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過去の記録
過去の記録 ～04/19｜本日 04/20 | 今後の予定 04/21～
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
早瀬友裕 氏 (東大数理)
On Cauchy noise loss in a stochastic parameter optimization of random matrices
早瀬友裕 氏 (東大数理)
On Cauchy noise loss in a stochastic parameter optimization of random matrices
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 号室
早稲田大学 西早稲田キャンパス 51 号館 18 階 06 室 での開催となります。
佐々田 槙子 氏 (東京大学大学院数理科学研究科)
ランダムな初期状態をもつ箱玉系とPitmanの定理 (JAPANESE)
早稲田大学 西早稲田キャンパス 51 号館 18 階 06 室 での開催となります。
佐々田 槙子 氏 (東京大学大学院数理科学研究科)
ランダムな初期状態をもつ箱玉系とPitmanの定理 (JAPANESE)
[ 講演概要 ]
箱玉系は1990年に高橋-薩摩によって導入されたソリトン的なふるまいを示すセルオートマトンである。その後、箱玉系はKdV方程式や可解格子模型と密接に関係していることが明らかになり、様々な方向からの研究が行われ、また多くの拡張モデルも提案されてきた。箱玉系は$\{0,1\}^{\mathbb{N}}$上の有限個の粒子をもつ配置に対する決定論的な力学系として定式化できる。近年、P. Ferrariらが、$\{0,1\}^{\mathbb{Z}}$上の無限個の粒子をもつ配置に対して箱玉系の定義域を拡張し、ランダムな初期分布の元での系のふるまいの研究を行った。特に彼らは、期待値が$1/2$未満のベルヌーイ直積分布がこの箱玉系の不変分布となることを示し、さらに一般の不変分布について、よいミキシングのもとでは、ソリトンのサイズに応じた直積分解を持つことを示した。
本研究では、箱玉系の状態空間をシンプルランダムウォークのパスの空間に変換することで、無限個の粒子を持つ箱玉系について様々な解析を行った。まず、箱玉系が定義される配置を決定し、さらに系が可逆になるクラス、さらに可逆かつ不変になるクラスの決定を行った。さらに、$\{0,1\}^{\mathbb{Z}}$上の確率測度が不変分布になるための十分条件を与え、ベルヌーイ直積分布を含むいくつかのクラスの確率測度がこの条件を満たすことを示した。さらに、原点でのカレント、tagged particleの漸近挙動についても、いくつかの不変分布の元で解析を行った。さらに、シンプルランダムウォークに対する極限定理によって自然に現れる「$\mathbb{R}$上の箱玉系」を導入した。これは、ブラウン運動に対するピットマンの定理に現れる変換そのものである。$\mathbb{Z}$上の結果からの自然な拡張として、正のドリフト付きのブラウン運動が、$\mathbb{R}$
上の箱玉系の不変分布となることが示されるが、これにより両側無限の場合のピットマンの変換に対する不変分布であることも得られた。
本研究はDavid Croydon氏、加藤毅氏、辻本諭氏との共同研究である。
箱玉系は1990年に高橋-薩摩によって導入されたソリトン的なふるまいを示すセルオートマトンである。その後、箱玉系はKdV方程式や可解格子模型と密接に関係していることが明らかになり、様々な方向からの研究が行われ、また多くの拡張モデルも提案されてきた。箱玉系は$\{0,1\}^{\mathbb{N}}$上の有限個の粒子をもつ配置に対する決定論的な力学系として定式化できる。近年、P. Ferrariらが、$\{0,1\}^{\mathbb{Z}}$上の無限個の粒子をもつ配置に対して箱玉系の定義域を拡張し、ランダムな初期分布の元での系のふるまいの研究を行った。特に彼らは、期待値が$1/2$未満のベルヌーイ直積分布がこの箱玉系の不変分布となることを示し、さらに一般の不変分布について、よいミキシングのもとでは、ソリトンのサイズに応じた直積分解を持つことを示した。
本研究では、箱玉系の状態空間をシンプルランダムウォークのパスの空間に変換することで、無限個の粒子を持つ箱玉系について様々な解析を行った。まず、箱玉系が定義される配置を決定し、さらに系が可逆になるクラス、さらに可逆かつ不変になるクラスの決定を行った。さらに、$\{0,1\}^{\mathbb{Z}}$上の確率測度が不変分布になるための十分条件を与え、ベルヌーイ直積分布を含むいくつかのクラスの確率測度がこの条件を満たすことを示した。さらに、原点でのカレント、tagged particleの漸近挙動についても、いくつかの不変分布の元で解析を行った。さらに、シンプルランダムウォークに対する極限定理によって自然に現れる「$\mathbb{R}$上の箱玉系」を導入した。これは、ブラウン運動に対するピットマンの定理に現れる変換そのものである。$\mathbb{Z}$上の結果からの自然な拡張として、正のドリフト付きのブラウン運動が、$\mathbb{R}$
上の箱玉系の不変分布となることが示されるが、これにより両側無限の場合のピットマンの変換に対する不変分布であることも得られた。
本研究はDavid Croydon氏、加藤毅氏、辻本諭氏との共同研究である。
2018年01月17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
Ana Caraiani 氏 (Imperial College)
On the vanishing of cohomology for certain Shimura varieties (ENGLISH)
Ana Caraiani 氏 (Imperial College)
On the vanishing of cohomology for certain Shimura varieties (ENGLISH)
[ 講演概要 ]
I will prove that the compactly supported cohomology of certain unitary or symplectic Shimura varieties at level Gamma_1(p^\infty) vanishes above the middle degree. The key ingredients come from p-adic Hodge theory and studying the Bruhat decomposition on the Hodge-Tate flag variety. I will describe the steps in the proof using modular curves as a toy model. I will also mention an application to Galois representations for torsion classes in the cohomology of locally symmetric spaces for GL_n. This talk is based on joint work in preparation with D. Gulotta, C.Y. Hsu, C. Johansson, L. Mocz, E. Reineke, and S.C. Shih.
