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過去の記録 ～04/22｜本日 04/23 | 今後の予定 04/24～
2012年07月18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
Shane Kelly 氏 (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
Shane Kelly 氏 (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
[ 講演概要 ]
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.
古典解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
関口 次郎 氏 (東京農工大学)
Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
関口 次郎 氏 (東京農工大学)
Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
[ 講演概要 ]
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.
2012年07月17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 コモンルーム
岡 睦雄 氏 (東京理科大学)
Contact structure of mixed links (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
岡 睦雄 氏 (東京理科大学)
Contact structure of mixed links (JAPANESE)
[ 講演概要 ]
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
GCOEレクチャーズ
16:30-18:00 数理科学研究科棟(駒場) 118号室
George Elliott 氏 (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)
George Elliott 氏 (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)
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
菅 徹 氏 (東北大学)
2次元円環領域におけるLiouville-Gel\\'fand方程式の非球対称解の構造 (JAPANESE)
菅 徹 氏 (東北大学)
2次元円環領域におけるLiouville-Gel\\'fand方程式の非球対称解の構造 (JAPANESE)
[ 講演概要 ]
指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。
指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。
Lie群論・表現論セミナー
17:00-18:30 数理科学研究科棟(駒場) 126号室
Eric Opdam 氏 (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
Eric Opdam 氏 (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
[ 講演概要 ]
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.
2012年07月14日(土)
調和解析駒場セミナー
13:30-17:00 数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.
和田出 秀光
氏 (岐阜大学) 13:30-15:00
臨界Sobolev-Lorentz空間を特徴付ける種々の不等式について
(JAPANESE)
) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
このセミナーは,月に1度程度,不定期に開催されます.
和田出 秀光
氏 (岐阜大学) 13:30-15:00
臨界Sobolev-Lorentz空間を特徴付ける種々の不等式について
(JAPANESE)
[ 講演概要 ]
臨界Sobolev-Lorentz空間は、臨界Sobolev空間と弱臨界Sobolev空間を実補間することにより得られる関数空間である。
本講演では臨界Sobolev空間上で知られているTrudinger-Moser型不等式等の臨界不等式を、臨界Sobolev-Lorentz空間上で考察する。
その結果、対応するTrudigner-Moser型不等式、対数型Hardyの不等式及び対数型Young関数による一般化されたMorrey空間への埋込み定理を導出する。
澤野 嘉宏 氏 (首都大学東京臨界Sobolev-Lorentz空間は、臨界Sobolev空間と弱臨界Sobolev空間を実補間することにより得られる関数空間である。
本講演では臨界Sobolev空間上で知られているTrudinger-Moser型不等式等の臨界不等式を、臨界Sobolev-Lorentz空間上で考察する。
その結果、対応するTrudigner-Moser型不等式、対数型Hardyの不等式及び対数型Young関数による一般化されたMorrey空間への埋込み定理を導出する。
) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
[ 講演概要 ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.
2012年07月12日(木)
講演会
16:30-17:30 数理科学研究科棟(駒場) 370号室
M. Lavrentiev 氏 (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
M. Lavrentiev 氏 (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
[ 講演概要 ]
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.
2012年07月11日(水)
古典解析セミナー
14:00-17:30 数理科学研究科棟(駒場) 128号室
西岡斉治 氏 (山形大学) 14:00-15:30
On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)
廣惠一希 氏 (京都大学) 16:00-17:30
First order systems of linear ordinary differential equations and
representations of quivers (ENGLISH)
西岡斉治 氏 (山形大学) 14:00-15:30
On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)
廣惠一希 氏 (京都大学) 16:00-17:30
First order systems of linear ordinary differential equations and
representations of quivers (ENGLISH)
2012年07月10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
牛越 惠理佳 氏 (東北大学)
Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition (JAPANESE)
牛越 惠理佳 氏 (東北大学)
Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition (JAPANESE)
[ 講演概要 ]
本講演では、遅い非圧縮粘性流体の運動を記述したStokes方程式におけるHadamard変分公式の導出について考察する。ここで、Hadamard変分公式とは、1908年にHadamardによって提唱された、領域にある摂動をさせた時に、Green函数に代表される領域に依存する函数が、どのような摂動をするのかを表現したものである。
変分公式は、領域摂動に伴う固有値の漸近挙動を明示的に表現したWeylの漸近公式と関連があるなど、領域摂動問題において大変有用なものとして導出されてきた。本講演において、まずは導入として、楕円型方程式で最も基本的なラプラス方程式のDirichlet問題に対する変分公式について言及し、その後に主結果であるStokes方程式におけるHadamard変分公式について述べる。
本講演では、遅い非圧縮粘性流体の運動を記述したStokes方程式におけるHadamard変分公式の導出について考察する。ここで、Hadamard変分公式とは、1908年にHadamardによって提唱された、領域にある摂動をさせた時に、Green函数に代表される領域に依存する函数が、どのような摂動をするのかを表現したものである。
変分公式は、領域摂動に伴う固有値の漸近挙動を明示的に表現したWeylの漸近公式と関連があるなど、領域摂動問題において大変有用なものとして導出されてきた。本講演において、まずは導入として、楕円型方程式で最も基本的なラプラス方程式のDirichlet問題に対する変分公式について言及し、その後に主結果であるStokes方程式におけるHadamard変分公式について述べる。
