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過去の記録
過去の記録 ～07/27｜本日 07/28 | 今後の予定 07/29～
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.
[ 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.
[ 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
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 III (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization III (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.
[ 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
2015年10月14日(水)
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 II (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization II (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.
[ 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
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
増本周平 氏 (東大数理)
Fraisse Theory for Metric Structures (English)
増本周平 氏 (東大数理)
Fraisse Theory for Metric Structures (English)
2015年10月13日(火)
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 I (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization I (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.
[ 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
FMSPレクチャーズ
15:00-16:30 数理科学研究科棟(駒場) 128号室
Jens Starke 氏 (Queen Mary University of London)
Implicit multiscale analysis of the macroscopic behaviour in microscopic models (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Starke.pdf
Jens Starke 氏 (Queen Mary University of London)
Implicit multiscale analysis of the macroscopic behaviour in microscopic models (ENGLISH)
[ 講演概要 ]
A numerical multiscale approach (equation-free analysis) is further improved in the framework of slow-fast dynamical systems and demonstrated for the example of a particle model for traffic flow. The method allows to perform numerical investigations of the macroscopic behavior of microscopically defined systems including continuation and bifurcation analysis on the coarse or macroscopic level where no explicit equations are available. This approach fills a gap in the analysis of many complex real-world applications including particle models with intermediate number of particles where the microscopic system is too large for a direct numerical analysis of the full system and too small to justify large-particle limits.
An implicit equation-free method is presented which reduces numerical errors of the equation-free analysis considerably. It can be shown that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold. The method is applied to perform a coarse bifurcation analysis of microscopic particle models describing car traffic on single lane highways. The results include an equation-free continuation of traveling wave solutions, identification of bifurcations as well as two-parameter continuations of bifurcation points. This is joint work with Christian Marschler and Jan Sieber.
[ 参考URL ]A numerical multiscale approach (equation-free analysis) is further improved in the framework of slow-fast dynamical systems and demonstrated for the example of a particle model for traffic flow. The method allows to perform numerical investigations of the macroscopic behavior of microscopically defined systems including continuation and bifurcation analysis on the coarse or macroscopic level where no explicit equations are available. This approach fills a gap in the analysis of many complex real-world applications including particle models with intermediate number of particles where the microscopic system is too large for a direct numerical analysis of the full system and too small to justify large-particle limits.
An implicit equation-free method is presented which reduces numerical errors of the equation-free analysis considerably. It can be shown that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold. The method is applied to perform a coarse bifurcation analysis of microscopic particle models describing car traffic on single lane highways. The results include an equation-free continuation of traveling wave solutions, identification of bifurcations as well as two-parameter continuations of bifurcation points. This is joint work with Christian Marschler and Jan Sieber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Starke.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)
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)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
David Sauzin 氏 (CNRS, France)
Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto) (English)
David Sauzin 氏 (CNRS, France)
Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto) (English)
[ 講演概要 ]
We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.
We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.
2015年10月06日(火)
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
齋藤 翔 氏 (カブリ数物連携宇宙研究機構)
Delooping theorem in K-theory (JAPANESE)
Tea : Common Room 16:30 -- 17:00
齋藤 翔 氏 (カブリ数物連携宇宙研究機構)
Delooping theorem in K-theory (JAPANESE)
[ 講演概要 ]
There is an important special class of infinite dimensional vector spaces, formed by those called Tate vector spaces. Since their first appearance in Tate’s work on residues of differentials on curves, they have been playing important roles in several different contexts including the study of formal loop spaces and semi-infinite Hodge theory. They have more sophisticated linear algebraic invariant than finite dimensional vector spaces, for instance the dimension of a Tate vector spaces is not a single integer, but a torsor acted upon by the all integers, and the determinant of an automorphism is not a single invertible scalar, but a torsor acted upon by the all invertible scalars. In this talk I will show how a delooping theorem in K-theory provides a clarified perspective on this phenomenon, using the recently developed higher categorical framework of infinity-topoi.
There is an important special class of infinite dimensional vector spaces, formed by those called Tate vector spaces. Since their first appearance in Tate’s work on residues of differentials on curves, they have been playing important roles in several different contexts including the study of formal loop spaces and semi-infinite Hodge theory. They have more sophisticated linear algebraic invariant than finite dimensional vector spaces, for instance the dimension of a Tate vector spaces is not a single integer, but a torsor acted upon by the all integers, and the determinant of an automorphism is not a single invertible scalar, but a torsor acted upon by the all invertible scalars. In this talk I will show how a delooping theorem in K-theory provides a clarified perspective on this phenomenon, using the recently developed higher categorical framework of infinity-topoi.