（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．
今回はパリからの中継です．）
I will prove that the compactly supported cohomology of certain unitary or symplectic Shimura varieties at level Gamma_1(p^\infty) vanishes above the middle degree. The key ingredients come from p-adic Hodge theory and studying the Bruhat decomposition on the Hodge-Tate flag variety. I will describe the steps in the proof using modular curves as a toy model. I will also mention an application to Galois representations for torsion classes in the cohomology of locally symmetric spaces for GL_n. This talk is based on joint work in preparation with D. Gulotta, C.Y. Hsu, C. Johansson, L. Mocz, E. Reineke, and S.C. Shih.
（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．
今回はパリからの中継です．）
離散数理モデリングセミナー
17:00-18:45 数理科学研究科棟(駒場) 056号室
Samuel Colin 氏 (CBPF, Rio de Janeiro, Brasil) 17:00-17:50
Quantum matter bounce with a dark energy expanding phase (ENGLISH)
Mass of the vacuum: a Newtonian perspective (ENGLISH)
Samuel Colin 氏 (CBPF, Rio de Janeiro, Brasil) 17:00-17:50
Quantum matter bounce with a dark energy expanding phase (ENGLISH)
[ 講演概要 ]
The ``matter bounce'' is an alternative scenario to inflationary cosmology, according to which the universe undergoes a contraction, followed by an expansion, the bounce occurring when the quantum effects become important. In my talk, I will show that such a scenario can be unambiguously analyzed in the de Broglie-Bohm pilot-wave interpretation of quantum mechanics. More specifically, I will apply the pilot-wave theory to a Wheeler-DeWitt equation obtained from the quantization of a simple classical mini-superspace model, and show that there are numerical solutions describing bouncing universes with many desirable physical features. For example, one solution contains a dark energy phase during the expansion, without the need to postulate the existence of a cosmological constant in the classical action.
This work was done in collaboration with Nelson Pinto-Neto (CBPF, Rio de Janeiro, Brasil). Further details available at https://arxiv.org/abs/1706.03037.
Thomas Durt 氏 (Aix Marseille Université, Centrale Marseille, Institut Fresnel) 17:50-18:40The ``matter bounce'' is an alternative scenario to inflationary cosmology, according to which the universe undergoes a contraction, followed by an expansion, the bounce occurring when the quantum effects become important. In my talk, I will show that such a scenario can be unambiguously analyzed in the de Broglie-Bohm pilot-wave interpretation of quantum mechanics. More specifically, I will apply the pilot-wave theory to a Wheeler-DeWitt equation obtained from the quantization of a simple classical mini-superspace model, and show that there are numerical solutions describing bouncing universes with many desirable physical features. For example, one solution contains a dark energy phase during the expansion, without the need to postulate the existence of a cosmological constant in the classical action.
This work was done in collaboration with Nelson Pinto-Neto (CBPF, Rio de Janeiro, Brasil). Further details available at https://arxiv.org/abs/1706.03037.
Mass of the vacuum: a Newtonian perspective (ENGLISH)
[ 講演概要 ]
One could believe that special relativity forces us to totally renounce to the idea of an aether, but the aether reappears in general relativity which teaches us that space-time is structured by the local metrics. It also reappears in quantum field theory which teaches us that even at zero temperature space is filled by the quantum vacuum energy. Finally, aether reappears in modern astronomy where it was necessary to introduce ill-defined concepts such as dark matter and dark energy in order to explain apparent deviations from Newtonian dynamics (at the level of galactic rotation curves).
Newton dynamics being the unique limit of general relativistic dynamics in the classical regime, dark matter and dark energy can be seen as an ultimate, last chance strategy, aimed at reconciling the predictions of general relativity with astronomical data.
In our talk we shall describe a simple model, derived in the framework of Newtonian dynamics, aimed at explaining puzzling astronomical observations realized at the level of the solar system (Pioneer anomaly) and at the galactic scale (rotation curves), without adopting ad hoc hypotheses about the existence of dark matter and/or dark energy.
The basic idea is that Newtonian gravity is modified due to the presence of a (negative) density, everywhere in space, of mass-energy.
