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過去の記録
過去の記録 ～04/26｜本日 04/27 | 今後の予定 04/28～
2015年02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) 126号室
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
[ 講演概要 ]
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
2015年01月28日(水)
FMSPレクチャーズ
12:00-16:00 数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books III
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books III
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 参考URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015年01月27日(火)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
大田 佳宏 氏 (東京大学 数理科学連携基盤センター)
遺伝子の転写機構解明のための数理モデル (Japanese)
大田 佳宏 氏 (東京大学 数理科学連携基盤センター)
遺伝子の転写機構解明のための数理モデル (Japanese)
[ 講演概要 ]
遺伝子の転写とは、DNA 配列を鋳型に RNA polymerase II (RNAP II) という酵素によって遺伝子が読まれ RNA が合成される現象を指し「生命の基本原理」とも考えられている。一方で、転写の生成物である RNA は時間変異性が高く微小不均一性を持つため、細胞を用いた実験において高時間分解能の現象観察を行うことは難しいのが現状である。そこで、観察不可能な領域における高分解能の検証を可能とし、構築したモデルの再現性を保証するため、超離散系や代数的トポロジーなどの数理科学的手法が必須となる。ここでは、セルオートマトンを用いた遺伝子転写機構の数理モデルの研究と、さらに「数学による新規創薬」を目標とした、タンパク質立体構造解析における数理モデルについて紹介したい。
遺伝子の転写とは、DNA 配列を鋳型に RNA polymerase II (RNAP II) という酵素によって遺伝子が読まれ RNA が合成される現象を指し「生命の基本原理」とも考えられている。一方で、転写の生成物である RNA は時間変異性が高く微小不均一性を持つため、細胞を用いた実験において高時間分解能の現象観察を行うことは難しいのが現状である。そこで、観察不可能な領域における高分解能の検証を可能とし、構築したモデルの再現性を保証するため、超離散系や代数的トポロジーなどの数理科学的手法が必須となる。ここでは、セルオートマトンを用いた遺伝子転写機構の数理モデルの研究と、さらに「数学による新規創薬」を目標とした、タンパク質立体構造解析における数理モデルについて紹介したい。
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
[ 講演概要 ]
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
Let $G$ be a connected simply connected simple complex algebraic group of type $ADE$ and $\mathfrak{g}$ the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of $U_q(\mathfrak{n}^+)$. Here, $U_q(\mathfrak{n}^+)$ denotes the positive part of the quantized enveloping algebra $U_q(\mathfrak{g})$. (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between $U_q(\mathfrak{n}^+)$ and the specific irreducible representations of the quantized function algebra $\mathbb{Q} _q[G]$. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right $U_q(\mathfrak{g})$-algebra structure of $\mathbb{Q}_q[G]$. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
FMSPレクチャーズ
13:00-16:20 数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books II
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books II
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 参考URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
2015年01月26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
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
[ 講演概要 ]
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
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
Jungkai Chen 氏 (National Taiwan University)
Positivity in varieties of maximal Albanese dimension (ENGLISH)
Jungkai Chen 氏 (National Taiwan University)
Positivity in varieties of maximal Albanese dimension (ENGLISH)
[ 講演概要 ]
Given a variety of maximal Albanese dimension, it is known that the holomorphic Euler characteristic is non-negative. It is an interesting question to characterize varieties with vanishing Euler characteristic.
In our previous work (jointly with Debarre and Jiang), we prove that Ein-Lazarsgfeld's example is essentially the only variety of maximal Albanese and Kodaira dimension with vanishing Euler characteristic in dimension three. In the recent joint work with Jiang, we prove a decomposition theorem for the push-forward of canonical sheaf. As a consequence, we are able to generalized our previous characterization. The purpose of this talk is give a survey of these two works.
Given a variety of maximal Albanese dimension, it is known that the holomorphic Euler characteristic is non-negative. It is an interesting question to characterize varieties with vanishing Euler characteristic.
