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過去の記録 ～04/24｜本日 04/25 | 今後の予定 04/26～
2015年01月16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
西納 武男 氏 (立教大学)
Degeneration and curves on K3 surfaces (Japanese)
西納 武男 氏 (立教大学)
Degeneration and curves on K3 surfaces (Japanese)
[ 講演概要 ]
There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of quartic K3 surfaces whose members fulfil the conjecture.
There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of quartic K3 surfaces whose members fulfil the conjecture.
統計数学セミナー
14:00-15:30 数理科学研究科棟(駒場) 052号室
Ajay Jasra 氏 (National University of Singapore)
A stable particle filter in high-dimensions
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html
Ajay Jasra 氏 (National University of Singapore)
A stable particle filter in high-dimensions
[ 講演概要 ]
We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.
This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).
[ 参考URL ]We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.
This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html
2015年01月15日(木)
東京無限可積分系セミナー
15:00-18:30 数理科学研究科棟(駒場) 002号室
土岡 俊介 氏 (東大数理) 15:00-16:30
On Gram matrices of the Shapovalov form of a basic representation of a
quantum affine group (ENGLISH)
Continuous and Infinitesimal Hecke algebras (ENGLISH)
土岡 俊介 氏 (東大数理) 15:00-16:30
On Gram matrices of the Shapovalov form of a basic representation of a
quantum affine group (ENGLISH)
[ 講演概要 ]
We consider Gram matrices of the Shapovalov form of a basic
representation
of a quantum affine group. We present a conjecture predicting the
invariant
factors of these matrices and proving that it gives the correct
invariants
when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in
certain ways.
This generalizes Evseev's theorem which settled affirmatively
the K\"{u}lshammer-Olsson-Robinson conjecture that predicts
the generalized Cartan invariants of the symmetric groups.
This is a joint work with Anton Evseev.
Alexander Tsymbaliuk 氏 (SCGP (Simons Center for Geometry and Physics)) 17:00-18:30We consider Gram matrices of the Shapovalov form of a basic
representation
of a quantum affine group. We present a conjecture predicting the
invariant
factors of these matrices and proving that it gives the correct
invariants
when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in
certain ways.
This generalizes Evseev's theorem which settled affirmatively
the K\"{u}lshammer-Olsson-Robinson conjecture that predicts
the generalized Cartan invariants of the symmetric groups.
This is a joint work with Anton Evseev.
Continuous and Infinitesimal Hecke algebras (ENGLISH)
[ 講演概要 ]
In the late 80's V. Drinfeld introduced the notion of the
degenerate affine Hecke algebras. The particular class of those, called
symplectic reflection algebras, has been rediscovered 15 years later by
[Etingof and Ginzburg]. The theory of those algebras (which include also
the rational Cherednik algebras) has attracted a lot of attention in the
last 15 years.
In this talk we will discuss their continuous and infinitesimal versions,
introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those
classical algebras to the simplest 1-block finite W-algebras.
In the late 80's V. Drinfeld introduced the notion of the
degenerate affine Hecke algebras. The particular class of those, called
symplectic reflection algebras, has been rediscovered 15 years later by
[Etingof and Ginzburg]. The theory of those algebras (which include also
the rational Cherednik algebras) has attracted a lot of attention in the
last 15 years.
In this talk we will discuss their continuous and infinitesimal versions,
introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those
classical algebras to the simplest 1-block finite W-algebras.
2015年01月14日(水)
代数学コロキウム
16:40-17:40 数理科学研究科棟(駒場) 056号室
Laurent Berger 氏 (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
Laurent Berger 氏 (ENS de Lyon)
Iterate extensions and relative Lubin-Tate groups
[ 講演概要 ]
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
賀卓豊 氏 (東大数理)
Canonical cyclic group actions on noncommutative tori
賀卓豊 氏 (東大数理)
Canonical cyclic group actions on noncommutative tori
2015年01月13日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room
吉田 建一 氏 (東京大学大学院数理科学研究科)
Stable presentation length of 3-manifold groups (JAPANESE)
Tea : 16:00-16:30 Common Room
吉田 建一 氏 (東京大学大学院数理科学研究科)
Stable presentation length of 3-manifold groups (JAPANESE)
[ 講演概要 ]
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.
