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過去の記録 ～04/22｜本日 04/23 | 今後の予定 04/24～
2007年01月12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) 123号室
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)
鳥海光弘 氏 (東京大学・大学院新領域創成科学研究科)
地球変動にまつわるおかしな現象、2題
1、プレート境界で砂と泥に起こる雪だるま現象
2、プレート境界地震は確率共鳴か
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)
鳥海光弘 氏 (東京大学・大学院新領域創成科学研究科)
地球変動にまつわるおかしな現象、2題
1、プレート境界で砂と泥に起こる雪だるま現象
2、プレート境界地震は確率共鳴か
[ 講演概要 ]
地球科学における興味ある現象2題‐巨大固液混合体はどのように振舞うか。
最近の固体地球科学の大きな関心はプレート境界付近における固体・流体混合物質の挙動と境界型地震破壊やすべり運動、火山活動などとの関係である。プレート境界は地球上でもっとも活動的な部分であり、地球表層部分と地球内部とのエネルギー交換や物質交換が最も多く行われる部分でもある。とくに日本海溝や伊豆マリアナ海溝、南海トラフ、琉球海溝などの沈み込み境界部付近の地震波探査、電磁気探査、ボーリング掘削、などの研究がんたくさんの新しい事実を描き出している。
今回興味ある話として紹介するのは、プレート沈み込み境界では、海溝底で堆積した砂泥層が海洋プレートに乗ってプレート境界に引きずり込まれ、排水する過程で砂と泥に分離し、巨大な砂の塊が泥の層の中に分散する現象である。この現象の数理は砂が水を保持して流動化する過程と、プレート境界に持ち込まれた含水地質体が長期にわたりせん断変形を受ける過程で、砂の部分が次第に雪だるま状に衝突・合体する過程で示され、歪により巨大化する砂の塊は数キロに達することもありえる。こうして出来るプレート境界の構造は、大きさ分布がべき的になる砂の塊が境界に沿って拡がった泥の層内にクラスター上に分布するパターンを形成するだう。こうした構造形成はプレート境界部の力学特性を決めているだろう。
第2の話題はプレート境界における破壊の確率共鳴というテーマである、最近の研究ではプレート境界において発生する中小規模の地震はrepeating earthquakesまたはsimilar earthquakesとも呼ばれ、同一場所で繰り返しおこるせん断クラックである。そのサイズは0.01‐1km程度である。一方、巨大地震はこれに比べて大きく100kmx10km以上の破壊面をもつ。しかしこの巨大さにもかかわらず、やはり同一箇所が繰り返し破壊し、これをアスペリティと呼んでいる。一方、こうしたアスペリティの周囲は非アスペリティとよばれ、ゆっくりと滑っていて、流体を保持した岩石が分布し、低密度となっている。問題は大小の規模の破壊がどのような関係にあるのかという古典的なテーマである。プレート境界面上のいろいろな大きさのアスペリティが互いに重ならないであり続けているのか、もしくは互いに重なっているのかは重大である。観測的には巨大地震の破壊面は他の小さい破壊面と重なっている。つまり、境界面では、中小の多数のアスペリティが確率的に活動していて、巨大破壊の時にはそれらのアスペリティが一斉に動き出すということであろう。今回の話題提供ではこうした現象を確率共鳴として考えてみよう。
地球科学における興味ある現象2題‐巨大固液混合体はどのように振舞うか。
最近の固体地球科学の大きな関心はプレート境界付近における固体・流体混合物質の挙動と境界型地震破壊やすべり運動、火山活動などとの関係である。プレート境界は地球上でもっとも活動的な部分であり、地球表層部分と地球内部とのエネルギー交換や物質交換が最も多く行われる部分でもある。とくに日本海溝や伊豆マリアナ海溝、南海トラフ、琉球海溝などの沈み込み境界部付近の地震波探査、電磁気探査、ボーリング掘削、などの研究がんたくさんの新しい事実を描き出している。
今回興味ある話として紹介するのは、プレート沈み込み境界では、海溝底で堆積した砂泥層が海洋プレートに乗ってプレート境界に引きずり込まれ、排水する過程で砂と泥に分離し、巨大な砂の塊が泥の層の中に分散する現象である。この現象の数理は砂が水を保持して流動化する過程と、プレート境界に持ち込まれた含水地質体が長期にわたりせん断変形を受ける過程で、砂の部分が次第に雪だるま状に衝突・合体する過程で示され、歪により巨大化する砂の塊は数キロに達することもありえる。こうして出来るプレート境界の構造は、大きさ分布がべき的になる砂の塊が境界に沿って拡がった泥の層内にクラスター上に分布するパターンを形成するだう。こうした構造形成はプレート境界部の力学特性を決めているだろう。
第2の話題はプレート境界における破壊の確率共鳴というテーマである、最近の研究ではプレート境界において発生する中小規模の地震はrepeating earthquakesまたはsimilar earthquakesとも呼ばれ、同一場所で繰り返しおこるせん断クラックである。そのサイズは0.01‐1km程度である。一方、巨大地震はこれに比べて大きく100kmx10km以上の破壊面をもつ。しかしこの巨大さにもかかわらず、やはり同一箇所が繰り返し破壊し、これをアスペリティと呼んでいる。一方、こうしたアスペリティの周囲は非アスペリティとよばれ、ゆっくりと滑っていて、流体を保持した岩石が分布し、低密度となっている。問題は大小の規模の破壊がどのような関係にあるのかという古典的なテーマである。プレート境界面上のいろいろな大きさのアスペリティが互いに重ならないであり続けているのか、もしくは互いに重なっているのかは重大である。観測的には巨大地震の破壊面は他の小さい破壊面と重なっている。つまり、境界面では、中小の多数のアスペリティが確率的に活動していて、巨大破壊の時にはそれらのアスペリティが一斉に動き出すということであろう。今回の話題提供ではこうした現象を確率共鳴として考えてみよう。