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 コモンルーム
Marcus Werner 氏 (Kavli IPMU)
Topology in Gravitational Lensing (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Marcus Werner 氏 (Kavli IPMU)
Topology in Gravitational Lensing (ENGLISH)
[ 講演概要 ]
General relativity implies that light is deflected by masses
due to the curvature of spacetime. The ensuing gravitational
lensing effect is an important tool in modern astronomy, and
topology plays a significant role in its properties. In this
talk, I will review topological aspects of gravitational lensing
theory: the connection of image numbers with Morse theory; the
interpretation of certain invariant sums of the signed image
magnification in terms of Lefschetz fixed point theory; and,
finally, a new partially topological perspective on gravitational
light deflection that emerges from the concept of optical geometry
and applications of the Gauss-Bonnet theorem.
General relativity implies that light is deflected by masses
due to the curvature of spacetime. The ensuing gravitational
lensing effect is an important tool in modern astronomy, and
topology plays a significant role in its properties. In this
talk, I will review topological aspects of gravitational lensing
theory: the connection of image numbers with Morse theory; the
interpretation of certain invariant sums of the signed image
magnification in terms of Lefschetz fixed point theory; and,
finally, a new partially topological perspective on gravitational
light deflection that emerges from the concept of optical geometry
and applications of the Gauss-Bonnet theorem.
2012年07月09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
久本 智之 氏 (東大数理)
次数付き線形系の体積と、定スカラー曲率ケーラー計量の存在問題 (JAPANESE)
久本 智之 氏 (東大数理)
次数付き線形系の体積と、定スカラー曲率ケーラー計量の存在問題 (JAPANESE)
[ 講演概要 ]
We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.
We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.
2012年07月06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) 002号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
S.R.Srinivasa Varadhan 氏 (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
S.R.Srinivasa Varadhan 氏 (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
[ 講演概要 ]
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.
2012年07月04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
Patrick Forré 氏 (東京大学数理科学研究科)
A cohomological Hasse principle of varieties over higher local fields and applications to higher dimensional class field theory (ENGLISH)
Patrick Forré 氏 (東京大学数理科学研究科)
A cohomological Hasse principle of varieties over higher local fields and applications to higher dimensional class field theory (ENGLISH)
[ 講演概要 ]
In this talk I will give an overview of the necessary tools for a description of the class field theory of varieties over higher local fields developed by sevaral mathematicians. On this I will motivate the importance of the proposal and verification of a cohomological Hasse principle for varieties over higher local fields, a generalization of Kato's conjectures, and sketch the recent progress on this.
In this talk I will give an overview of the necessary tools for a description of the class field theory of varieties over higher local fields developed by sevaral mathematicians. On this I will motivate the importance of the proposal and verification of a cohomological Hasse principle for varieties over higher local fields, a generalization of Kato's conjectures, and sketch the recent progress on this.
古典解析セミナー
15:30-17:00 数理科学研究科棟(駒場) 128号室
名古屋 創 氏 (神戸大学)
Symmetries of quantum Lax equations for the Painlev\\'e equations (JAPANESE)
名古屋 創 氏 (神戸大学)
Symmetries of quantum Lax equations for the Painlev\\'e equations (JAPANESE)
2012年06月27日(水)
古典解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
山川大亮 氏 (東京工業大学)
分岐不確定特異点を許した主束上の有理型接続のモジュライ空間 (JAPANESE)
山川大亮 氏 (東京工業大学)
分岐不確定特異点を許した主束上の有理型接続のモジュライ空間 (JAPANESE)
2012年06月26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
伊藤 健一 氏 (筑波大学)
Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)
伊藤 健一 氏 (筑波大学)
Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)
[ 講演概要 ]
We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).
We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).
