-to-one correspondence with $H^1(\mathbf CP^1;\mathcal O(-2))$, the moduli space of non-trivial invariant connections modulo gauge transformations is identified with the quotient space of $H^1(\mathbf CP^1;\mathcal O(-2))$ by $S^1$-action. The positivity of the mean curvature of the pull-back connection implies that the moduli spaces of $\text{SU}(2)$ equivariant holomorphic embeddings are the open intervals $(0,l)$, where $l$ depends only on the ${\it degree}$ of the map.
Next, we describe moduli spaces of holomorphic isometric embeddings of the complex projective line into complex quadric hypersurfaces of the projective spaces. A harmonic map from a Riemannian manifold into a Grassmannian is characterized by the universal quotient bundle, a space of sections of the bundle and the Laplace operator. This characterization can be considered as a generalization of Theorem of Takahashi on minimal immersions into a sphere (J.Math.Soc.Japan 18 (1966)). Due to this, we can generalize do Carmo-Wallach theory. We apply a generalized do Carmo-Wallach theory to obtain the moduli spaces. This method also gives a description of the moduli space of Einstein-Hermitian harmonic maps with constant Kähler angles of the complex projective line into complex quadrics. It turns out that the moduli space is diffeomorphic to the moduli of holomorphic isometric embeddings of the same degree.
We suppose that Grassmannians are equipped with the standard Kähler metrics of Fubini-Study type. This means that the ${\it universal \ quotient}$ bundles over Grassmannians are provided with not only fibre metrics but also connections. Such connections are called the ${\it canonical}$ connection.
First of all, we classify $\text{SU}(2)$ equivariant holomorphic embeddings of the complex projective line into complex Grassmannians of $2$-planes. To do so, we focus our attention on the pull-back connection of the canonical connection, which is an $\text{SU}(2)$ invariant connection by our hypothesis. We use ${\it extensions}$ of vector bundles to classify $\text{SU}(2)$ invariant connections on vector bundles of rank $2$ over the complex projective line. Since the extensions are in one-to-one correspondence with $H^1(\mathbf CP^1;\mathcal O(-2))$, the moduli space of non-trivial invariant connections modulo gauge transformations is identified with the quotient space of $H^1(\mathbf CP^1;\mathcal O(-2))$ by $S^1$-action. The positivity of the mean curvature of the pull-back connection implies that the moduli spaces of $\text{SU}(2)$ equivariant holomorphic embeddings are the open intervals $(0,l)$, where $l$ depends only on the ${\it degree}$ of the map.
Next, we describe moduli spaces of holomorphic isometric embeddings of the complex projective line into complex quadric hypersurfaces of the projective spaces. A harmonic map from a Riemannian manifold into a Grassmannian is characterized by the universal quotient bundle, a space of sections of the bundle and the Laplace operator. This characterization can be considered as a generalization of Theorem of Takahashi on minimal immersions into a sphere (J.Math.Soc.Japan 18 (1966)). Due to this, we can generalize do Carmo-Wallach theory. We apply a generalized do Carmo-Wallach theory to obtain the moduli spaces. This method also gives a description of the moduli space of Einstein-Hermitian harmonic maps with constant Kähler angles of the complex projective line into complex quadrics. It turns out that the moduli space is diffeomorphic to the moduli of holomorphic isometric embeddings of the same degree.
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
北島雄一郎 氏 (日大生産工)
A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
北島雄一郎 氏 (日大生産工)
A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
2017年06月28日(水)
数理人口学・数理生物学セミナー
14:55-15:45 数理科学研究科棟(駒場) 122号室
Malay Banerjee 氏 (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
Malay Banerjee 氏 (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
[ 講演概要 ]
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
数理人口学・数理生物学セミナー
15:50-16:40 数理科学研究科棟(駒場) 122号室
Moitri Sen 氏 (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
Moitri Sen 氏 (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
[ 講演概要 ]
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
< 前へ 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186 次へ >
