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過去の記録
過去の記録 ～04/18｜本日 04/19 | 今後の予定 04/20～
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
佐藤 正寿 氏 (東京電機大学)
On the cohomology ring of the handlebody mapping class group of genus two (JAPANESE)
Tea : Common Room 16:30 -- 17:00
佐藤 正寿 氏 (東京電機大学)
On the cohomology ring of the handlebody mapping class group of genus two (JAPANESE)
[ 講演概要 ]
The genus two handlebody mapping class group acts on a tree
constructed by Kramer from the disk complex,
and decomposes into an amalgamated product of two subgroups.
We determine the integral cohomology ring of the genus two handlebody
mapping class group by examining these two subgroups
and the Mayer-Vietoris exact sequence.
Using this result, we estimate the ranks of low dimensional homology
groups of the genus three handlebody mapping class group.
The genus two handlebody mapping class group acts on a tree
constructed by Kramer from the disk complex,
and decomposes into an amalgamated product of two subgroups.
We determine the integral cohomology ring of the genus two handlebody
mapping class group by examining these two subgroups
and the Mayer-Vietoris exact sequence.
Using this result, we estimate the ranks of low dimensional homology
groups of the genus three handlebody mapping class group.
Lie群論・表現論セミナー
17:00-18:45 数理科学研究科棟(駒場) 号室
Birgit Speh 氏 (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 1 (English)
Birgit Speh 氏 (Cornell University)
Introduction to the cohomology of discrete groups and modular symbols 1 (English)
[ 講演概要 ]
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.
The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.
On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.
In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.
The course is an introduction to the cohomology of torsion free discrete subgroups $\Gamma \subset G $ of a semi simple group $G$. The discrete group $\Gamma$ acts freely on the symmetric space $X= G/K$ and we will always assume that $\Gamma \backslash G/K$ is compact or has finite volume. An example is a torsion free subgroup $\Gamma_n $ of finite index n in Sl(2,Z) acting on $Sl(2.R)/SO(2) \simeq {\mathcal H}=\{z=x+iy \in C| y >0 \}$ by fractional linear transformations. $\Gamma_n \backslash {\mathcal H}$ can be determined explicitly and it can be visualized as an area in the upper half plane glued at the boundary. It is easy to see that it has some nice compactifications.
The cohomology $H^*(\Gamma, C)$ of the group $\Gamma$ is equal to the deRham cohomology $H^*_{deRham}(\Gamma \backslash X, C)$ of the manifold $\Gamma\backslash X$. This cohomology is studied by proving that it is isomorphic to the $H^*(g,K,{\mathcal A}(\Gamma \backslash G))$. Here ${\mathcal A}(\Gamma \backslash G)$ of automorphic functions on $\Gamma \backslash G$. In the case $\Gamma_n \subset Sl(2,Z)$ the space ${\mathcal A}(\Gamma \backslash G)$ is the space of classical automorphic functions on the upper half plane containing holomorphic cusp form, Eisenstein series, Maass forms and it is often introduced in an introductory course in analytic number theory.
On the geometric side we will construct some of the cycles (modular symbols) in the homology $H_*(\Gamma\backslash X)$ which are dual to the cohomology classes we constructed. In our example $\Gamma_n\backslash Sl(2,R)/SO(2)$ these cycles correspond to geodesics and can easily be visualized.
In this course I will explain these results and show how to use them to prove vanishing and non vanishing theorem for $H^*_{deRham}(\Gamma \backslash X)$. I will state the results in full generality, but I will prove them only in the classical case: G=SL$(2,R)$ and the subgroup $\Gamma= \Gamma_n$ a congruence subgroup. Some familiarity with Lie groups and Lie algebras is only prerequisite for the course.
2015年11月18日(水)
FMSPレクチャーズ
15:00-16:00,16:30-17:00 数理科学研究科棟(駒場) 大講義室号室
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
FMSPレクチャーズ
10:30-11:30 数理科学研究科棟(駒場) 056号室
Alfred Ramani 氏 (Ecole Polytechnique)
Discretising systematically integrable systems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani1118.pdf
Alfred Ramani 氏 (Ecole Polytechnique)
Discretising systematically integrable systems (ENGLISH)
[ 講演概要 ]
We present various methods for discretising integrable systerms inspired by the works of Hirota and Mickens. We apply these methods to the systematical discretisation of Painlevé equations.
