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過去の記録 ～04/19｜本日 04/20 | 今後の予定 04/21～
2012年11月27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
野澤 啓 氏 (JSPS-IHES フェロー)
葉層構造の特性類の有限的側面について (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
野澤 啓 氏 (JSPS-IHES フェロー)
葉層構造の特性類の有限的側面について (JAPANESE)
[ 講演概要 ]
Thurstonの例により、葉層構造の二次特性類は有界でないことが知られている。本講演では、横断的な共形平坦構造などを持つ葉層構造に対しては(例外的な場合を除き)二次特性類が有限性を持つことを、非有界性や葉層構造の剛性との関連と共に説明する。
(本講演はSantiago de Compostela大学のJesús Antonio Álvarez
López氏との共同研究 arXiv:1205.3375に基づく。)
Thurstonの例により、葉層構造の二次特性類は有界でないことが知られている。本講演では、横断的な共形平坦構造などを持つ葉層構造に対しては(例外的な場合を除き)二次特性類が有限性を持つことを、非有界性や葉層構造の剛性との関連と共に説明する。
(本講演はSantiago de Compostela大学のJesús Antonio Álvarez
López氏との共同研究 arXiv:1205.3375に基づく。)
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
今野宏 氏 (東京大学大学院数理科学研究科)
旗多様体のケーラー偏極の実偏極への収束 (JAPANESE)
今野宏 氏 (東京大学大学院数理科学研究科)
旗多様体のケーラー偏極の実偏極への収束 (JAPANESE)
[ 講演概要 ]
In this talk we will discuss geometric quantization of a flag manifold. In particular, we construct a family of complex structures on a flag manifold that converge 'at the quantum level' to the real polarization coming from the Gelfand-Cetlin integrable system.
Our construction is based on a toric degeneration of flag varieties and a deformation of K¥"ahler structure on toric varieties by symplectic potentials.
This is a joint work with Mark Hamilton.
In this talk we will discuss geometric quantization of a flag manifold. In particular, we construct a family of complex structures on a flag manifold that converge 'at the quantum level' to the real polarization coming from the Gelfand-Cetlin integrable system.
Our construction is based on a toric degeneration of flag varieties and a deformation of K¥"ahler structure on toric varieties by symplectic potentials.
This is a joint work with Mark Hamilton.
2012年11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
桂 利行 氏 (法政大学理工学部)
超特殊K3曲面上の有理曲線の配置について (JAPANESE)
桂 利行 氏 (法政大学理工学部)
超特殊K3曲面上の有理曲線の配置について (JAPANESE)
[ 講演概要 ]
正標数の代数的閉体$k$上の超特異K3曲面のArtin不変量が1のとき超特殊K3曲面という。標数が3以上であれば、このようなK3曲面は、2つの超特異楕円曲線の直積であるアーべル曲面からつくられるKummer曲面になることが知られている。この講演では$S$上の有理曲線の配置をアーベル曲面の因子の構造を用いて考察し、標数が2ならば$(21)_5$-symmetric configurationが存在すること、また標数3ならば$(16)_{10}$-symmetric configurationと$(280_{4}, 112_{10})$-configurationが存在することを示す。また、後者は、$p^{a} + 1$次のFermat hypersurfaceのline configurationや、N\\'eron-S\\'everi群${\\rm NS}(S)$がLeech latticeを用いて捉えられることと関係することを述べる。
正標数の代数的閉体$k$上の超特異K3曲面のArtin不変量が1のとき超特殊K3曲面という。標数が3以上であれば、このようなK3曲面は、2つの超特異楕円曲線の直積であるアーべル曲面からつくられるKummer曲面になることが知られている。この講演では$S$上の有理曲線の配置をアーベル曲面の因子の構造を用いて考察し、標数が2ならば$(21)_5$-symmetric configurationが存在すること、また標数3ならば$(16)_{10}$-symmetric configurationと$(280_{4}, 112_{10})$-configurationが存在することを示す。また、後者は、$p^{a} + 1$次のFermat hypersurfaceのline configurationや、N\\'eron-S\\'everi群${\\rm NS}(S)$がLeech latticeを用いて捉えられることと関係することを述べる。
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
納谷 信 氏 (名古屋大学大学院多元数理科学研究科)
四元数CR幾何 (JAPANESE)
納谷 信 氏 (名古屋大学大学院多元数理科学研究科)
四元数CR幾何 (JAPANESE)
[ 講演概要 ]
四元数CR構造は、四元数多様体の実超曲面をモデルとする幾何構造である。本講演では、この構造の定義や基本事項を説明した後に、O.Biquardの四元数接触構造との比較、ならびにツイスターCR多様体の構成について述べる。
四元数CR構造は、四元数多様体の実超曲面をモデルとする幾何構造である。本講演では、この構造の定義や基本事項を説明した後に、O.Biquardの四元数接触構造との比較、ならびにツイスターCR多様体の構成について述べる。
2012年11月22日(木)
講演会
13:30-14:15 数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type (ENGLISH)
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type (ENGLISH)
[ 講演概要 ]
A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in $\\R^N$, with $N \\geq 2$. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the class of reaction-diffusion equations, which we consider. This is joint work with Marie Henry and Cyrill Muratov.