In our previous work (jointly with Debarre and Jiang), we prove that Ein-Lazarsgfeld's example is essentially the only variety of maximal Albanese and Kodaira dimension with vanishing Euler characteristic in dimension three. In the recent joint work with Jiang, we prove a decomposition theorem for the push-forward of canonical sheaf. As a consequence, we are able to generalized our previous characterization. The purpose of this talk is give a survey of these two works.
FMSPレクチャーズ
12:30-13:30 数理科学研究科棟(駒場) 128号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups III
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups III
[ 講演概要 ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ 参考URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
FMSPレクチャーズ
9:30-10:30 数理科学研究科棟(駒場) 122号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Nontempered Characters
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Nontempered Characters
[ 講演概要 ]
In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures.
[ 参考URL ]In this talk, we will survey the results of Rossmann and Schmid-Vilonen on geometric formulas for nontempered characters of reductive groups, and we will mention an old result of Barbasch-Vogan on the special case A_q(lambda). We will discuss what nontempered character formulas would be necessary to generalize the main formula of the second talk, and we will make conjectures.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
FMSPレクチャーズ
13:00-17:00 数理科学研究科棟(駒場) 126号室
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books I
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
Frédéric Abergel 氏 (École Centrale Paris)
Limit order books I
[ 講演概要 ]
In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
[ 参考URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Abergel.pdf
FMSPレクチャーズ
11:00-12:00 数理科学研究科棟(駒場) 122号室
Raul Gomez 氏 (Cornell University)
Local Theta lifting of generalized Whittaker models.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez 氏 (Cornell University)
Local Theta lifting of generalized Whittaker models.
[ 講演概要 ]
In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu.
[ 参考URL ]In this talk, we describe the behavior of the space of generalized Whittaker models attached to a nilpotent orbit under the local theta correspondence. This description is a generalization of a result of Moeglin in the p-adic setting. This is joint work with Chengbo Zhu.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2015年01月25日(日)
FMSPレクチャーズ
12:30-13:30 数理科学研究科棟(駒場) 126号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups II
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups II
[ 講演概要 ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ 参考URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
FMSPレクチャーズ
11:00-12:00 数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Harmonic Analysis
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Harmonic Analysis
[ 講演概要 ]
In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result.
[ 参考URL ]In this talk, we will present recent joint work with Tobias Weich. When G is a real, reductive algebraic group and X is a homogeneous space for G with an invariant measure, we will completely describe the regular, semisimple asymptotics of the support of the Plancherel measure for L^2(X). We will give concrete examples of this theorem, describing what can and cannot be deduced from this result.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
FMSPレクチャーズ
9:30-10:30 数理科学研究科棟(駒場) 126号室
Raul Gomez 氏 (Cornell University)
Generalized and degenerate Whittaker models associated to nilpotent orbits.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez 氏 (Cornell University)
Generalized and degenerate Whittaker models associated to nilpotent orbits.
[ 講演概要 ]
In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications.
This is joint work with Dmitry Gourevitch and Siddhartha Sahi.
[ 参考URL ]In this talk, we examine the relation between the different spaces of Whittaker models that can be attached to a nilpotent orbit. We will also explore their relation to other nilpotent invariants (like the wave front set) and show some examples and applications.
This is joint work with Dmitry Gourevitch and Siddhartha Sahi.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2015年01月24日(土)
FMSPレクチャーズ
13:00-14:00 数理科学研究科棟(駒場) 126号室
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups I
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
Peter Trapa 氏 (University of Utah)
Unitary representations of reductive Lie groups I
[ 講演概要 ]
Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
[ 参考URL ]Let G be a real reductive group. I will describe an algorithm to determine the unitary dual of G. More precisely, I will describe an algorithm to determine if an irreducible (g,K) module (specified in the Langlands classification) is unitary in the sense that it admits a positive definite invariant Hermitian form.
This is joint work with Jeffrey Adams, Marc van Leeuwen, and David Vogan.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Trapa.pdf
FMSPレクチャーズ
16:30-17:30 数理科学研究科棟(駒場) 126号室
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Tempered Characters
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
Benjamin Harris 氏 (Oklahoma State University)
The Geometry of Tempered Characters
[ 講演概要 ]
In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R).