We will introduce the stable presentation length
of a finitely presented group, which is defined
by stabilizing the presentation length for the
finite index subgroups. The stable presentation
length of the fundamental group of a 3-manifold
is an analogue of the simplicial volume and the
stable complexity introduced by Francaviglia,
Frigerio and Martelli. We will explain some
similarities of stable presentation length with
simplicial volume and stable complexity.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Wojciech Zajączkowski 氏 (Institute of Mathematics Polish Academy of Sciences)
Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)
Wojciech Zajączkowski 氏 (Institute of Mathematics Polish Academy of Sciences)
Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)
[ 講演概要 ]
We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.
We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.
2015年01月10日(土)
調和解析駒場セミナー
13:00-18:00 数理科学研究科棟(駒場) 128号室
貝塚 公一 氏 (学習院大学) 13:30-15:00
Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)
貝塚 公一 氏 (学習院大学) 13:30-15:00
Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)
[ 講演概要 ]
非コンパクト型対称空間上のラプラシアンに対する散乱理論について紹介する. ラプラシアンのレゾルベントに対する極限吸収原理,レゾルベントとPoisson 作用素に対する無限遠での漸近展開,Helmholtz方程式の解の特徴づけ等の散乱理論における基本的な定理について解説する. 特に, 対称空間上のRadon変換を用いた, 一様Fourier制限評価について詳しく述べる.
猪奥 倫左 氏 (愛媛大学) 15:30-17:00非コンパクト型対称空間上のラプラシアンに対する散乱理論について紹介する. ラプラシアンのレゾルベントに対する極限吸収原理,レゾルベントとPoisson 作用素に対する無限遠での漸近展開,Helmholtz方程式の解の特徴づけ等の散乱理論における基本的な定理について解説する. 特に, 対称空間上のRadon変換を用いた, 一様Fourier制限評価について詳しく述べる.
スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)
[ 講演概要 ]
Hardyの不等式は，劣臨界指数の場合には伸縮に関するスケール不変性を持つ事が知られている．一方，臨界指数の場合には対数型の特異性に起因して通常の伸縮不変性は破綻する． 本講演では，「伸縮に関するスケール不変性を持つ平均振動型の臨界Hardyの不等式」および「非線形スケール不変性を持つ対数補正型臨界 Hardyの不等式」の二種を導出する．更にその最良定数は達成されないことを，対応する変分問題を解析することで証明する.
Hardyの不等式は，劣臨界指数の場合には伸縮に関するスケール不変性を持つ事が知られている．一方，臨界指数の場合には対数型の特異性に起因して通常の伸縮不変性は破綻する． 本講演では，「伸縮に関するスケール不変性を持つ平均振動型の臨界Hardyの不等式」および「非線形スケール不変性を持つ対数補正型臨界 Hardyの不等式」の二種を導出する．更にその最良定数は達成されないことを，対応する変分問題を解析することで証明する.
2015年01月07日(水)
代数学コロキウム
16:40-17:40 数理科学研究科棟(駒場) 056号室
Sandra Rozensztajn 氏 (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
Sandra Rozensztajn 氏 (ENS de Lyon)
Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)
[ 講演概要 ]
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
早瀬友裕 氏 (東大数理)
De Finetti theorems related to Boolean independence (English)
早瀬友裕 氏 (東大数理)
De Finetti theorems related to Boolean independence (English)
2015年01月06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
Elio Eduardo Espejo 氏 (National University of Colombia / Osaka University)
Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)
Elio Eduardo Espejo 氏 (National University of Colombia / Osaka University)
Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)
[ 講演概要 ]
There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.
There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.
2014年12月22日(月)
数理人口学・数理生物学セミナー
15:00-16:20 数理科学研究科棟(駒場) 122号室
Don Yueping 氏 (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)
Estimating the seroincidence of pertussis in Japan
Don Yueping 氏 (Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)
Estimating the seroincidence of pertussis in Japan
[ 講演概要 ]
Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.
Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.
2014年12月19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
蒲谷祐一 氏 (京都大学)
Exotic components in linear slices of quasi-Fuchsian groups
蒲谷祐一 氏 (京都大学)
Exotic components in linear slices of quasi-Fuchsian groups
[ 講演概要 ]
The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.