[ 参考URL ]We present various methods for discretising integrable systerms inspired by the works of Hirota and Mickens. We apply these methods to the systematical discretisation of Painlevé equations.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ramani1118.pdf
数理人口学・数理生物学セミナー
14:55-16:40 数理科学研究科棟(駒場) 128号室
高須夫悟 氏 (奈良女子大学理学部情報科学科)
Spatial population dynamics as a point pattern dynamics (JAPANESE)
http://www.ics.nara-wu.ac.jp/jp/staff/takasu.html
高須夫悟 氏 (奈良女子大学理学部情報科学科)
Spatial population dynamics as a point pattern dynamics (JAPANESE)
[ 講演概要 ]
Spatial population dynamics has been conventionally described as
dynamical system where population size (or population density) changes
with time over space as a continuous "real-valued" variable; these are
often given as partial differential equations as reaction-diffusion
models. In this approach, we implicitly assume infinitely large
population thereby population size changes smoothly and
deterministically. In reality, however, a population is a collection of
a certain number of individuals each of which gives birth or dies with
some stochasticity in a space and the population size as the number of
individuals is "integer-valued". In this talk, I introduce an approach
to reconstruct conventional spatial population dynamics in terms of
point pattern dynamics as a stochastic process. I discuss how to
mathematically describe such spatial stochastic processes using the
moments of increasing order of dimension; densities of points, pairs,
and triplets, etc. are described by integro-differential equations.
Quantification of a point pattern is the key issue here. As examples, I
introduce spatial epidemic SIS and SIR models as point pattern dynamics;
each individual has a certain "mark" depending on its health status; a
snapshot of individuals’ distribution over space is represented by a
marked point pattern and this marked point pattern dynamically changes
with time.
[ 参考URL ]Spatial population dynamics has been conventionally described as
dynamical system where population size (or population density) changes
with time over space as a continuous "real-valued" variable; these are
often given as partial differential equations as reaction-diffusion
models. In this approach, we implicitly assume infinitely large
population thereby population size changes smoothly and
deterministically. In reality, however, a population is a collection of
a certain number of individuals each of which gives birth or dies with
some stochasticity in a space and the population size as the number of
individuals is "integer-valued". In this talk, I introduce an approach
to reconstruct conventional spatial population dynamics in terms of
point pattern dynamics as a stochastic process. I discuss how to
mathematically describe such spatial stochastic processes using the
moments of increasing order of dimension; densities of points, pairs,
and triplets, etc. are described by integro-differential equations.
Quantification of a point pattern is the key issue here. As examples, I
introduce spatial epidemic SIS and SIR models as point pattern dynamics;
each individual has a certain "mark" depending on its health status; a
snapshot of individuals’ distribution over space is represented by a
marked point pattern and this marked point pattern dynamically changes
with time.
http://www.ics.nara-wu.ac.jp/jp/staff/takasu.html
統計数学セミナー
17:00-18:10 数理科学研究科棟(駒場) 056号室
Ioane Muni Toke 氏 (University of New Caledonia)
Order flow intensities for limit order book modelling
Ioane Muni Toke 氏 (University of New Caledonia)
Order flow intensities for limit order book modelling
[ 講演概要 ]
Limit order books are at the core of electronic financial markets. Mathematical models of limit order books use point processes to model the arrival of limit, market and cancellation orders in the order book, but it is not clear what a "good" parametric model for the intensities of these point processes should be.
In the first part of the talk, we show that despite their simplicity basic Poisson processes can be used to accurately model a few features of the order book that more advanced models reproduce with volume-dependent intensities.
In the second part of the talk we present ongoing investigations in a more advanced statistical modelling of these order flow intensities using in particular normal mixture distributions and exponential models.
Limit order books are at the core of electronic financial markets. Mathematical models of limit order books use point processes to model the arrival of limit, market and cancellation orders in the order book, but it is not clear what a "good" parametric model for the intensities of these point processes should be.
In the first part of the talk, we show that despite their simplicity basic Poisson processes can be used to accurately model a few features of the order book that more advanced models reproduce with volume-dependent intensities.
In the second part of the talk we present ongoing investigations in a more advanced statistical modelling of these order flow intensities using in particular normal mixture distributions and exponential models.
2015年11月17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
片長 敦子 氏 (信州大学)
Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)
Tea : Common Room 16:30 -- 17:00
片長 敦子 氏 (信州大学)
Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)
[ 講演概要 ]
In this talk, we deal with hypersurface isolated singularities. First, we will recall
some topological results of singularities. Next, we will sketch the classification of
singularities in algebraic geometry. Finally, we will focus on the three-dimensional
case and discuss some results obtained so far.
In this talk, we deal with hypersurface isolated singularities. First, we will recall
some topological results of singularities. Next, we will sketch the classification of
singularities in algebraic geometry. Finally, we will focus on the three-dimensional
case and discuss some results obtained so far.
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意ください
Dennis Gaitsgory 氏 (Harvard University & IHES)
The Tamagawa number formula over function fields. (English)
いつもと曜日が異なりますのでご注意ください
Dennis Gaitsgory 氏 (Harvard University & IHES)
The Tamagawa number formula over function fields. (English)
[ 講演概要 ]
Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.
The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.