[ 参考URL ]A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in $\\R^N$, with $N \\geq 2$. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the class of reaction-diffusion equations, which we consider. This is joint work with Marie Henry and Cyrill Muratov.
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
講演会
14:25-15:10 数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Thanh Nam Ngyuen 氏 (University of Paris-Sud)
Formal asymptotic limit of a diffuse interface tumor-growth model (ENGLISH)
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Thanh Nam Ngyuen 氏 (University of Paris-Sud)
Formal asymptotic limit of a diffuse interface tumor-growth model (ENGLISH)
[ 講演概要 ]
We consider a diffuse interface tumor-growth model, which has the form of a phase-field system. We discuss the singular limit of this problem. More precisely, we formally prove that as the reaction coefficient tends to zero, the solution converges to the solution of a free boundary problem.
This is a joint work with Danielle Hilhorst, Johannes Kampmann and Kristoffer G. van der Zee.
[ 参考URL ]We consider a diffuse interface tumor-growth model, which has the form of a phase-field system. We discuss the singular limit of this problem. More precisely, we formally prove that as the reaction coefficient tends to zero, the solution converges to the solution of a free boundary problem.
This is a joint work with Danielle Hilhorst, Johannes Kampmann and Kristoffer G. van der Zee.
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
講演会
15:30-16:15 数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Peter Gordon 氏 (Akron University)
Gelfand type problem for two phase porous media (ENGLISH)
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Peter Gordon 氏 (Akron University)
Gelfand type problem for two phase porous media (ENGLISH)
[ 講演概要 ]
In this talk I will introduce a generalization of well known Gelfand problem arising in a Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two phase materials, where, in contrast to classical Gelfand problem which utilizes single temperature approach, the state of the system is described by two different temperatures. As a result the problem is modeled by a system of two coupled nonlinear heat equations. The new ingredient in such a generalized Gelfand problem is a presence of inter-phase heat exchange which can be viewed as a strength of coupling for the system.
I will show that similar to classical Gelfand problem the thermal explosion (blow up of solution) for generalized Gelfand problem occurs exclusively due to the absence of stationary temperature distribution, that is non-existence of solution of corresponding elliptic problem. I also will show that the presence of inter-phase heat exchange delays a thermal explosion. Moreover, in the limit of infinite heat exchange between phases the problem of thermal explosion in two phase porous media reduces to classical Gelfand problem with re-normalized constants. The latter result partially justifies a single temperature approach to two phase systems often used in a physical literature.
This is a joint work with Vitaly Moroz (Swansea University).
[ 参考URL ]In this talk I will introduce a generalization of well known Gelfand problem arising in a Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two phase materials, where, in contrast to classical Gelfand problem which utilizes single temperature approach, the state of the system is described by two different temperatures. As a result the problem is modeled by a system of two coupled nonlinear heat equations. The new ingredient in such a generalized Gelfand problem is a presence of inter-phase heat exchange which can be viewed as a strength of coupling for the system.
I will show that similar to classical Gelfand problem the thermal explosion (blow up of solution) for generalized Gelfand problem occurs exclusively due to the absence of stationary temperature distribution, that is non-existence of solution of corresponding elliptic problem. I also will show that the presence of inter-phase heat exchange delays a thermal explosion. Moreover, in the limit of infinite heat exchange between phases the problem of thermal explosion in two phase porous media reduces to classical Gelfand problem with re-normalized constants. The latter result partially justifies a single temperature approach to two phase systems often used in a physical literature.