2007年01月11日(木)
講演会
16:00-17:30 数理科学研究科棟(駒場) 123号室
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
2007年01月10日(水)
講演会
16:00-17:30 数理科学研究科棟(駒場) 118号室
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
2007年01月09日(火)
講演会
16:00-17:30 数理科学研究科棟(駒場) 118号室
連続講演 1月9日,10日,11日
「魅力ある大学院教育」イニシアティブにより以下の講演を行います。
担当 山本昌宏
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
連続講演 1月9日,10日,11日
「魅力ある大学院教育」イニシアティブにより以下の講演を行います。
担当 山本昌宏
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
[ 講演概要 ]
We show that 1-D Burgers equation is globally uncontrollable with control acting at two endpoints. Then we establish the global controllability of the 2-D Burgers equation. Finally we show that for 2-D Navier-Stokes system the problem of global exact controllability is solvable for the dense set of the initial data with a control acting on part of the boundary.
We show that 1-D Burgers equation is globally uncontrollable with control acting at two endpoints. Then we establish the global controllability of the 2-D Burgers equation. Finally we show that for 2-D Navier-Stokes system the problem of global exact controllability is solvable for the dense set of the initial data with a control acting on part of the boundary.
2006年12月28日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Roberto Longo 氏 (University of Rome)
Operator Algebras and Conformal Field Theory II
Roberto Longo 氏 (University of Rome)
Operator Algebras and Conformal Field Theory II
2006年12月25日(月)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
研究集会の情報 氏 (なし)
なし
研究集会の情報 氏 (なし)
なし
[ 講演概要 ]
秋から、少しお休みしていますので、替わりにまとめて集会をします。
12月25日午後から27日午後3時くらいまでです。詳細はURL:
https://www.ms.u-tokyo.ac.jp/activity/meeting061225.htm
をご覧下さい。織田孝幸
秋から、少しお休みしていますので、替わりにまとめて集会をします。
12月25日午後から27日午後3時くらいまでです。詳細はURL:
https://www.ms.u-tokyo.ac.jp/activity/meeting061225.htm
をご覧下さい。織田孝幸
2006年12月21日(木)
アジア数学史セミナー
17:00-18:30 数理科学研究科棟(駒場) 123号室
楠葉隆徳 氏 (大阪経済大学人間科学部)
インド数学における証明
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
楠葉隆徳 氏 (大阪経済大学人間科学部)
インド数学における証明
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
Susan Friedlander 氏 (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
Susan Friedlander 氏 (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
[ 講演概要 ]
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.