諸分野のための数学研究会
13:30-14:30 数理科学研究科棟(駒場) 056号室
※ 通常の時間と異なります。
Mohammad Hassan Farshbaf Shaker 氏 (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
※ 通常の時間と異なります。
Mohammad Hassan Farshbaf Shaker 氏 (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
[ 講演概要 ]
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.
2015年10月05日(月)
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
石渡 聡 氏 (山形大学理学部)
Heat kernel on connected sums of parabolic manifolds (日本語)
石渡 聡 氏 (山形大学理学部)
Heat kernel on connected sums of parabolic manifolds (日本語)
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
丸亀 泰二 氏 (東京大学)
On the volume expansion of the Blaschke metric on strictly convex domains
丸亀 泰二 氏 (東京大学)
On the volume expansion of the Blaschke metric on strictly convex domains
[ 講演概要 ]
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
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
Evangelos Routis 氏 (IPMU)
Weighted Compactifications of Configuration Spaces (English)
Evangelos Routis 氏 (IPMU)
Weighted Compactifications of Configuration Spaces (English)
[ 講演概要 ]
In the early 90's, Fulton and MacPherson provided a natural and beautiful way of compactifying the configuration space F(X,n) of n distinct labeled points on an arbitrary nonsingular variety. In this talk, I will present an alternate compactification of F(X,n), which generalizes the work of Fulton and MacPherson and is parallel to Hassett's weighted generalization of the moduli space of n-pointed stable curves. After discussing its main properties, I will give a presentation of its intersection ring and as an application, I will describe the intersection ring of Hassett's spaces in genus 0. Finally, as time permits, I will discuss some additional moduli problems associated with weighted compactifications.
In the early 90's, Fulton and MacPherson provided a natural and beautiful way of compactifying the configuration space F(X,n) of n distinct labeled points on an arbitrary nonsingular variety. In this talk, I will present an alternate compactification of F(X,n), which generalizes the work of Fulton and MacPherson and is parallel to Hassett's weighted generalization of the moduli space of n-pointed stable curves. After discussing its main properties, I will give a presentation of its intersection ring and as an application, I will describe the intersection ring of Hassett's spaces in genus 0. Finally, as time permits, I will discuss some additional moduli problems associated with weighted compactifications.
2015年10月03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
加藤 睦也 氏 (名古屋大学) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
(日本語)
最小の滑らかさの仮定の下での多重線形フーリエマルチプライヤーについて
(日本語)
加藤 睦也 氏 (名古屋大学) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
(日本語)
[ 講演概要 ]
$\alpha$--モジュレーション空間($0 \leq \alpha \leq 1$)はGr\"obnerによって導入された空間であり、モジュレーション空間は$\alpha=0$の特別な場合である。
本講演で は$\alpha$--モジュレーション空間と$L^p$--ソボレフ空間($1 \leq p \leq \infty$)との包含関係について紹介する。
モジュレーション空間とソボレフ空間との包含関係は Kobayashi--
Sugimotoによって最適なものが得られており、今 回の結果は$\alpha=0$としたときに彼らのものと完全に一致する。また、時間が許せば局所ハーディー空間と$\alpha$--モジュレーション空間との関係についても紹介したい。
冨田 直人 氏 (大阪大学) 15:30-17:00$\alpha$--モジュレーション空間($0 \leq \alpha \leq 1$)はGr\"obnerによって導入された空間であり、モジュレーション空間は$\alpha=0$の特別な場合である。
本講演で は$\alpha$--モジュレーション空間と$L^p$--ソボレフ空間($1 \leq p \leq \infty$)との包含関係について紹介する。
モジュレーション空間とソボレフ空間との包含関係は Kobayashi--
Sugimotoによって最適なものが得られており、今 回の結果は$\alpha=0$としたときに彼らのものと完全に一致する。また、時間が許せば局所ハーディー空間と$\alpha$--モジュレーション空間との関係についても紹介したい。
最小の滑らかさの仮定の下での多重線形フーリエマルチプライヤーについて
(日本語)
[ 講演概要 ]
線形の場合に，Hormanderのマルチプライヤー定理が主張することは,次元をnとするときに，滑らかさがn/2を超えるソボレフノルムでの適切な評価をマルチプライヤーに課せば，その対応する作用素のL^p-有界性が導かれるというものである．
この結果は，滑らかさをn/2からn/p-n/2に，L^p空間をHardy空間に置き換えることにより，pが1以下の場合にも成り立つことが，Calderon-Torchinskyによって示されている．