One could believe that special relativity forces us to totally renounce to the idea of an aether, but the aether reappears in general relativity which teaches us that space-time is structured by the local metrics. It also reappears in quantum field theory which teaches us that even at zero temperature space is filled by the quantum vacuum energy. Finally, aether reappears in modern astronomy where it was necessary to introduce ill-defined concepts such as dark matter and dark energy in order to explain apparent deviations from Newtonian dynamics (at the level of galactic rotation curves).
Newton dynamics being the unique limit of general relativistic dynamics in the classical regime, dark matter and dark energy can be seen as an ultimate, last chance strategy, aimed at reconciling the predictions of general relativity with astronomical data.
In our talk we shall describe a simple model, derived in the framework of Newtonian dynamics, aimed at explaining puzzling astronomical observations realized at the level of the solar system (Pioneer anomaly) and at the galactic scale (rotation curves), without adopting ad hoc hypotheses about the existence of dark matter and/or dark energy.
The basic idea is that Newtonian gravity is modified due to the presence of a (negative) density, everywhere in space, of mass-energy.
2018年01月16日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Jimenez Pascual Adrian 氏 (東京大学大学院数理科学研究科)
On adequacy and the crossing number of satellite knots (JAPANESE)
Tea: Common Room 16:30-17:00
Jimenez Pascual Adrian 氏 (東京大学大学院数理科学研究科)
On adequacy and the crossing number of satellite knots (JAPANESE)
[ 講演概要 ]
It has always been difficult to prove results regarding the (minimal) crossing number of knots. In particular, apparently easy problems such as knowing the crossing number of the connected sum of knots, or bounding the crossing number of satellite knots have been conjectured through decades, yet still remain open. Focusing on this latter problem, in this talk I will prove that the crossing number of a satellite knot is bounded from below by the crossing number of its companion, when the companion is adequate.
It has always been difficult to prove results regarding the (minimal) crossing number of knots. In particular, apparently easy problems such as knowing the crossing number of the connected sum of knots, or bounding the crossing number of satellite knots have been conjectured through decades, yet still remain open. Focusing on this latter problem, in this talk I will prove that the crossing number of a satellite knot is bounded from below by the crossing number of its companion, when the companion is adequate.
トポロジー火曜セミナー
18:00-19:00 数理科学研究科棟(駒場) 056号室
川島 夢人 氏 (東京大学大学院数理科学研究科)
A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory (JAPANESE)
川島 夢人 氏 (東京大学大学院数理科学研究科)
A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory (JAPANESE)
[ 講演概要 ]
A relation between the dilatation of pseudo-Anosov braids and fixed point theory was studied by Ivanov. In this talk we reveal a new relationship between the above two subjects by showing a formula for the dilatation of pseudo-Anosov braids by means of the representations of braid groups due to B. Jiang and H. Zheng.
A relation between the dilatation of pseudo-Anosov braids and fixed point theory was studied by Ivanov. In this talk we reveal a new relationship between the above two subjects by showing a formula for the dilatation of pseudo-Anosov braids by means of the representations of braid groups due to B. Jiang and H. Zheng.
FMSPレクチャーズ
10:30-11:30 数理科学研究科棟(駒場) 056号室
FMSP Tokyo-Princeton joint student seminar
Federico Pasqualotto 氏 (Princeton) -
Large data global solutions for the shallow water system in one space dimension
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf
Naoto Kaziwara 氏 (U. Tokyo) -
Introduction to the maximal Lp-regularity and its applications to the quasi-linear parabolic equations
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf
FMSP Tokyo-Princeton joint student seminar
Federico Pasqualotto 氏 (Princeton) -
Large data global solutions for the shallow water system in one space dimension
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf
Naoto Kaziwara 氏 (U. Tokyo) -
Introduction to the maximal Lp-regularity and its applications to the quasi-linear parabolic equations
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSP_180116.pdf
2018年01月15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
赤川 晋哉 氏 (大阪大学)
Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds
赤川 晋哉 氏 (大阪大学)
Vanishing theorems of $L^2$-cohomology groups on Hessian manifolds
[ 講演概要 ]
A Hessian manifold is a Riemannian manifold whose metric is locally given by the Hessian of a function with respect to flat coordinates. In this talk, we discuss vanishing theorems of $L^2$-cohomology groups on complete Hessian Manifolds coupled with flat line bundles. In particular, we obtain stronger vanishing theorems on regular convex cones with the Cheng-Yau metrics. Further we show that the Cheng-Yau metrics on regular convex cones give rise to harmonic maps to the positive symmetric matrices.
A Hessian manifold is a Riemannian manifold whose metric is locally given by the Hessian of a function with respect to flat coordinates. In this talk, we discuss vanishing theorems of $L^2$-cohomology groups on complete Hessian Manifolds coupled with flat line bundles. In particular, we obtain stronger vanishing theorems on regular convex cones with the Cheng-Yau metrics. Further we show that the Cheng-Yau metrics on regular convex cones give rise to harmonic maps to the positive symmetric matrices.