This is joint work with Alexey Cheskidov and Natasa Pavlovic.
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.
This is joint work with Alexey Cheskidov and Natasa Pavlovic.
作用素環セミナー
14:45-18:00 数理科学研究科棟(駒場) 126号室
Benoit Collins 氏 (Univ. Claude Bernard Lyon 1) 14:45-16:15
Convergence of unitary matrix integrals and free probability
Roberto Longo 氏 (University of Rome) 16:30-18:00
Operator Algebras and Conformal Field Theory
Benoit Collins 氏 (Univ. Claude Bernard Lyon 1) 14:45-16:15
Convergence of unitary matrix integrals and free probability
Roberto Longo 氏 (University of Rome) 16:30-18:00
Operator Algebras and Conformal Field Theory
2006年12月20日(水)
代数学コロキウム
16:30-18:45 数理科学研究科棟(駒場) 117号室
2講演です
Anna Cadoret 氏 (RIMS/JSPS) 16:30-17:30
On the profinite regular inverse Galois problem
An elementary perspective on modular representation theory
2講演です
Anna Cadoret 氏 (RIMS/JSPS) 16:30-17:30
On the profinite regular inverse Galois problem
[ 講演概要 ]
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \\textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\\\\
\\indent Let $p\\geq 2$ be a prime, then a profinite group
$G$ is said to be \\textit{$p$-obstructed} if it fits in a profinite group extension
$$1\\rightarrow K\\rightarrow G\\rightarrow G_{0}\\rightarrow 1$$
with $G_{0}$ a finite group and $K\\twoheadrightarrow
\\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\\\\
\\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \\textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\\not= p$.\\\\
\\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\\rightarrow
X_{G})_{n\\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander 氏 (Northwestern) 17:45-18:45Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \\textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\\\\
\\indent Let $p\\geq 2$ be a prime, then a profinite group
$G$ is said to be \\textit{$p$-obstructed} if it fits in a profinite group extension
$$1\\rightarrow K\\rightarrow G\\rightarrow G_{0}\\rightarrow 1$$
with $G_{0}$ a finite group and $K\\twoheadrightarrow
\\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\\\\
\\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \\textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\\not= p$.\\\\
\\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\\rightarrow
X_{G})_{n\\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
An elementary perspective on modular representation theory
2006年12月19日(火)
トポロジー火曜セミナー
16:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
境 圭一 氏 (東京大学大学院数理科学研究科) 16:30-17:30
Poisson structures on the homology of the spaces of knots
On projections of pseudo-ribbon sphere-links
Tea: 16:00 - 16:30 コモンルーム
境 圭一 氏 (東京大学大学院数理科学研究科) 16:30-17:30
Poisson structures on the homology of the spaces of knots
[ 講演概要 ]
We study the homological properties of the space $K$ of (framed) long knots in $\\R^n$, $n>3$, in particular its Poisson algebra structures.
We had known two kinds of Poisson structures, both of which are based on the action of little disks operad. One definition is via the action on the space $K$. Another comes from the action of chains of little disks on the Hochschild complex of an operad, which appears as $E^1$-term of certain spectral sequence converging to $H_* (K)$. The main result is that these two Poisson structures are the same.
We compute the first non-trivial example of the Poisson bracket. We show that this gives a first example of the homology class of $K$ which does not directly correspond to any chord diagrams.
吉田 享平 氏 (東京大学大学院数理科学研究科) 17:30-18:30We study the homological properties of the space $K$ of (framed) long knots in $\\R^n$, $n>3$, in particular its Poisson algebra structures.
We had known two kinds of Poisson structures, both of which are based on the action of little disks operad. One definition is via the action on the space $K$. Another comes from the action of chains of little disks on the Hochschild complex of an operad, which appears as $E^1$-term of certain spectral sequence converging to $H_* (K)$. The main result is that these two Poisson structures are the same.
We compute the first non-trivial example of the Poisson bracket. We show that this gives a first example of the homology class of $K$ which does not directly correspond to any chord diagrams.