This is a joint work with Vitaly Moroz (Swansea University).
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
講演会
16:25-17:10 数理科学研究科棟(駒場) 002号室
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Cyrill Muratov 氏 (New Jersey Institute of Technology)
On the shape of charged drops: an isoperimetric problem with a competing non-local term (ENGLISH)
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
本講演は,GCOEミニワークショップ「Reaction-Diffusion Equations and its Applications」の一環として行われます.
Cyrill Muratov 氏 (New Jersey Institute of Technology)
On the shape of charged drops: an isoperimetric problem with a competing non-local term (ENGLISH)
[ 講演概要 ]
In this talk I will give an overview of my recent work with H. Knuepfer on the analysis of a class of geometric problems in the calculus of variations. I will discuss the basic questions of existence and non-existence of energy minimizers for the isoperimetric problem with a competing non-local term. A complete answer will be given for the case of slowly decaying kernels in two space dimensions, and qualitative properties of the minimizers will be established for general Riesz kernels.
[ 参考URL ]In this talk I will give an overview of my recent work with H. Knuepfer on the analysis of a class of geometric problems in the calculus of variations. I will discuss the basic questions of existence and non-existence of energy minimizers for the isoperimetric problem with a competing non-local term. A complete answer will be given for the case of slowly decaying kernels in two space dimensions, and qualitative properties of the minimizers will be established for general Riesz kernels.
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html
2012年11月21日(水)
PDE実解析研究会
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(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。
Giovanni Pisante 氏 (Seconda Università degli Studi di Napoli)
Shape Optimization And Asymptotic For The Twisted Dirichlet Eigenvalue (ENGLISH)
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。
Giovanni Pisante 氏 (Seconda Università degli Studi di Napoli)
Shape Optimization And Asymptotic For The Twisted Dirichlet Eigenvalue (ENGLISH)
[ 講演概要 ]
Aim of the talk is to discuss some recent results obtained with G. Croce and A. Henrot on a generalization of the functional defining the first twisted eigenvalue.
We look at the set functional defined by minimizing a Rayleigh quotient involving Lebesgue norms with different exponents p and q among functions satisfying a zero boundary condition as well as a zero mean condition of order q.
First under suitable conditions on p and q, that ensure the existence of a minimizing function, we investigate the validity of an isoperimetric type inequality of the Reyleigh-Faber-Krahn type.
Then we study the limit of the functional for p and q tending to 1 and to infinity and discuss the relation with the limits of the second eigenvalues of the p-laplacian operator.
Aim of the talk is to discuss some recent results obtained with G. Croce and A. Henrot on a generalization of the functional defining the first twisted eigenvalue.
We look at the set functional defined by minimizing a Rayleigh quotient involving Lebesgue norms with different exponents p and q among functions satisfying a zero boundary condition as well as a zero mean condition of order q.
First under suitable conditions on p and q, that ensure the existence of a minimizing function, we investigate the validity of an isoperimetric type inequality of the Reyleigh-Faber-Krahn type.
Then we study the limit of the functional for p and q tending to 1 and to infinity and discuss the relation with the limits of the second eigenvalues of the p-laplacian operator.
古典解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
Philip Boalch 氏 (ENS-DMA & CNRS Paris)
Beyond the fundamental group (ENGLISH)
Philip Boalch 氏 (ENS-DMA & CNRS Paris)
Beyond the fundamental group (ENGLISH)
[ 講演概要 ]
Moduli spaces of representations of the fundamental group of a Riemann surface have been studied from numerous points of view and appear in many parts of mathematics and theoretical physics. They form an interesting class of symplectic manifolds, they often have Kahler or hyperkahler metrics (in which case they are diffeomorphic to spaces of Higgs bundles, i.e. Hitchin integrable systems), and they admit nonlinear actions of braid groups and mapping class groups with fascinating dynamical properties. The aim of this talk is to describe some aspects of this story and sketch their extension to the context of the "wild fundamental group", which naturally appears when one considers {\\em meromorphic} connections on Riemann surfaces. In particular some new examples of hyperkahler manifolds appear in this way, some of which are familiar from classical work on the Painleve equations.