ここで現れた滑らかさn/2, n/p-n/2というオーダーは最小であることが知られている．そして，双線形の場合には，この線形の場合に対応する結果を，宮地晶彦氏との共同研究で得ていた．
今回の講演では，さらに，多重線形の場合にも同様の結果が成り立つことをご報告したい．
結果としては，線形，双線形の場合の一般化ではあるが，これらの場合の議論をそのまま焼き直せばよいという単純なものではないことをお話したい．なお，この講演は，L. Grafakos氏，宮地晶彦氏，H. Nguyen氏との共同研究に基づく．
線形の場合に，Hormanderのマルチプライヤー定理が主張することは,次元をnとするときに，滑らかさがn/2を超えるソボレフノルムでの適切な評価をマルチプライヤーに課せば，その対応する作用素のL^p-有界性が導かれるというものである．
この結果は，滑らかさをn/2からn/p-n/2に，L^p空間をHardy空間に置き換えることにより，pが1以下の場合にも成り立つことが，Calderon-Torchinskyによって示されている．
ここで現れた滑らかさn/2, n/p-n/2というオーダーは最小であることが知られている．そして，双線形の場合には，この線形の場合に対応する結果を，宮地晶彦氏との共同研究で得ていた．
今回の講演では，さらに，多重線形の場合にも同様の結果が成り立つことをご報告したい．
結果としては，線形，双線形の場合の一般化ではあるが，これらの場合の議論をそのまま焼き直せばよいという単純なものではないことをお話したい．なお，この講演は，L. Grafakos氏，宮地晶彦氏，H. Nguyen氏との共同研究に基づく．
2015年10月02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
高橋良輔 氏 (名古屋大学 多元数理科学研究科)
ケーラー・リッチソリトンの漸近的安定性 (Japanese)
高橋良輔 氏 (名古屋大学 多元数理科学研究科)
ケーラー・リッチソリトンの漸近的安定性 (Japanese)
[ 講演概要 ]
ケーラー・リッチソリトンは，Hamilton のリッチフローのような幾何解析に起源をもつ Fano 多様体上の標準計量であり，ここ数年広範囲に渡って研究されてきた．標準計量の存在は何らかの幾何学的不変式論的安定性と密接に関係することが期待されている．例えば，Donaldsonは，スカラー曲率一定ケーラー計量を許容しかつ自己同型群が離散な任意の偏極多様体は balanced 計量の列を持ち，さらにこの列はスカラー曲率一定ケーラー計量に収束することを証明した．本講演では，同じような結果がケーラー・リッチソリトンに対しても成り立つことを説明する．なお，この結果は Berman-Witt Nystr¥"om の先行結果を一般化するものであり，端的ケーラー計量の漸近的相対 Chow 安定性に関する満渕氏の結果の類似を与えている．
ケーラー・リッチソリトンは，Hamilton のリッチフローのような幾何解析に起源をもつ Fano 多様体上の標準計量であり，ここ数年広範囲に渡って研究されてきた．標準計量の存在は何らかの幾何学的不変式論的安定性と密接に関係することが期待されている．例えば，Donaldsonは，スカラー曲率一定ケーラー計量を許容しかつ自己同型群が離散な任意の偏極多様体は balanced 計量の列を持ち，さらにこの列はスカラー曲率一定ケーラー計量に収束することを証明した．本講演では，同じような結果がケーラー・リッチソリトンに対しても成り立つことを説明する．なお，この結果は Berman-Witt Nystr¥"om の先行結果を一般化するものであり，端的ケーラー計量の漸近的相対 Chow 安定性に関する満渕氏の結果の類似を与えている．
2015年09月30日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
Alan Lauder 氏 (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ 講演概要 ]
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
2015年09月29日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Tuomo Kuusi 氏 (Aalto University)
Nonlocal self-improving properties (English)
Tuomo Kuusi 氏 (Aalto University)
Nonlocal self-improving properties (English)
[ 講演概要 ]
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 126号室
Otto Liess 氏 (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
Otto Liess 氏 (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
[ 講演概要 ]
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{＼"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ ＼rho $ (respectively for every $ ＼rho $ of form log |h| with h holomorphic) on U: if we know that $ ＼rho ＼leq f$ on the boundary of U and if $ (＼rho - f)$ is bounded on U, then it must follow that $ ＼rho ＼leq g$ on U. ($＼rho ＼leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (＼rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) ＼leq u(z) ＼leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ ＼rho'= ＼rho+u$ to obtain at first $ ＼rho' ＼leq 0$ and then $ ＼rho ＼leq - u ＼leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{＼"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ ＼rho $ (respectively for every $ ＼rho $ of form log |h| with h holomorphic) on U: if we know that $ ＼rho ＼leq f$ on the boundary of U and if $ (＼rho - f)$ is bounded on U, then it must follow that $ ＼rho ＼leq g$ on U. ($＼rho ＼leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (＼rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) ＼leq u(z) ＼leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ ＼rho'= ＼rho+u$ to obtain at first $ ＼rho' ＼leq 0$ and then $ ＼rho ＼leq - u ＼leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.
2015年09月28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
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
[ 講演概要 ]
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
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