2017年12月26日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
藤田 健人 氏 (RIMS)
K-stability of log Fano hyperplane arrangements (English)
藤田 健人 氏 (RIMS)
K-stability of log Fano hyperplane arrangements (English)
[ 講演概要 ]
We completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.
We completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.
2017年12月25日(月)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
小澤登高 氏 (京大数理研)
Kazhdan's property (T) and semidefinite programming
小澤登高 氏 (京大数理研)
Kazhdan's property (T) and semidefinite programming
2017年12月21日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
森洋一朗 氏 (ミネソタ大学)
Well-posedness and qualitative behavior of Peskin's problem of an immersed elastic filament in 2D Stokes flow
(Japanese)
森洋一朗 氏 (ミネソタ大学)
Well-posedness and qualitative behavior of Peskin's problem of an immersed elastic filament in 2D Stokes flow
(Japanese)
[ 講演概要 ]
A prototypical fluid-structure interaction (FSI) problem is that of a closed elastic filament immersed in 2D Stokes flow, where the fluids inside and outside the closed filament have equal viscosity. This problem was introduced in the context of Peskin's immersed boundary method, and is often used to test computational methods for FSI problems. Here, we study the well-posedness and qualitative behavior of this problem.
We show local existence and uniqueness with initial configuration in the Holder space C^{1,\alpha}, 0<\alpha<1, and show furthermore that the solution is smooth for positive time. We show that the circular configurations are the only stationary configurations, and show exponential asymptotic stability with an explicit decay rate. Finally, we identify a scalar quantity that goes to infinity if and only if the solution ceases to exist. If this quantity is bounded for all time, we show that the solution must converge exponentially to a circle.
This is joint work with Analise Rodenberg and Dan Spirn.
A prototypical fluid-structure interaction (FSI) problem is that of a closed elastic filament immersed in 2D Stokes flow, where the fluids inside and outside the closed filament have equal viscosity. This problem was introduced in the context of Peskin's immersed boundary method, and is often used to test computational methods for FSI problems. Here, we study the well-posedness and qualitative behavior of this problem.
We show local existence and uniqueness with initial configuration in the Holder space C^{1,\alpha}, 0<\alpha<1, and show furthermore that the solution is smooth for positive time. We show that the circular configurations are the only stationary configurations, and show exponential asymptotic stability with an explicit decay rate. Finally, we identify a scalar quantity that goes to infinity if and only if the solution ceases to exist. If this quantity is bounded for all time, we show that the solution must converge exponentially to a circle.
This is joint work with Analise Rodenberg and Dan Spirn.
数理人口学・数理生物学セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
山道真人 氏 (東京大学大学院総合文化研究科)
生態-進化フィードバックを理解するための理論的アプローチ
山道真人 氏 (東京大学大学院総合文化研究科)
生態-進化フィードバックを理解するための理論的アプローチ
[ 講演概要 ]
近年になって、短期間で起こる適応的な進化（遺伝子頻度の変化）が、生態学的プロセスに大きな影響を与えることが明らかになってきた。一方、生態学的プロセスは適応進化を駆動するため、生態と進化の間には複雑なフィードバックが生じることになる。このような動態を理解するために、プランクトンの培養実験系と数理モデルを組み合わせてさかんに研究が進められている。本発表では、この分野での研究の展開について紹介するとともに、最近取り組んでいる共進化モデルと進化的救助モデルについての結果を紹介し、今後の展開を議論したい。
近年になって、短期間で起こる適応的な進化（遺伝子頻度の変化）が、生態学的プロセスに大きな影響を与えることが明らかになってきた。一方、生態学的プロセスは適応進化を駆動するため、生態と進化の間には複雑なフィードバックが生じることになる。このような動態を理解するために、プランクトンの培養実験系と数理モデルを組み合わせてさかんに研究が進められている。本発表では、この分野での研究の展開について紹介するとともに、最近取り組んでいる共進化モデルと進化的救助モデルについての結果を紹介し、今後の展開を議論したい。
2017年12月19日(火)
数値解析セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
三浦達彦 氏 (東京大学大学院数理科学研究科)
Finite volume scheme for the Hamilton-Jacobi equation on an evolving surface (Japanese)
三浦達彦 氏 (東京大学大学院数理科学研究科)
Finite volume scheme for the Hamilton-Jacobi equation on an evolving surface (Japanese)
[ 講演概要 ]
In this talk we consider the first-order Hamilton-Jacobi equation on a given closed evolving surface embedded into the three-dimensional Euclidean space, which describes the motion of a closed curve on the evolving surface. Our aim is to give a numerical scheme and establish its convergence and an error estimate between numerical and viscosity solutions.
Based on a finite volume scheme for the Hamilton-Jacobi equation on a flat domain introduced by Kim and Li (J. Comput. Math., 2015), we construct a numerical scheme on triangulated surfaces and prove its monotonicity and consistency without assuming that the triangulation is acute. Then applying these results we show the convergence of a numerical solution to a viscosity solution and an error estimate of the same order as in the case of a flat stationary domain.
This talk is based on a joint work with Prof. Klaus Deckelnick (Otto von Guericke University Magdeburg) and Prof. Charles M. Elliott (University of Warwick).