[ 参考URL ]In this introductory talk, we will briefly recall parts of Harish-Chandra's theory of characters for reductive groups and the geometric formula of Rossmann and Duflo for tempered characters of reductive groups. Examples will be given in the case G=SL(2,R).
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Harris.pdf
FMSPレクチャーズ
14:30-15:30 数理科学研究科棟(駒場) 126号室
Raul Gomez 氏 (Cornell University)
The Tor and Ext functors for smooth representations of real algebraic groups.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
Raul Gomez 氏 (Cornell University)
The Tor and Ext functors for smooth representations of real algebraic groups.
[ 講演概要 ]
Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh.
[ 参考URL ]Inspired by the recent work of Dipendra Prasad in the $p$-adic setting, we define the Tor and Ext functors for an appropriate category of smooth representations of a real algebraic group $G$, and give some applications. This is joint work with Birgit Speh.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gomez.pdf
2015年01月23日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 大講義室号室
Luc Illusie 氏 (Université de Paris-Sud)
Grothendieck and algebraic geometry
Luc Illusie 氏 (Université de Paris-Sud)
Grothendieck and algebraic geometry
[ 講演概要 ]
Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.
Between 1957 and 1970 Grothendieck deeply and durably transformed algebraic geometry. I will discuss some of his revolutionary contributions.
2015年01月22日(木)
東京無限可積分系セミナー
13:00-16:30 数理科学研究科棟(駒場) 002号室
松本 ディオゴけんじ 氏 (早稲田理工) 13:00-14:30
Dynamical braceを用いたダイナミカル・ヤン・バクスター写像の構成について (JAPANESE)
ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成 (JAPANESE)
松本 ディオゴけんじ 氏 (早稲田理工) 13:00-14:30
Dynamical braceを用いたダイナミカル・ヤン・バクスター写像の構成について (JAPANESE)
[ 講演概要 ]
ダイナミカル・ヤン・バクスター写像はダイナミカル・ヤン・バクスター方程式の集合論的解として導入された概念である．本講演では，brace(積$a*b:=ab+a+b$に関して群構造を持つ環$(R,+,¥cdot)$の一般化として得られる代数系)をダイナミカル化した代数系dynamical braceを導入し，ユニタリ条件を満たす右非退化なダイナミカル・ヤン・バクスター写像を構成する方法について述べる．またdynamical braceの性質と分類およびbraceとの関係についても紹介をする予定である．
澁川 陽一 氏 (北大数学) 15:00-16:30ダイナミカル・ヤン・バクスター写像はダイナミカル・ヤン・バクスター方程式の集合論的解として導入された概念である．本講演では，brace(積$a*b:=ab+a+b$に関して群構造を持つ環$(R,+,¥cdot)$の一般化として得られる代数系)をダイナミカル化した代数系dynamical braceを導入し，ユニタリ条件を満たす右非退化なダイナミカル・ヤン・バクスター写像を構成する方法について述べる．またdynamical braceの性質と分類およびbraceとの関係についても紹介をする予定である．
ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成 (JAPANESE)
[ 講演概要 ]
FelderやEtingof-Varchenkoは，量子ダイナミカル・ヤン・バクスター方程式の解であるダイナミカルR行列から，ホップ代数の一般化であるホップ亜代数を構成した．この構成方法に現れる量子ダイナミカル・ヤン・バクスター方程式は一般化されており，その解もダイナミカル・ヤン・バクスター写像という名前でいくつか求められている．そこで本講演では，ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成について紹介する．さらに時間が許せば，ダイナミカル・ヤン・バクスター写像に付随して定まる有限次元L-operator全体のなすテンソル圏
(これは，対応するホップ亜代数のある種の有限次元表現全体のなすテンソル圏と見なせる) がリジッドとなることを説明したい．
FelderやEtingof-Varchenkoは，量子ダイナミカル・ヤン・バクスター方程式の解であるダイナミカルR行列から，ホップ代数の一般化であるホップ亜代数を構成した．この構成方法に現れる量子ダイナミカル・ヤン・バクスター方程式は一般化されており，その解もダイナミカル・ヤン・バクスター写像という名前でいくつか求められている．そこで本講演では，ダイナミカル・ヤン・バクスター写像を用いたホップ亜代数の構成について紹介する．さらに時間が許せば，ダイナミカル・ヤン・バクスター写像に付随して定まる有限次元L-operator全体のなすテンソル圏
(これは，対応するホップ亜代数のある種の有限次元表現全体のなすテンソル圏と見なせる) がリジッドとなることを説明したい．
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
Arnaud Ducrot 氏 (ボルドー大学)
On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data
(ENGLISH)
Arnaud Ducrot 氏 (ボルドー大学)
On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data
(ENGLISH)
[ 講演概要 ]
In this talk we discuss the asymptotic behaviour of a multi-dimensional Fisher-KPP equation posed in an asymptotically homogeneous medium and supplemented together with a compactly supported initial datum. We derive precise estimates for the location of the front before proving the convergence of the solutions towards travelling front. In particular we show that the location of the front drastically depends on the rate at which the medium become homogeneous at infinity. Fast rate of convergence only changes the location by some constant while lower rate of convergence induces further logarithmic delay.