Moduli spaces of representations of the fundamental group of a Riemann surface have been studied from numerous points of view and appear in many parts of mathematics and theoretical physics. They form an interesting class of symplectic manifolds, they often have Kahler or hyperkahler metrics (in which case they are diffeomorphic to spaces of Higgs bundles, i.e. Hitchin integrable systems), and they admit nonlinear actions of braid groups and mapping class groups with fascinating dynamical properties. The aim of this talk is to describe some aspects of this story and sketch their extension to the context of the "wild fundamental group", which naturally appears when one considers {\\em meromorphic} connections on Riemann surfaces. In particular some new examples of hyperkahler manifolds appear in this way, some of which are familiar from classical work on the Painleve equations.
2012年11月20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
長尾 健太郎 氏 (名古屋大学多元数理科学研究科)
3次元双曲幾何と団代数 (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
長尾 健太郎 氏 (名古屋大学多元数理科学研究科)
3次元双曲幾何と団代数 (JAPANESE)
[ 講演概要 ]
クラスター代数は2000年にFomin-Zelevinskyによって発見された代数系である.
近年,クラスター代数の構造は量子群の理論,低次元トポロジー・離散可積分系・Donaldson-Thomas理論・弦理論など様々な分野で発見され,ダイナミックに研究が進展している.
今回は弦理論におけるある種の双対性を背景とした,3次元双曲幾何とクラスター代数の関係について紹介する.
クラスター代数は2000年にFomin-Zelevinskyによって発見された代数系である.
近年,クラスター代数の構造は量子群の理論,低次元トポロジー・離散可積分系・Donaldson-Thomas理論・弦理論など様々な分野で発見され,ダイナミックに研究が進展している.
今回は弦理論におけるある種の双対性を背景とした,3次元双曲幾何とクラスター代数の関係について紹介する.
Lie群論・表現論セミナー
16:30-17:30 数理科学研究科棟(駒場) 126号室
Ali Baklouti 氏 (Sfax University)
On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)
Ali Baklouti 氏 (Sfax University)
On the geometry of discontinuous subgroups acting on some homogeneous spaces (ENGLISH)
[ 講演概要 ]
Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. I first introduce the deformation space ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ of the action of $\\Gamma$ on $G/H$ in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form ${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space ${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$ of marked $(G,H)$-structures on ${\\mathcal{X}}$ in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ and ${\\mathcal{T}}^{G_o}(\\Gamma, G, H)$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly.
Let $G$ be a Lie group, $H$ a closed subgroup of $G$ and \\Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. I first introduce the deformation space ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ of the action of $\\Gamma$ on $G/H$ in the sense of Kobayashi and some of its refined versions, namely the Clifford--Klein space of deformations of the form ${\\mathcal{X}}=\\Gamma \\backslash G/H$. The deformation space ${\\mathcal{T}}^{G_o}(\\Gamma, G,H)$ of marked $(G,H)$-structures on ${\\mathcal{X}}$ in the sense of Goldman is also introduced. As an important motivation, I will explain the connection between the spaces ${\\mathcal{T}}^{K_o}(\\Gamma, G, H)$ and ${\\mathcal{T}}^{G_o}(\\Gamma, G, H)$ and study some of their topological features, namely the rigidity in the sense of Selberg--Weil--Kobayashi and the stability in the sense of Kobayashi--Nasrin. The latter appears to be of major interest to write down the connection explicitly.
2012年11月19日(月)
講演会
16:45-17:45 数理科学研究科棟(駒場) 126号室
Hendrik Weber 氏 (University of Warwick)
Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size (ENGLISH)
Hendrik Weber 氏 (University of Warwick)
Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size (ENGLISH)
[ 講演概要 ]
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. We are interested in the competition between the ``energy'' that should be minimized due to the small noise strength and the ``entropy'' that is induced by the large system size.
Our methods handle system sizes that are exponential with respect to the inverse noise strength, up to the ``critical'' exponential size predicted by the heuristics. We capture the competition between energy and entropy through upper and lower bounds on the probability of extra transitions between $\\pm 1$. These bounds are sharp on the exponential scale and imply in particular that the probability of having one and only one transition from -1 to +1 is exponentially close to one. In addition, we show that the position of the transition layer is uniformly distributed over the system on scales larger than the logarithm of the inverse noise strength.