The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.
2014年12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) 117号室
いつもと教室が異なりますのでご注意ください
Konstantin Ardakov 氏 (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
いつもと教室が異なりますのでご注意ください
Konstantin Ardakov 氏 (University of Oxford)
Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces
(English)
[ 講演概要 ]
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
(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.)
Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.
(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.)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
Valentin Zagrebnov 氏 (Univ. d'Aix-Marseille)
Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)
Valentin Zagrebnov 氏 (Univ. d'Aix-Marseille)
Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)
数理人口学・数理生物学セミナー
14:50-16:20 数理科学研究科棟(駒場) 122号室
矢作由美 氏 (東京都市大学)
細胞性粘菌の集合体形成現象モデルにおける確率論的解釈
(JAPANESE)
矢作由美 氏 (東京都市大学)
細胞性粘菌の集合体形成現象モデルにおける確率論的解釈
(JAPANESE)
[ 講演概要 ]
細胞性粘菌は飢餓状態に陥ると、集合してナメクジのような集合体を形成します。また、そのときに走化性物質を放出し
ます。その動きはケラーシーゲル系と呼ばれる連立偏微分方程式系を用いて記述されます。本研究においては、標準的ブラウン運動によって駆動される確率過程を導入した確率微分方程式を用いることによって、ケラーシーゲル系の解に確率論的表記を与えることが目標です。また、モンテカルロ法を用いた近似解の構成方法について発表します。
細胞性粘菌は飢餓状態に陥ると、集合してナメクジのような集合体を形成します。また、そのときに走化性物質を放出し
ます。その動きはケラーシーゲル系と呼ばれる連立偏微分方程式系を用いて記述されます。本研究においては、標準的ブラウン運動によって駆動される確率過程を導入した確率微分方程式を用いることによって、ケラーシーゲル系の解に確率論的表記を与えることが目標です。また、モンテカルロ法を用いた近似解の構成方法について発表します。
2014年12月16日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
水谷 治哉 氏 (大阪大学・理学研究科)
Global Strichartz estimates for Schr¥”odinger equations on
asymptotically conic manifolds (Japanese)
水谷 治哉 氏 (大阪大学・理学研究科)
Global Strichartz estimates for Schr¥”odinger equations on
asymptotically conic manifolds (Japanese)
トポロジー火曜セミナー
17:10-18:10 数理科学研究科棟(駒場) 056号室
Tea : 16:50-17:10 Common Room
岩瀬 則夫 氏 (九州大学)
Differential forms in diffeological spaces (JAPANESE)
Tea : 16:50-17:10 Common Room
岩瀬 則夫 氏 (九州大学)
Differential forms in diffeological spaces (JAPANESE)
[ 講演概要 ]
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.
The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.
Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.
2014年12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) 126号室
辻 元 氏 (上智大学)
The limits of Kähler-Ricci flows
辻 元 氏 (上智大学)
The limits of Kähler-Ricci flows
[ 講演概要 ]
ケーラー・リッチ流を、離散化することで、その極限を解析する。
ケーラー・リッチ流を、離散化することで、その極限を解析する。
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
三内 顕義 氏 (東京大学数理科学研究科)
A characterization of ordinary abelian varieties in positive characteristic (JAPANESE)
三内 顕義 氏 (東京大学数理科学研究科)
A characterization of ordinary abelian varieties in positive characteristic (JAPANESE)
[ 講演概要 ]
This is joint work with Hiromu Tanaka. In this talk, we study F^e_*O_X on a projective variety over the algebraic closed field of positive characteristic. For an ordinary abelian variety X, F^e_*O_X is decomposed into line bundles for every positive integer e. Conversely, if a smooth projective variety X satisfies this property and its Kodaira dimension is non-negative, then X is an ordinary abelian variety.
This is joint work with Hiromu Tanaka. In this talk, we study F^e_*O_X on a projective variety over the algebraic closed field of positive characteristic. For an ordinary abelian variety X, F^e_*O_X is decomposed into line bundles for every positive integer e. Conversely, if a smooth projective variety X satisfies this property and its Kodaira dimension is non-negative, then X is an ordinary abelian variety.