In this talk we consider the first-order Hamilton-Jacobi equation on a given closed evolving surface embedded into the three-dimensional Euclidean space, which describes the motion of a closed curve on the evolving surface. Our aim is to give a numerical scheme and establish its convergence and an error estimate between numerical and viscosity solutions.
Based on a finite volume scheme for the Hamilton-Jacobi equation on a flat domain introduced by Kim and Li (J. Comput. Math., 2015), we construct a numerical scheme on triangulated surfaces and prove its monotonicity and consistency without assuming that the triangulation is acute. Then applying these results we show the convergence of a numerical solution to a viscosity solution and an error estimate of the same order as in the case of a flat stationary domain.
This talk is based on a joint work with Prof. Klaus Deckelnick (Otto von Guericke University Magdeburg) and Prof. Charles M. Elliott (University of Warwick).
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
宮地 秀樹 氏 (大阪大学)
Deformation of holomorphic quadratic differentials and its applications (JAPANESE)
Tea: Common Room 17:00-17:30
宮地 秀樹 氏 (大阪大学)
Deformation of holomorphic quadratic differentials and its applications (JAPANESE)
[ 講演概要 ]
Quadratic differentials are standard and important objects in Teichmuller theory. The deformation space (moduli space) of the quadratic differentials is applied to many fields of mathematics. In this talk, I will develop the deformation of quadratic differentials. Indeed, following pioneer works by A. Douady, J. Hubbard, H. Masur and W. Veech, we describe the infinitesimal deformations in the odd (co)homology groups on the double covering spaces defined from the square roots of the quadratic differentials. We formulate the decomposition theorem for the infinitesimal deformations with keeping in mind of the induced deformation of the moduli of underlying complex structures. As applications, we obtain the Levi form of the Teichmuller distance, and an alternate proof of the Krushkal formula on the pluricomplex Green function on the Teichmuller space.
Quadratic differentials are standard and important objects in Teichmuller theory. The deformation space (moduli space) of the quadratic differentials is applied to many fields of mathematics. In this talk, I will develop the deformation of quadratic differentials. Indeed, following pioneer works by A. Douady, J. Hubbard, H. Masur and W. Veech, we describe the infinitesimal deformations in the odd (co)homology groups on the double covering spaces defined from the square roots of the quadratic differentials. We formulate the decomposition theorem for the infinitesimal deformations with keeping in mind of the induced deformation of the moduli of underlying complex structures. As applications, we obtain the Levi form of the Teichmuller distance, and an alternate proof of the Krushkal formula on the pluricomplex Green function on the Teichmuller space.
2017年12月18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
久本 智之 氏 (名古屋大学)
Gradient flow of the Ding functional
久本 智之 氏 (名古屋大学)
Gradient flow of the Ding functional
[ 講演概要 ]
This is a joint work with T. Collins and R. Takahashi. We introduce the flow in the title to study the stability of a Fano manifold. The first result is the long-time existence of the flow. In the stable case it then converges to the Kähler-Einstein metric. In general the flow is expected to produce the optimally destabilizing degeneration of a Fano manifold. We confirm this expectation in the toric case.
This is a joint work with T. Collins and R. Takahashi. We introduce the flow in the title to study the stability of a Fano manifold. The first result is the long-time existence of the flow. In the stable case it then converges to the Kähler-Einstein metric. In general the flow is expected to produce the optimally destabilizing degeneration of a Fano manifold. We confirm this expectation in the toric case.
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
賀卓豊 氏 (東大数理)
Isomorphism and Morita equivalence classes for crossed product of irrational rotation algebras by cyclic subgroups of $SL_2({\mathbb Z})$ (English)
賀卓豊 氏 (東大数理)
Isomorphism and Morita equivalence classes for crossed product of irrational rotation algebras by cyclic subgroups of $SL_2({\mathbb Z})$ (English)
2017年12月14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) 123号室
普段と曜日・部屋が異なります
Gerard van der Geer 氏 (Universiteit van Amsterdam)
Algebraic curves and modular forms of low degree (English)
普段と曜日・部屋が異なります
Gerard van der Geer 氏 (Universiteit van Amsterdam)
Algebraic curves and modular forms of low degree (English)
[ 講演概要 ]
For genus 2 and 3 modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such modular forms for genus 2 and 3 using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.
For genus 2 and 3 modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such modular forms for genus 2 and 3 using invariant theory and give some applications. This is based on joint work with Fabien Clery and Carel Faber.
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
158から128に変更されました．
I-Kun, Chen 氏 (Kyoto University)
Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain
(English)
158から128に変更されました．
I-Kun, Chen 氏 (Kyoto University)
Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain
(English)
[ 講演概要 ]
We consider the diffuse reflection boundary problem for the linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a $C^2$ strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. Velocity averaging effect for stationary solutions as well as observations in geometry are used in this research.
We consider the diffuse reflection boundary problem for the linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a $C^2$ strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. Velocity averaging effect for stationary solutions as well as observations in geometry are used in this research.