On projections of pseudo-ribbon sphere-links
[ 講演概要 ]
Suppose $F$ is an embedded closed surface in $R^4$.
We call $F$ a pseudo-ribbon surface link
if its projection is an immersion of $F$ into $R^3$
whose self-intersection set $\\Gamma(F)$ consists of disjointly embedded circles.
H. Aiso classified pseudo-ribbon sphere-knots ($F$ is a sphere.)
when $\\Gamma(F)$ consists of less than 6 circles.
We classify pseudo-ribbon sphere-links
when $F$ is two spheres and $\\Gamma(F)$ consists of less than 7 circles.
Suppose $F$ is an embedded closed surface in $R^4$.
We call $F$ a pseudo-ribbon surface link
if its projection is an immersion of $F$ into $R^3$
whose self-intersection set $\\Gamma(F)$ consists of disjointly embedded circles.
H. Aiso classified pseudo-ribbon sphere-knots ($F$ is a sphere.)
when $\\Gamma(F)$ consists of less than 6 circles.
We classify pseudo-ribbon sphere-links
when $F$ is two spheres and $\\Gamma(F)$ consists of less than 7 circles.
2006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
川口 周 氏 (京都大学大学院理学研究科)
Height functions and affine space regular automorphisms
川口 周 氏 (京都大学大学院理学研究科)
Height functions and affine space regular automorphisms
2006年12月14日(木)
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
山田 澄生 氏 (東北大・大学院理学研究科・理学部
数学専攻)
特異点を持つ極小部分多様体の変分原理
山田 澄生 氏 (東北大・大学院理学研究科・理学部
数学専攻)
特異点を持つ極小部分多様体の変分原理
[ 講演概要 ]
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは
今までによく知られている現象である。幾何学的測度論は、それらの特異点
を許容する存在定理の枠組みを提供する為に発展してきた。こうして
現れる部分集合の幾何学的特徴付けを、写像の持つエネルギー関数の最小化というJ.Douglas
の方法論を発展させることによって試みる。また特異点周辺の面積密度の
単調性公式についても言及したい。
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは
今までによく知られている現象である。幾何学的測度論は、それらの特異点
を許容する存在定理の枠組みを提供する為に発展してきた。こうして
現れる部分集合の幾何学的特徴付けを、写像の持つエネルギー関数の最小化というJ.Douglas
の方法論を発展させることによって試みる。また特異点周辺の面積密度の
単調性公式についても言及したい。
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
Chongying Dong 氏 (UC Santa Cruz)
On uniqueness of the moonshine vertex operator algebra
Chongying Dong 氏 (UC Santa Cruz)
On uniqueness of the moonshine vertex operator algebra
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
山田 澄生
氏 (東北大学・大学院理学研究科)
特異点を持つ極小部分多様体の変分原理
山田 澄生
氏 (東北大学・大学院理学研究科)
特異点を持つ極小部分多様体の変分原理
[ 講演概要 ]
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは今までによく知られている現象である.幾何学的測度論は,それらの特異点を許容する存在定理の枠組みを提供する為に発展してきた.こうして現れる部分集合の幾何学的特徴付けを,写像の持つエネルギー関数の最小化というJ.Douglas の方法論を発展させることによって試みる.また特異点周辺の面積密度の単調性公式についても言及したい.
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは今までによく知られている現象である.幾何学的測度論は,それらの特異点を許容する存在定理の枠組みを提供する為に発展してきた.こうして現れる部分集合の幾何学的特徴付けを,写像の持つエネルギー関数の最小化というJ.Douglas の方法論を発展させることによって試みる.また特異点周辺の面積密度の単調性公式についても言及したい.
2006年12月13日(水)
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
C. M. Elliott 氏 (University of Sussex)
Computational Methods for Geometric PDEs
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
C. M. Elliott 氏 (University of Sussex)
Computational Methods for Geometric PDEs
[ 講演概要 ]
Computational approaches to evolutionary geometric partial differential equations such as anisotropic motion by mean curvature and surface diffusion are reviewed. We consider methods based on graph, parametric , level set and phase field descriptions of the surface. We also discuss the approximation of partial differential equations which hold on the evolving surfaces. Numerical results will be presented along with some approximation results.