Our arguments rely on local large deviation bounds, the strong Markov property, the symmetry of the potential, and measure-preserving reflections.
This is a joint work with Felix Otto and Maria Westdickenberg.
We study the invariant measure of the one-dimensional stochastic Allen-Cahn equation for a small noise strength and a large but finite system. We endow the system with inhomogeneous Dirichlet boundary conditions that enforce at least one transition from -1 to 1. We are interested in the competition between the ``energy'' that should be minimized due to the small noise strength and the ``entropy'' that is induced by the large system size.
Our methods handle system sizes that are exponential with respect to the inverse noise strength, up to the ``critical'' exponential size predicted by the heuristics. We capture the competition between energy and entropy through upper and lower bounds on the probability of extra transitions between $\\pm 1$. These bounds are sharp on the exponential scale and imply in particular that the probability of having one and only one transition from -1 to +1 is exponentially close to one. In addition, we show that the position of the transition layer is uniformly distributed over the system on scales larger than the logarithm of the inverse noise strength.
Our arguments rely on local large deviation bounds, the strong Markov property, the symmetry of the potential, and measure-preserving reflections.
This is a joint work with Felix Otto and Maria Westdickenberg.
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
戸田 幸伸 氏 (IPMU)
Stability conditions and birational geometry (JAPANESE)
戸田 幸伸 氏 (IPMU)
Stability conditions and birational geometry (JAPANESE)
[ 講演概要 ]
I propose a conjecture which claims that MMP for a smooth projective variety is realized as a variation of Bridgeland moduli spaces of semistable objects in the derived category of coherent sheaves. I will discuss the surface case and extremal contractions for 3-folds. In the former case, the conjecture is completely solved. In the latter case, I will construct the perverse t-structure associated to the extremal contraction, and construct a candidate of the desired stability condition as a double tilting of the perverse heart.
I propose a conjecture which claims that MMP for a smooth projective variety is realized as a variation of Bridgeland moduli spaces of semistable objects in the derived category of coherent sheaves. I will discuss the surface case and extremal contractions for 3-folds. In the former case, the conjecture is completely solved. In the latter case, I will construct the perverse t-structure associated to the extremal contraction, and construct a candidate of the desired stability condition as a double tilting of the perverse heart.
GCOEセミナー
15:30-17:00 数理科学研究科棟(駒場) 056号室
Alfred Ramani 氏 (Ecole Polytechnique)
Linearisable mappings (ENGLISH)
Alfred Ramani 氏 (Ecole Polytechnique)
Linearisable mappings (ENGLISH)
[ 講演概要 ]
We present a series of results on linearisable second-order mappings.
Three distinct families of such mappings do exist: projective, mappings of Gambier type and mappings which we have dubbed "of third kind".
Our starting point are the linearisable mappings belonging to the QRT family. We show how they can be linearised and how in some cases their explicit solution can be constructed. We discuss also the growth property of these mappings, a property intimately related to linearisability.
In the second part of the talk we address the question of the extension of these mappings to a non-autonomous form.
We show that the QRT invariant can also be extended (to a quantity which depends explicitly on the independent variable). Using this non-autonomous form we show that it is possible to construct the explicit solution of all third-kind mappings. We discuss also the relation of mappings of the third kind to Gambier-type mappings. We show that a large subclass of third-kind mappings can be considered as the discrete derivative of Gambier-type ones.
We present a series of results on linearisable second-order mappings.
Three distinct families of such mappings do exist: projective, mappings of Gambier type and mappings which we have dubbed "of third kind".
Our starting point are the linearisable mappings belonging to the QRT family. We show how they can be linearised and how in some cases their explicit solution can be constructed. We discuss also the growth property of these mappings, a property intimately related to linearisability.
In the second part of the talk we address the question of the extension of these mappings to a non-autonomous form.