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 123号室
Linquan Ma 氏 (University of Utah)
Perfectoid test ideals (English)
Linquan Ma 氏 (University of Utah)
Perfectoid test ideals (English)
[ 講演概要 ]
Inspired by the recent solution of the direct summand conjecture
of Andre and Bhatt, we introduce perfectoid multiplier/test ideals in mixed
characteristic. As an application, we obtain a uniform bound on the growth
of symbolic powers in regular local rings of mixed characteristic analogous
to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal
characteristic. This is joint work with Karl Schwede.
Inspired by the recent solution of the direct summand conjecture
of Andre and Bhatt, we introduce perfectoid multiplier/test ideals in mixed
characteristic. As an application, we obtain a uniform bound on the growth
of symbolic powers in regular local rings of mixed characteristic analogous
to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal
characteristic. This is joint work with Karl Schwede.
数理人口学・数理生物学セミナー
13:00-16:40 数理科学研究科棟(駒場) 126号室
江夏洋一 氏 (東京理科大学) 13:00-13:30
On a mosquito-borne disease transmission by Wolbachia infection (JAPANESE)
Delayed feedback controls in an Escherichia coli and Tetrahymena system (ENGLISH)
構造人口モデルにおける固有関数と生活史進化 (JAPANESE)
Reinfection epidemic models in a heterogeneous host population (JAPANESE)
Time evolution of Tajima's D of a pathogen during its outbreak (JAPANESE)
Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)
江夏洋一 氏 (東京理科大学) 13:00-13:30
On a mosquito-borne disease transmission by Wolbachia infection (JAPANESE)
[ 講演概要 ]
Symbiotic bacteria called Wolbachia pipientis inside mosquitoes are experimentally observed to prevent transmission of Zika virus. Wolbachia-infected mosquitoes have been widely released and it is reported that they reduce vector competence for Zika virus.
In order to study dynamical behavior of the population of the mosquitoes, Xue et al. (2017) formulated a system of ODEs and investigated stability of three equilibria; a disease-free
equilibrium, a complete infection equilibrium and an endemic equilibrium. In this presentation, we propose a system of DDEs to investigate the effect of a time lag from the egg stage to the aquatic stage. Out talk is based on a collaborated work with Professor Emiko Ishiwata and Mr. Masatoshi Kanamori.
Don Yueping 氏 (青山学院大学) 13:30-14:00Symbiotic bacteria called Wolbachia pipientis inside mosquitoes are experimentally observed to prevent transmission of Zika virus. Wolbachia-infected mosquitoes have been widely released and it is reported that they reduce vector competence for Zika virus.
In order to study dynamical behavior of the population of the mosquitoes, Xue et al. (2017) formulated a system of ODEs and investigated stability of three equilibria; a disease-free
equilibrium, a complete infection equilibrium and an endemic equilibrium. In this presentation, we propose a system of DDEs to investigate the effect of a time lag from the egg stage to the aquatic stage. Out talk is based on a collaborated work with Professor Emiko Ishiwata and Mr. Masatoshi Kanamori.
Delayed feedback controls in an Escherichia coli and Tetrahymena system (ENGLISH)
[ 講演概要 ]
In this talk, we develop a novel mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by Shiga-toxin and neutrophils in a community. By applying the quasi steady state approximation, the proposed model can be reduced to a Lotka-Volterra predator-prey type system with two discrete delays. By investigating the distributions of the roots of the characteristic equation, the local stability as well as Hopf bifurcation are well studied when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delays plane always enlarge as the increase of negative feedback control coefficients, and especially the controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as quasi-periodic behaviors and chaotic behaviours.
大泉嶺 氏 (国立社会保障・人口問題研究所) 14:00-14:30In this talk, we develop a novel mathematical model to investigate the interaction between Shiga-toxin producing Escherichia coli and Tetrahymena with delayed feedback controls by Shiga-toxin and neutrophils in a community. By applying the quasi steady state approximation, the proposed model can be reduced to a Lotka-Volterra predator-prey type system with two discrete delays. By investigating the distributions of the roots of the characteristic equation, the local stability as well as Hopf bifurcation are well studied when two delays are present. Numerical simulations are carried out to verify the analytical results. Our findings reveal that the instability regions of coexistence equilibrium in two delays plane always enlarge as the increase of negative feedback control coefficients, and especially the controls on Tetrahymena population play a dominant role in the destabilization of coexistence equilibrium. Besides, we observe some interesting phenomena such as quasi-periodic behaviors and chaotic behaviours.