2012年06月25日(月)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
小木曽啓示 氏 (大阪大学)
Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)
小木曽啓示 氏 (大阪大学)
Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)
[ 講演概要 ]
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.
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
林本 厚志 氏 (長野高専)
スライス構造を持つCR多様体のCR同値問題 (JAPANESE)
林本 厚志 氏 (長野高専)
スライス構造を持つCR多様体のCR同値問題 (JAPANESE)
2012年06月20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
時本一樹 氏 (東京大学数理科学研究科)
On the reduction modulo p of representations of a quaternion
division algebra over a p-adic field (JAPANESE)
時本一樹 氏 (東京大学数理科学研究科)
On the reduction modulo p of representations of a quaternion
division algebra over a p-adic field (JAPANESE)
[ 講演概要 ]
The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.
In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.
The simplest case has already been treated by Vign¥'eras. We deal with more cases.
The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.
In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.
The simplest case has already been treated by Vign¥'eras. We deal with more cases.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Paolo Maremonti 氏 (Seconda Università degli Studi di Napoli)
On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Paolo Maremonti 氏 (Seconda Università degli Studi di Napoli)
On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)
[ 講演概要 ]
We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.
We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.
2012年06月19日(火)
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 コモンルーム
松本 幸夫 氏 (学習院大学)
On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
Tea: 16:50 - 17:10 コモンルーム
松本 幸夫 氏 (学習院大学)
On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
[ 講演概要 ]
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
緒方秀教 氏 (電気通信大学大学院情報理工学研究科)
代用電荷法とその発展
(JAPANESE)
http://www.infsup.jp/utnas/
本セミナーは、グローバルCOE事業「数学新展開の研究教育拠点」(東京大学)の援助を受け、GCOEセミナーして行われています。
https://www.ms.u-tokyo.ac.jp/gcoe/index.html
緒方秀教 氏 (電気通信大学大学院情報理工学研究科)
代用電荷法とその発展
(JAPANESE)
[ 講演概要 ]
代用電荷法は偏微分方程式の数値解法のひとつである。元来は電気力学の問題の解法であり、電位ポテンシャルを複数の点電荷ポテンシャルの重ね合わせで近似するという素朴な方法である。計算は簡単であるが、ある条件のもとでは高精度を達成する(指数関数的収束する)ことが知られており、流体力学、波動問題、弾性問題など数多くの分野で応用されている。今回の講演では、代用電荷法に関する基礎事項を俯瞰して、講演者の代用電荷法に関する研究結果を紹介する。具体的には、周期的場の問題に対する代用電荷法、波動問題(ヘルムホルツ方程式境界値問題)に対する代用電荷法の理論誤差評価、双極子を用いた代用電荷法などを予定している。
[ 参考URL ]代用電荷法は偏微分方程式の数値解法のひとつである。元来は電気力学の問題の解法であり、電位ポテンシャルを複数の点電荷ポテンシャルの重ね合わせで近似するという素朴な方法である。計算は簡単であるが、ある条件のもとでは高精度を達成する(指数関数的収束する)ことが知られており、流体力学、波動問題、弾性問題など数多くの分野で応用されている。今回の講演では、代用電荷法に関する基礎事項を俯瞰して、講演者の代用電荷法に関する研究結果を紹介する。具体的には、周期的場の問題に対する代用電荷法、波動問題(ヘルムホルツ方程式境界値問題)に対する代用電荷法の理論誤差評価、双極子を用いた代用電荷法などを予定している。
http://www.infsup.jp/utnas/
2012年06月18日(月)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
山ノ井克俊 氏 (東京工業大学)
アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)
山ノ井克俊 氏 (東京工業大学)
アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)
[ 講演概要 ]
アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複
素曲線について、
高次元ネヴァンリンナ理論の立場からお話します。
アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複
素曲線について、
高次元ネヴァンリンナ理論の立場からお話します。
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
早乙女 飛成 氏 (台湾中央研究院)
CR Q曲率流とCR Paneitz作用素について (JAPANESE)
早乙女 飛成 氏 (台湾中央研究院)
CR Q曲率流とCR Paneitz作用素について (JAPANESE)
[ 講演概要 ]
3次元CR多様体上のCR Paneitz作用素とQ-曲率に関するCR幾何学の研究について幾何解析的な視点から最近得られた結果などについて話をしたいと思います。
3次元CR多様体上のCR Paneitz作用素とQ-曲率に関するCR幾何学の研究について幾何解析的な視点から最近得られた結果などについて話をしたいと思います。
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