[ 参考URL ]Computational approaches to evolutionary geometric partial differential equations such as anisotropic motion by mean curvature and surface diffusion are reviewed. We consider methods based on graph, parametric , level set and phase field descriptions of the surface. We also discuss the approximation of partial differential equations which hold on the evolving surfaces. Numerical results will be presented along with some approximation results.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
数理ファイナンスセミナー
17:30-19:00 数理科学研究科棟(駒場) 118号室
関根 順 氏 (京都大)
動的なファンドプロテクションと最適化について
関根 順 氏 (京都大)
動的なファンドプロテクションと最適化について
2006年12月12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
Maxim Kazarian 氏 (Steklov Math. Institute)
Thom polynomials for maps of curves with isolated singularities
(joint with S. Lando)
Tea: 16:00 - 16:30 コモンルーム
Maxim Kazarian 氏 (Steklov Math. Institute)
Thom polynomials for maps of curves with isolated singularities
(joint with S. Lando)
[ 講演概要 ]
Thom (residual) polynomials in characteristic classes are used in
the analysis of geometry of functional spaces. They serve as a
tool in description of classes Poincar\\'e dual to subvarieties of
functions of prescribed types. We give explicit universal
expressions for residual polynomials in spaces of functions on
complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These
expressions lead to a partial explicit description of a
stratification of Hurwitz spaces.
Thom (residual) polynomials in characteristic classes are used in
the analysis of geometry of functional spaces. They serve as a
tool in description of classes Poincar\\'e dual to subvarieties of
functions of prescribed types. We give explicit universal
expressions for residual polynomials in spaces of functions on
complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These
expressions lead to a partial explicit description of a
stratification of Hurwitz spaces.
2006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
相原義弘 氏 (沼津高専)
Modified deficiencies of holomorphic curves and defect relation
相原義弘 氏 (沼津高専)
Modified deficiencies of holomorphic curves and defect relation
2006年12月08日(金)
講演会
10:30-12:00 数理科学研究科棟(駒場) 056号室
Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
[ 講演概要 ]
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
代数幾何学セミナー
15:00-16:25 数理科学研究科棟(駒場) 126号室
Stefan Kebekus 氏 氏 (Mathematisches Institut
Universität zu Köln
)
Rationally connected
foliations
Stefan Kebekus 氏 氏 (Mathematisches Institut
Universität zu Köln
)
Rationally connected
foliations
2006年12月07日(木)
講演会
13:00-14:30 数理科学研究科棟(駒場) 056号室
大学院イニシアティブ特別講演会(平成18年度-冬)
組織委員:儀我美一(東京大学大学院数理科学研究科)連絡先:丸菱美佳 (labgiga@ms.u-tokyo.ac.jp)
Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
https://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
大学院イニシアティブ特別講演会(平成18年度-冬)
組織委員:儀我美一(東京大学大学院数理科学研究科)連絡先:丸菱美佳 (labgiga@ms.u-tokyo.ac.jp)
Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
[ 講演概要 ]
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
[ 参考URL ]In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
https://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 126号室
山下真 氏 (東大数理)
An introduction to analytic endomotives (after Connes-Consani-Marcolli)
山下真 氏 (東大数理)
An introduction to analytic endomotives (after Connes-Consani-Marcolli)
2006年12月06日(水)
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
横山悦郎 氏 (学習院大学)
Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
横山悦郎 氏 (学習院大学)
Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model
[ 講演概要 ]
Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.
In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
[ 参考URL ]Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.
In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
代数学コロキウム
16:30-18:45 数理科学研究科棟(駒場) 117号室
2講演です
Vincent Maillot 氏 (Jussieu/京大数理研) 16:30-17:30
New applications of the arithmetic Riemann-Roch theorem
Don Blasius 氏 (UCLA) 17:45-18:45
Zariski Closures of Automorphic Galois Representations
2講演です
Vincent Maillot 氏 (Jussieu/京大数理研) 16:30-17:30
New applications of the arithmetic Riemann-Roch theorem
Don Blasius 氏 (UCLA) 17:45-18:45
Zariski Closures of Automorphic Galois Representations
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