We show that the QRT invariant can also be extended (to a quantity which depends explicitly on the independent variable). Using this non-autonomous form we show that it is possible to construct the explicit solution of all third-kind mappings. We discuss also the relation of mappings of the third kind to Gambier-type mappings. We show that a large subclass of third-kind mappings can be considered as the discrete derivative of Gambier-type ones.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
小森 洋平 氏 (早稲田大学)
トーラス上の種数２のリーマン面の退化族について (JAPANESE)
小森 洋平 氏 (早稲田大学)
トーラス上の種数２のリーマン面の退化族について (JAPANESE)
[ 講演概要 ]
ある固定したトーラスの2重分岐被覆として得られる種数2のリーマン面を一般ファイバーに持つ、リーマン面の退化族を構成し、その特異ファイバーと正則切断を決定する。
ある固定したトーラスの2重分岐被覆として得られる種数2のリーマン面を一般ファイバーに持つ、リーマン面の退化族を構成し、その特異ファイバーと正則切断を決定する。
2012年11月16日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 002号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
二木昭人 氏 (東京大学)
複素微分幾何に現れる積分不変量について (JAPANESE)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
二木昭人 氏 (東京大学)
複素微分幾何に現れる積分不変量について (JAPANESE)
[ 講演概要 ]
コンパクト複素多様体のもっともなじみ深い不変量は Chern 類であろう.この講演ではその secondary classes にあたる正則ベクトル場を含んだ積分不変量の族で,次のような3つを含むものについて紹介する.
(1) 各 k に対し,k 次 Chern 形式が調和形式であるようなケーラー計量が存在するための障害となる不変量.
(2) 非ケーラー多様体でも定義される不変量で,横断的正則葉層構造の特性類やLefchetz 数などから自然に得られる不変量.
(3) 代数多様体に対し,漸近的 Chow 半安定性の障害となる不変量.
これらの3つの族の共通部分にケーラー・アインシュタイン計量が存在するための障害がある.
コンパクト複素多様体のもっともなじみ深い不変量は Chern 類であろう.この講演ではその secondary classes にあたる正則ベクトル場を含んだ積分不変量の族で,次のような3つを含むものについて紹介する.
(1) 各 k に対し,k 次 Chern 形式が調和形式であるようなケーラー計量が存在するための障害となる不変量.
(2) 非ケーラー多様体でも定義される不変量で,横断的正則葉層構造の特性類やLefchetz 数などから自然に得られる不変量.
(3) 代数多様体に対し,漸近的 Chow 半安定性の障害となる不変量.
これらの3つの族の共通部分にケーラー・アインシュタイン計量が存在するための障害がある.
GCOEセミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
Dietmar Bisch 氏 (Vanderbilt University)
Subfactors with small Jones index (ENGLISH)
Dietmar Bisch 氏 (Vanderbilt University)
Subfactors with small Jones index (ENGLISH)
2012年11月14日(水)
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
いつもと時間・場所が異なりますのでご注意ください.
Pierre Berthelot 氏 (Université de Rennes 1)
De Rham-Witt complexes with coefficients and rigid cohomology
(ENGLISH)
いつもと時間・場所が異なりますのでご注意ください.
Pierre Berthelot 氏 (Université de Rennes 1)
De Rham-Witt complexes with coefficients and rigid cohomology
(ENGLISH)
[ 講演概要 ]
For a smooth scheme over a perfect field of characteristic p, we will explain a generalization of the classical comparison theorem between crystalline cohomology and de Rham-Witt cohomology to the case of cohomologies with coefficients in a p-torsion free crystal. This provides in particular a description of the rigid cohomology of a proper singular scheme in terms of a de Rham-Witt complex built from a closed immersion into a smooth scheme.
(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.)
For a smooth scheme over a perfect field of characteristic p, we will explain a generalization of the classical comparison theorem between crystalline cohomology and de Rham-Witt cohomology to the case of cohomologies with coefficients in a p-torsion free crystal. This provides in particular a description of the rigid cohomology of a proper singular scheme in terms of a de Rham-Witt complex built from a closed immersion into a smooth scheme.
(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.)
幾何コロキウム
10:30-12:00 数理科学研究科棟(駒場) 128号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
河井公大朗 氏 (東北大学)
Construction of coassociative submanifolds (JAPANESE)
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
河井公大朗 氏 (東北大学)
Construction of coassociative submanifolds (JAPANESE)
[ 講演概要 ]
The notion of coassociative submanifolds is defined as the special class of the minimal submanifolds in G_2 manifolds. In this talk, we introduce the method to construct coassociative submanifolds by using the symmetry of the Lie group action. As an application, we give explicit examples in the 7-dimensional Euclidean space and in the anti-self-dual bundle over the 4-sphere.