2014年12月11日(木)
東京無限可積分系セミナー
15:00-18:30 数理科学研究科棟(駒場) 002号室
鹿島 洋平 氏 (東大数理) 15:00-16:30
多体電子系における繰り込み群の方法 (JAPANESE)
Unitary transformations and multivariate special
orthogonal polynomials (JAPANESE)
鹿島 洋平 氏 (東大数理) 15:00-16:30
多体電子系における繰り込み群の方法 (JAPANESE)
[ 講演概要 ]
格子上を移動し、相互作用する
電子たちからなる量子多体系を正の温度下で考える。
各次の項を厳密に書き下すことが原理的には可能であ
るという点で、電子間の結合定数に関する摂動級数
展開が物理量を計算するための有効な手法と考えられ
ている。各次の項を直接的に評価することにより、結合
定数が温度のある巾乗よりも小さいならば摂動級数が
収束することが示される。しかし、低温で相互作用する
電子の模型においてこれは厳しい制約である。多体電子
系の物理量の結合定数に関する解析性を低温で証明する
ために、近年繰り込み群の方法が開発されてきた。
そのひとつの発展として、多体電子系の典型的な模型
である平方格子上のhalf-filledのハバード模型に対し
て繰り込み群の方法を構成し、以下のことを証明する。
もし系に格子の最小の正方形あたりの磁束がπ (mod 2π)
である外部磁場が与えられているならば、系の自由エネ
ルギー密度は結合定数に関して体積、温度に依存しない
原点の近傍で解析的であり、無限体積、絶対零度への極限に
一様に収束する。この外部磁場に関する条件は自由エネ
ルギー密度が最小となるための十分条件であることが知ら
れている。したがって、系の最小自由エネルギー密度
についても同様の解析性と絶対零度への収束性が成り立つ。
渋川 元樹 氏 (九州大学マス・フォア・インダストリ研究所) 17:00-18:30格子上を移動し、相互作用する
電子たちからなる量子多体系を正の温度下で考える。
各次の項を厳密に書き下すことが原理的には可能であ
るという点で、電子間の結合定数に関する摂動級数
展開が物理量を計算するための有効な手法と考えられ
ている。各次の項を直接的に評価することにより、結合
定数が温度のある巾乗よりも小さいならば摂動級数が
収束することが示される。しかし、低温で相互作用する
電子の模型においてこれは厳しい制約である。多体電子
系の物理量の結合定数に関する解析性を低温で証明する
ために、近年繰り込み群の方法が開発されてきた。
そのひとつの発展として、多体電子系の典型的な模型
である平方格子上のhalf-filledのハバード模型に対し
て繰り込み群の方法を構成し、以下のことを証明する。
もし系に格子の最小の正方形あたりの磁束がπ (mod 2π)
である外部磁場が与えられているならば、系の自由エネ
ルギー密度は結合定数に関して体積、温度に依存しない
原点の近傍で解析的であり、無限体積、絶対零度への極限に
一様に収束する。この外部磁場に関する条件は自由エネ
ルギー密度が最小となるための十分条件であることが知ら
れている。したがって、系の最小自由エネルギー密度
についても同様の解析性と絶対零度への収束性が成り立つ。
Unitary transformations and multivariate special
orthogonal polynomials (JAPANESE)
[ 講演概要 ]
ユニタリ変換を用いた直交函数系の研究は古くから知られている.
すなわち, 既知の直交系のユニタリ変換（Fourier変換等）の像を求めることで
新たな直交系を導出し, ユニタリ性からその基本的性質（直交性, 母函数, 微分
方程式等）を解明する, というのがその基本方針である. 一変数の直交函数系に
関してはこのような技法は古くから知られていたが, 近年ではその多変数化(
matrix arguments)の研究もDavidson, Olafsson, Zhang, Faraut, Wakayama et.
alにより行われている.
本講演では, 特にShenによるcircular Jacobi多項式のFourier変換による描写
を紹介し, その多変数化について述べる. このようにして構成される多変数直交
多項式(多変数circular Jacobi多項式)は, 球多項式の一般化（2-パラメータ変
形）になっているが, 球多項式の拡張として良く知られているJack多項式や
Macdonald多項式とも異なる直交系である. 更にそのweight函数はBourgade et
al.により導入されたcircular Jacobi ensembleとなっており, そのCayley変換
はある種の擬微分関係式を満たすこともわかる.