構造人口モデルにおける固有関数と生活史進化 (JAPANESE)
[ 講演概要 ]
年齢構造モデルの基本であるMacKendrick方程式は, 支配的な特性根に対する左右固
有関数がそれぞれ繁殖価と定常年齢構造に対応することはよく知られた事実である．
本研究では，年齢構造のに加え，拡散過程を含む状態構造を持つ構造人口モデルに対
して左右固有関数による展開を試みた．結果として，これら固有関数は繁殖価と定常
年齢構造を状態構造を含むものに拡張できる事を示した．本講演では繁殖価を与える
固有関数が満たす条件から，状態の成長に関する生活史の進化を解析する制御方程式
を導出するとともに，密度効果や環境変動下での生活史進化への応用について報告し
たい．
中田行彦 氏 (島根大学) 14:40-15:10年齢構造モデルの基本であるMacKendrick方程式は, 支配的な特性根に対する左右固
有関数がそれぞれ繁殖価と定常年齢構造に対応することはよく知られた事実である．
本研究では，年齢構造のに加え，拡散過程を含む状態構造を持つ構造人口モデルに対
して左右固有関数による展開を試みた．結果として，これら固有関数は繁殖価と定常
年齢構造を状態構造を含むものに拡張できる事を示した．本講演では繁殖価を与える
固有関数が満たす条件から，状態の成長に関する生活史の進化を解析する制御方程式
を導出するとともに，密度効果や環境変動下での生活史進化への応用について報告し
たい．
Reinfection epidemic models in a heterogeneous host population (JAPANESE)
[ 講演概要 ]
In our recent studies, interplay of heterogeneous susceptible
population and reinfection indicates fragility of the threshold
phenomena, which is frequently observed in epidemic models, with
respect to the basic reproduction number. To elaborate this aspect, we
formulate a mathematical model by a system of ODEs and analyze its
equilibrium structure. If time permits, we analyze the transient
solution in detail for a special case and discuss the complexity in
the epidemic dynamics induced by the heterogeneous susceptibility.
大森亮介 氏 (北海道大学) 15:10-15:40In our recent studies, interplay of heterogeneous susceptible
population and reinfection indicates fragility of the threshold
phenomena, which is frequently observed in epidemic models, with
respect to the basic reproduction number. To elaborate this aspect, we
formulate a mathematical model by a system of ODEs and analyze its
equilibrium structure. If time permits, we analyze the transient
solution in detail for a special case and discuss the complexity in
the epidemic dynamics induced by the heterogeneous susceptibility.
Time evolution of Tajima's D of a pathogen during its outbreak (JAPANESE)
[ 講演概要 ]
Tajima’s D measures the selection pressure by calculating the difference between two estimates of genetic diversity in a given sample set of nucleic acid sequences, however, it is believed that Tajima’s D is biased by the population dynamics. To analyze the impact of population dynamics of infectious disease pathogen, which described by the standard SIR model on Tajima’s D, we developed an inductive algorithm for calculating the site-specific nucleotide frequencies from a standard multi-strain susceptible-infective-removed model (both deterministic and stochastic). We show that these frequencies are fully determined by the mutation rate and the initial condition of the frequencies. We prove that the sign of Tajima’s D is independent of the disease population dynamics in the deterministic model. We also show that the stochasticity in the transmission and evolution dynamics induces the dependency of Tajima’s D on the population dynamics of pathogens.
Xu Yaya 氏 (東京大学大学院数理科学研究科) 15:40-16:10Tajima’s D measures the selection pressure by calculating the difference between two estimates of genetic diversity in a given sample set of nucleic acid sequences, however, it is believed that Tajima’s D is biased by the population dynamics. To analyze the impact of population dynamics of infectious disease pathogen, which described by the standard SIR model on Tajima’s D, we developed an inductive algorithm for calculating the site-specific nucleotide frequencies from a standard multi-strain susceptible-infective-removed model (both deterministic and stochastic). We show that these frequencies are fully determined by the mutation rate and the initial condition of the frequencies. We prove that the sign of Tajima’s D is independent of the disease population dynamics in the deterministic model. We also show that the stochasticity in the transmission and evolution dynamics induces the dependency of Tajima’s D on the population dynamics of pathogens.
Mathematical analysis for HBV model and HBV-HDV coinfection model (ENGLISH)
[ 講演概要 ]
The hepatitis beta virus (HBV) and hepatitis delta viurs (HDV)
are two common forms of viral hepatitis. However HDV is dependent
on coinfection with HBV since replication of HDV requires the hepati-
tis B surface antigen (HBsAg) which can only been produced by HBV.
Here we start with analyzing HBV only model, the dynamics between
healthy cells, HBV infected cells and free HBV.We show that a postive
equilbrium exsits and it's globally asmptotically stable for R0 > 1, an
infection free equilibrium is globally asymptotically stable for R0 < 1.
Then we introduce HDV to form a coinfection model which contains
three more variables, HDV infected cells, coinfected cells and free HDV.
Additionally, we investigate two coinfection models, one without and
one with treatment by oral drugs which are valid for HBV only. We
consider several durgs with variable eciencies. As a result, compari-
son of model simulations indicate that treatment is necessary to taking
contiously for choric infection.
The hepatitis beta virus (HBV) and hepatitis delta viurs (HDV)
are two common forms of viral hepatitis. However HDV is dependent
on coinfection with HBV since replication of HDV requires the hepati-
tis B surface antigen (HBsAg) which can only been produced by HBV.
Here we start with analyzing HBV only model, the dynamics between
healthy cells, HBV infected cells and free HBV.We show that a postive
equilbrium exsits and it's globally asmptotically stable for R0 > 1, an
infection free equilibrium is globally asymptotically stable for R0 < 1.