The notion of coassociative submanifolds is defined as the special class of the minimal submanifolds in G_2 manifolds. In this talk, we introduce the method to construct coassociative submanifolds by using the symmetry of the Lie group action. As an application, we give explicit examples in the 7-dimensional Euclidean space and in the anti-self-dual bundle over the 4-sphere.
2012年11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
北山 貴裕 氏 (京都大学数理解析研究所，日本学術振興会PD)
The virtual fibering theorem and sutured manifold hierarchies (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
北山 貴裕 氏 (京都大学数理解析研究所，日本学術振興会PD)
The virtual fibering theorem and sutured manifold hierarchies (JAPANESE)
[ 講演概要 ]
In 2007 Agol showed that every irreducible 3-manifold whose fundamental
group is nontrivial and virtually residually finite rationally solvable
(RFRS) is virtually fibered. In the proof he used the theory of
least-weight taut normal surfaces introduced and developed by Oertel and
Tollefson-Wang. We give another proof using complexities of sutured
manifolds. This is a joint work with Stefan Friedl (University of
Cologne).
In 2007 Agol showed that every irreducible 3-manifold whose fundamental
group is nontrivial and virtually residually finite rationally solvable
(RFRS) is virtually fibered. In the proof he used the theory of
least-weight taut normal surfaces introduced and developed by Oertel and
Tollefson-Wang. We give another proof using complexities of sutured
manifolds. This is a joint work with Stefan Friedl (University of
Cologne).
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
Oskar Hamlet 氏 (Chalmers University)
Tight maps, a classification (ENGLISH)
Oskar Hamlet 氏 (Chalmers University)
Tight maps, a classification (ENGLISH)
[ 講演概要 ]
Tight maps/homomorphisms were introduced during the study of rigidity properties of surface groups in Hermitian Lie groups. In this talk I'll discuss the properties of tight maps, their connection to rigidity theory and my work classifying them.
Tight maps/homomorphisms were introduced during the study of rigidity properties of surface groups in Hermitian Lie groups. In this talk I'll discuss the properties of tight maps, their connection to rigidity theory and my work classifying them.
2012年11月12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
安武 和範 氏 (九州大学大学院数理学研究院)
On Fano fourfolds with nef vector bundles $Λ^2T_X$ (JAPANESE)
安武 和範 氏 (九州大学大学院数理学研究院)
On Fano fourfolds with nef vector bundles $Λ^2T_X$ (JAPANESE)
[ 講演概要 ]
By using results about extremal contractions on smooth fourfolds, we give a classification of fano fourfolds whose the second exterior power of tangent bundles are numerically effective.
By using results about extremal contractions on smooth fourfolds, we give a classification of fano fourfolds whose the second exterior power of tangent bundles are numerically effective.
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
A.G. Aleksandrov 氏 (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
A.G. Aleksandrov 氏 (Institute of Control Sciences, Russian Acad. of Sci.)
Residues of meromorphic differential forms (ENGLISH)
[ 講演概要 ]
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.
The purpose of the talk is to discuss several interesting aspects
of the classical residue theory originated by H. Poincar\\'e, J. de Rham and J. Leray and their followers. Focus topics of our studies are some of the less known applications, developed by the author in the past few years in complex analysis, topology and geometry of singular varieties and in the theory of differential equations. Almost all considerations are based essentially on properties of a special class of meromorphic differential forms called logarithmic or multi-logarithmic forms.
2012年11月10日(土)
調和解析駒場セミナー
13:00-18:00 数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
松山 登喜夫 氏 (中央大学) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
Spectral stability of the p-Laplacian (JAPANESE)
このセミナーは,月に1度程度,不定期に開催されます.
松山 登喜夫 氏 (中央大学) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
[ 講演概要 ]
In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
杉本 充 氏 (名古屋大学) 14:40-16:00In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
[ 講演概要 ]
Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for slutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Victor I. Burenkov 氏 (Russia/United Kingdom) 16:30-17:50Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for slutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Spectral stability of the p-Laplacian (JAPANESE)
[ 講演概要 ]
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).
References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).
References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.
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