加えて多変数circular Jacobi多項式はJack多項式を含むような一般化も可能
である. この一般化多変数circular Jacobi多項式に関するいくつかの予想及び
問題も述べる.
また時間があれば, 離散型の直交多項式系の代表例であるMeixner, Charlier,
Krawtchouk多項式のユニタリ変換を用いた描写を述べ, その多変数化に関しても
触れる.
ユニタリ変換を用いた直交函数系の研究は古くから知られている.
すなわち, 既知の直交系のユニタリ変換（Fourier変換等）の像を求めることで
新たな直交系を導出し, ユニタリ性からその基本的性質（直交性, 母函数, 微分
方程式等）を解明する, というのがその基本方針である. 一変数の直交函数系に
関してはこのような技法は古くから知られていたが, 近年ではその多変数化(
matrix arguments)の研究もDavidson, Olafsson, Zhang, Faraut, Wakayama et.
alにより行われている.
本講演では, 特にShenによるcircular Jacobi多項式のFourier変換による描写
を紹介し, その多変数化について述べる. このようにして構成される多変数直交
多項式(多変数circular Jacobi多項式)は, 球多項式の一般化（2-パラメータ変
形）になっているが, 球多項式の拡張として良く知られているJack多項式や
Macdonald多項式とも異なる直交系である. 更にそのweight函数はBourgade et
al.により導入されたcircular Jacobi ensembleとなっており, そのCayley変換
はある種の擬微分関係式を満たすこともわかる.
加えて多変数circular Jacobi多項式はJack多項式を含むような一般化も可能
である. この一般化多変数circular Jacobi多項式に関するいくつかの予想及び
問題も述べる.
また時間があれば, 離散型の直交多項式系の代表例であるMeixner, Charlier,
Krawtchouk多項式のユニタリ変換を用いた描写を述べ, その多変数化に関しても
触れる.
2014年12月10日(水)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
岸本晶孝 氏 (北大)
Approximately inner flows on $C^*$-algebras (English)
岸本晶孝 氏 (北大)
Approximately inner flows on $C^*$-algebras (English)
FMSPレクチャーズ
16:00-17:30 数理科学研究科棟(駒場) 118号室
Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium
[ 講演概要 ]
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
This talk is concerned with a mathematical model for the storage of radioactive waste. The model which we study deals with the diffusion of chemical species transported by water, with possible dissolution or precipitation and for a rather general kinetics law. In this talk, we consider a three-component reaction-diffusion system with a fast precipitation and dissolution reaction term. We investigate its singular limit as the reaction rate tends to infinity. The limit problem is described by the combination of a Stefan problem and a linear heat equation. The rate of convergence with respect to the reaction rate is established in a specific case. This is joint work with Hideki Murakawa.
2014年12月09日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room
藤原 耕二 氏 (京都大学大学院理学研究科)
Stable commutator length on mapping class groups (JAPANESE)
Tea : 16:00-16:30 Common Room
藤原 耕二 氏 (京都大学大学院理学研究科)
Stable commutator length on mapping class groups (JAPANESE)
[ 講演概要 ]
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.
Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.
Let MCG(S) be the mapping class group of a closed orientable surface S.
We give a precise condition (in terms of the Nielsen-Thurston
decomposition) when an element
in MCG(S) has positive stable commutator length.
Stable commutator length tends to be positive if there is "negative
curvature".
The proofs use our earlier construction in the paper "Constructing group
actions on quasi-trees and applications to mapping class groups" of
group actions on quasi-trees.
This is a joint work with Bestvina and Bromberg.
2014年12月08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) 126号室
泊 昌孝 氏 (日本大学)
擬斉次2次元正規特異点および星型特異点の極大イデアルサイクルと基本サイクルについて(都丸正氏との共同研究) (JAPANESE)
泊 昌孝 氏 (日本大学)
擬斉次2次元正規特異点および星型特異点の極大イデアルサイクルと基本サイクルについて(都丸正氏との共同研究) (JAPANESE)
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