In this talk we discuss the asymptotic behaviour of a multi-dimensional Fisher-KPP equation posed in an asymptotically homogeneous medium and supplemented together with a compactly supported initial datum. We derive precise estimates for the location of the front before proving the convergence of the solutions towards travelling front. In particular we show that the location of the front drastically depends on the rate at which the medium become homogeneous at infinity. Fast rate of convergence only changes the location by some constant while lower rate of convergence induces further logarithmic delay.
2015年01月21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
Ofer Gabber 氏 (CNRS, IHES)
Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)
Ofer Gabber 氏 (CNRS, IHES)
Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)
[ 講演概要 ]
(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.
(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.)
(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.
(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.)
古典解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
神本 晋吾 氏 (京都大学)
Remarks on the number of accessory parameters (JAPANESE)
神本 晋吾 氏 (京都大学)
Remarks on the number of accessory parameters (JAPANESE)
[ 講演概要 ]
代数的な常微分作用素を考える.
このような作用素(の族)の大域的な構造を考察する上で,
アクセサリーパラメータは重要な役割を果たす.
本講演では特異摂動論的な立場から,
このアクセサリーパラメータに関する考察を行う.
代数的な常微分作用素を考える.
このような作用素(の族)の大域的な構造を考察する上で,
アクセサリーパラメータは重要な役割を果たす.
本講演では特異摂動論的な立場から,
このアクセサリーパラメータに関する考察を行う.
2015年01月20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
Italo Capuzzo Dolcetta 氏 (Università degli Studi di Roma "La Sapienza")
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)
Italo Capuzzo Dolcetta 氏 (Università degli Studi di Roma "La Sapienza")
Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)
[ 講演概要 ]
In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.
The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.
We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.
In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.
We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.
The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.
We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.
トポロジー火曜セミナー
16:30-17:30 数理科学研究科棟(駒場) 056号室
Tea : 16:00-16:30 Common Room
吉安 徹 氏 (東京大学大学院数理科学研究科)
On Lagrangian caps and their applications (JAPANESE)
Tea : 16:00-16:30 Common Room
吉安 徹 氏 (東京大学大学院数理科学研究科)
On Lagrangian caps and their applications (JAPANESE)
[ 講演概要 ]
In 2013, Y. Eliashberg and E. Murphy established the $h$-principle for
exact Lagrangian embeddings with a concave Legendrian boundary. In this
talk, I will explain a modification of their $h$-principle and show
applications to Lagrangian submanifolds in the complex projective spaces.
In 2013, Y. Eliashberg and E. Murphy established the $h$-principle for
exact Lagrangian embeddings with a concave Legendrian boundary. In this
talk, I will explain a modification of their $h$-principle and show
applications to Lagrangian submanifolds in the complex projective spaces.
2015年01月19日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
山口博史 氏 (滋賀大学 名誉教授)
Hyperbolic span and pseudoconvexity (Japanese)
山口博史 氏 (滋賀大学 名誉教授)
Hyperbolic span and pseudoconvexity (Japanese)
[ 講演概要 ]
We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.
We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.
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