Then we introduce HDV to form a coinfection model which contains
three more variables, HDV infected cells, coinfected cells and free HDV.
Additionally, we investigate two coinfection models, one without and
one with treatment by oral drugs which are valid for HBV only. We
consider several durgs with variable eciencies. As a result, compari-
son of model simulations indicate that treatment is necessary to taking
contiously for choric infection.
2017年12月13日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Javier Fresán 氏 (École polytechnique)
Exponential motives (ENGLISH)
Javier Fresán 氏 (École polytechnique)
Exponential motives (ENGLISH)
[ 講演概要 ]
What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the étale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums.
Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an étale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).
（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．今回はパリからの中継です．）
What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the étale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums.
Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an étale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).
（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．今回はパリからの中継です．）
FMSPレクチャーズ
17:00-17:45 数理科学研究科棟(駒場) 470号室
Anar Rahimov 氏 (The Institute of Control Systems of ANAS and Baku State University)
An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rahimov.pdf
Anar Rahimov 氏 (The Institute of Control Systems of ANAS and Baku State University)
An approach to numerical solution to inverse source problems with nonlocal conditions (ENGLISH)
[ 講演概要 ]
We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.
[ 参考URL ]We consider two inverse source problems for a parabolic equation under nonlocal, final, and boundary conditions. A numerical method is proposed to solve the inverse source problems, which is based on the use of the method of lines. The initial problems are reduced to a system of ordinary differential equations with unknown parameters. To solve this system, we propose an approach based on the sweep method type. We present the results of numerical experiments on test problems. This is joint work with Prof. K. Aida-zade.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rahimov.pdf
2017年12月12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
Alex Mahalov 氏 (Arizona State University)
Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics (English)
Alex Mahalov 氏 (Arizona State University)
Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics (English)
[ 講演概要 ]
We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework by bootstrapping from global regularity of the averaged stochastic resonant equations. The averaged covariance operator couples stochastic and wave effects. We also present theoretical results for 3D nonlinear dynamics.
We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework by bootstrapping from global regularity of the averaged stochastic resonant equations. The averaged covariance operator couples stochastic and wave effects. We also present theoretical results for 3D nonlinear dynamics.
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
清水 達郎 氏 (京都大学数理解析研究所)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
Tea: Common Room 16:30-17:00
清水 達郎 氏 (京都大学数理解析研究所)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
[ 講演概要 ]
閉$n$次元有向多様体$M$から$R^p$へのMorin写像と呼ばれるクラスの可微分写像の特異点集合は，$M$の部分多様体をなすことが知られている．この特異点集合の$k$重自己交差が定めるホモロジー類と，$M$から$R^{p+k-1}$へのgenericな写像の(Jacobianが)$k$階退化した特異点集合が定めるホモロジー類が，2を法として一致することを示す（ただし$n>p+k-2$）．この事実自体はThom多項式等を用いる方法で間接的に示すことができると思われれるが，本講演では幾何的な直接の対応を与える．この証明の利点の１つは$M$が境界を持つ場合に拡張できることである．その応用として3次元多様体の接束の自明化（枠）の不変量である不足符号数と特異点を用いた解釈を与える．ただし，2を法にしている．
閉$n$次元有向多様体$M$から$R^p$へのMorin写像と呼ばれるクラスの可微分写像の特異点集合は，$M$の部分多様体をなすことが知られている．この特異点集合の$k$重自己交差が定めるホモロジー類と，$M$から$R^{p+k-1}$へのgenericな写像の(Jacobianが)$k$階退化した特異点集合が定めるホモロジー類が，2を法として一致することを示す（ただし$n>p+k-2$）．この事実自体はThom多項式等を用いる方法で間接的に示すことができると思われれるが，本講演では幾何的な直接の対応を与える．この証明の利点の１つは$M$が境界を持つ場合に拡張できることである．その応用として3次元多様体の接束の自明化（枠）の不変量である不足符号数と特異点を用いた解釈を与える．ただし，2を法にしている．
2017年12月11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
大沢 健夫 氏 (名古屋大学)
Nishino's rigidity theorem and questions on locally pseudoconvex maps
大沢 健夫 氏 (名古屋大学)
Nishino's rigidity theorem and questions on locally pseudoconvex maps
[ 講演概要 ]
Nishino proved in 1969 that locally Stein maps with fibers $\cong \mathbb{C}$ are locally trivial. Yamaguchi gave an alternate proof of Nishino's theorem which later developed into a the theory of variations of the Bergman kernel. The proofs of Nishino and Yamaguchi will be reviewed and questions suggested by the result will be discussed. A new application of the $L^2$ extension theorem will be also presented in this context.
Nishino proved in 1969 that locally Stein maps with fibers $\cong \mathbb{C}$ are locally trivial. Yamaguchi gave an alternate proof of Nishino's theorem which later developed into a the theory of variations of the Bergman kernel. The proofs of Nishino and Yamaguchi will be reviewed and questions suggested by the result will be discussed. A new application of the $L^2$ extension theorem will be also presented in this context.
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