The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
2015年11月16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
宮地 秀樹 氏 (大阪大学)
Towards the complex geometry of Teichmuller space with extremal length (English)
宮地 秀樹 氏 (大阪大学)
Towards the complex geometry of Teichmuller space with extremal length (English)
[ 講演概要 ]
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.
FMSPレクチャーズ
15:00-16:00,16:30-17:00 数理科学研究科棟(駒場) 大講義室号室
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
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
Artan Sheshmani 氏 (IPMU/ Ohio State University)
Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)
Artan Sheshmani 氏 (IPMU/ Ohio State University)
Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)
[ 講演概要 ]
I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.
I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.
2015年11月14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
中村 昌平 氏 (首都大学東京) 13:30-15:00
The sufficient condition for the Fatou property of weighted block spaces
(日本語)
空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性
(日本語)
中村 昌平 氏 (首都大学東京) 13:30-15:00
The sufficient condition for the Fatou property of weighted block spaces
(日本語)
[ 講演概要 ]
In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.
Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.
Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.
町原 秀二 氏 (埼玉大学) 15:30-17:00In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.
Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.
Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.
空間1次元Chern-Simons-Dirac方程式系の初期値問題の非適切性
(日本語)
[ 講演概要 ]
空間1次元Chern-Simons-Dirac方程式系の初期値問題の適切性をソボレフ空間で考える。問題が適切である指数の範囲と非適切である指数の範囲を紹介し、
方程式の構造やソボレフ空間の積評価との関係を観察する。証明は特に非適切性に関して紹介したい。特殊な初期値を設定することにより、解表示を得て、その解関数に対するソボレフ空間での取り扱いについて議論する。本研究は信州大学岡本葵氏との共同研究である。
空間1次元Chern-Simons-Dirac方程式系の初期値問題の適切性をソボレフ空間で考える。問題が適切である指数の範囲と非適切である指数の範囲を紹介し、
方程式の構造やソボレフ空間の積評価との関係を観察する。証明は特に非適切性に関して紹介したい。特殊な初期値を設定することにより、解表示を得て、その解関数に対するソボレフ空間での取り扱いについて議論する。本研究は信州大学岡本葵氏との共同研究である。
2015年11月13日(金)
FMSPレクチャーズ
15:00-16:00,16:30-17:30 数理科学研究科棟(駒場) 大講義室号室
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
中央大学ENCOUNTER with MATHEMATICS共催
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 参考URL ]The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
http://faculty.ms.u-tokyo.ac.jp/Eliashberg201511.html
幾何コロキウム
10:00-11:30 数理科学研究科棟(駒場) 126号室
正井 秀俊 氏 (東京大学)
ランダム閉３次元写像トーラスの対称性について (Japanese)
正井 秀俊 氏 (東京大学)
ランダム閉３次元写像トーラスの対称性について (Japanese)
[ 講演概要 ]
閉曲面の写像類群上のランダムウォークを考え，それらから得られる写像トーラスをランダム写像トーラスと呼ぶ．ランダム写像トーラスは漸近的に確率１で閉双曲多様体になることが知られている．また，閉双曲多様体の写像類群は有限群となることが知られている．この講演ではランダム写像トーラスの写像類群は漸近的に確率１で自明となることを証明する.
閉曲面の写像類群上のランダムウォークを考え，それらから得られる写像トーラスをランダム写像トーラスと呼ぶ．ランダム写像トーラスは漸近的に確率１で閉双曲多様体になることが知られている．また，閉双曲多様体の写像類群は有限群となることが知られている．この講演ではランダム写像トーラスの写像類群は漸近的に確率１で自明となることを証明する.
2015年11月10日(火)
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
五味 清紀 氏 (信州大学理学部)
Topological T-duality for "Real" circle bundle (JAPANESE)
Tea : Common Room 17:00 -- 17:30
五味 清紀 氏 (信州大学理学部)
Topological T-duality for "Real" circle bundle (JAPANESE)
[ 講演概要 ]
Topological T-duality originates from T-duality in superstring theory,
and is first studied by Bouwkneght, Evslin and Mathai. The duality
basically consists of two parts: The first part is that, for any pair
of a principal circle bundle with `H-flux', there is another `T-dual'
pair on the same base space. The second part states that the twisted
K-groups of the total spaces of principal circle bundles in duality
are isomorphic under degree shift. This is the most simple topological
T-duality following Bunke and Schick, and there are a number of
generalizations. The generalization I will talk about is a topological
T-duality for "Real" circle bundles, motivated by T-duality in type II
orbifold string theory. In this duality, a variant of Z_2-equivariant
K-theory appears.
Topological T-duality originates from T-duality in superstring theory,
and is first studied by Bouwkneght, Evslin and Mathai. The duality
basically consists of two parts: The first part is that, for any pair
of a principal circle bundle with `H-flux', there is another `T-dual'
pair on the same base space. The second part states that the twisted
K-groups of the total spaces of principal circle bundles in duality
are isomorphic under degree shift. This is the most simple topological
T-duality following Bunke and Schick, and there are a number of
generalizations. The generalization I will talk about is a topological
T-duality for "Real" circle bundles, motivated by T-duality in type II
orbifold string theory. In this duality, a variant of Z_2-equivariant
K-theory appears.
2015年11月09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
伊藤由佳理 氏 (名古屋大学)
3-dimensional McKay correspondence (English)
伊藤由佳理 氏 (名古屋大学)
3-dimensional McKay correspondence (English)
[ 講演概要 ]
The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.
The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.
2015年11月05日(木)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 126号室
いつもと部屋と曜日が違います。The day of the week and room are different from usual.
大川新之介 氏 (阪大)
Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)
いつもと部屋と曜日が違います。The day of the week and room are different from usual.
大川新之介 氏 (阪大)
Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)
[ 講演概要 ]
I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.
I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 123号室
部屋が普段と異なるのでご注意ください
Henri Berestycki 氏 (フランス高等社会科学院(EHESS))
The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)
部屋が普段と異なるのでご注意ください
Henri Berestycki 氏 (フランス高等社会科学院(EHESS))
The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)
[ 講演概要 ]
I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.
I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.
2015年11月02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
下部 博一 氏 (大阪大学)
A class of non-Kahler manifolds (Japanese)
下部 博一 氏 (大阪大学)
A class of non-Kahler manifolds (Japanese)
[ 講演概要 ]
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials
[ 講演概要 ]
多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．
このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが
原点からある点へ移動するために必要とするコスト(到達コスト)を考える．
到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，
到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．
多次元正方格子の各点に，(独立同分布に)ランダムなポテンシャルを配置する．
このとき，ポテンシャルによって重み付けられた測度の下で，ランダムウォークが
原点からある点へ移動するために必要とするコスト(到達コスト)を考える．
到達コストの大まかな漸近挙動は，ZernerやMourratにより既に調べられている．
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで，
到達コストとその期待値の誤差を評価し，漸近挙動についてより詳しく調べる．
2015年10月30日(金)
FMSPレクチャーズ
15:00-16:15 数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
[ 参考URL ]In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ducrot.pdf
FMSPレクチャーズ
16:30-17:45 数理科学研究科棟(駒場) 128号室
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
[ 講演概要 ]
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
[ 参考URL ]Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bates.pdf
2015年10月28日(水)
数理人口学・数理生物学セミナー
14:55-16:40 数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
[ 講演概要 ]
r/K 選択説が提唱されてから半世紀になろうとしている．この仮説は生物の生活
史戦略の中で現れる、短命多産多死、長寿少産少死の戦略を持つ種の違いをロジ
スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて
種がその人口規模に応じてどちらか一方のパラメータを最大化させる戦略の違い
であると論じたものである．この説は発表当初から賛否両論を巻き起こしてきた．
特に論争の的となったのは人口密度が環境収容力付近にある場合に、生活史進化
が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である．実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた．2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か？”
という疑問を残したまま停滞している．そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この
問題に適用した．その結果、密度効果と確率制御理論の持つ生活史ノイズを組み
合わせることによって、飽和人口における最適戦略は従来のr/K選択説よりも多
様である事が示せた．本講演では、その結果を紹介したい．
r/K 選択説が提唱されてから半世紀になろうとしている．この仮説は生物の生活
史戦略の中で現れる、短命多産多死、長寿少産少死の戦略を持つ種の違いをロジ
スティック方程式を構成するパラメータ、内的増加率rと環境収容力Kをもちいて
種がその人口規模に応じてどちらか一方のパラメータを最大化させる戦略の違い
であると論じたものである．この説は発表当初から賛否両論を巻き起こしてきた．
特に論争の的となったのは人口密度が環境収容力付近にある場合に、生活史進化
が環境収容力を最大化するために少産少死長寿という特質を獲得するという主張
である．実証研究はこの主張をウミガメや樹木、サルの群れ構造などの例を用い
て反駁してきた．2000年代に入るまでに様々な理論モデルや実証研究結果が示さ
れたが、議論の盛り上がりは“飽和した人口の中で起こる生活史進化とは何か？”
という疑問を残したまま停滞している．そこで、本研究では非線形齢―状態構造
モデルと生活史戦略理論を確率制御理論によって統合したモデルを構築し、この
問題に適用した．その結果、密度効果と確率制御理論の持つ生活史ノイズを組み
合わせることによって、飽和人口における最適戦略は従来のr/K選択説よりも多
様である事が示せた．本講演では、その結果を紹介したい．
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 118号室
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions
2015年10月27日(火)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 002号室
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
曜日・部屋がいつもと異なりますのでご注意ください
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
[ 講演概要 ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.
(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)
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