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過去の記録
過去の記録 ～04/15｜本日 04/16 | 今後の予定 04/17～
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 002号室
吉田 朋広 氏 (東京大学)
確率過程の分散共分散構造推定およびYUIMAパッケージの適用 (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html
吉田 朋広 氏 (東京大学)
確率過程の分散共分散構造推定およびYUIMAパッケージの適用 (JAPANESE)
[ 講演概要 ]
伊藤過程の分散および共分散構造の推定に関連した
極限定理と漸近展開について話す.
確率微分方程式に対する,統計解析とシミュレーションのための
統計パッケージYUIMAによる数値例も紹介する.
[ 参考URL ]伊藤過程の分散および共分散構造の推定に関連した
極限定理と漸近展開について話す.
確率微分方程式に対する,統計解析とシミュレーションのための
統計パッケージYUIMAによる数値例も紹介する.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html
2010年05月18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
門田 直之 氏 (大阪大学大学院理学研究科)
On roots of Dehn twists (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
門田 直之 氏 (大阪大学大学院理学研究科)
On roots of Dehn twists (JAPANESE)
[ 講演概要 ]
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.
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
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
[ 講演概要 ]
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
2010年05月17日(月)
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
尾高 悠志 氏 (京都大学数理解析研究所(RIMS))
On the GIT stability of Polarized Varieties (JAPANESE)
尾高 悠志 氏 (京都大学数理解析研究所(RIMS))
On the GIT stability of Polarized Varieties (JAPANESE)
[ 講演概要 ]
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.
Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.
As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".
(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.
Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.
As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".
(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)
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
田辺 正晴 氏 (東工大)
On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)
田辺 正晴 氏 (東工大)
On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)
2010年05月15日(土)
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
成田 宏秋 氏 (熊本大学理学部数学教室) 13:30-14:30
Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
超幾何層に付随するカラビヤウ多様体とその応用について (JAPANESE)
成田 宏秋 氏 (熊本大学理学部数学教室) 13:30-14:30
Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
[ 講演概要 ]
この講演では、荒川リフトというGSp(2)の内部形式上の保型形式に対する、
ある次数8のRankin-Selberg型のL関数の中心値が正となる例について紹介
する。このL関数は岡崎武生氏がGO(2,2)からのテータリフトにより
構成したGSp(2)上のparamodular形式のそれと一致する場合があり、
GSp(2)のRankin-Selberg型のL関数の中心値が正となる例も与える。
山内卓也 氏 (大阪府立大学総合教育研究機構) 15:00-16:00この講演では、荒川リフトというGSp(2)の内部形式上の保型形式に対する、
ある次数8のRankin-Selberg型のL関数の中心値が正となる例について紹介
する。このL関数は岡崎武生氏がGO(2,2)からのテータリフトにより
構成したGSp(2)上のparamodular形式のそれと一致する場合があり、
GSp(2)のRankin-Selberg型のL関数の中心値が正となる例も与える。
超幾何層に付随するカラビヤウ多様体とその応用について (JAPANESE)
[ 講演概要 ]
射影直線から3点を抜いた開曲線U上の階数1のある局所系の畳み込みを帰納的に繰り返すことで超幾何層を定義し、この局所系を中間次数(偶数次数のときはup to 代数的サイクル)に持つようなU上のカラビヤウ多様体の族の構成とその各ファイバーの潜在的保型性やUnit root formula など数論への応用を述べる。以上は都築暢夫氏(東北大学)との共同研究である。
射影直線から3点を抜いた開曲線U上の階数1のある局所系の畳み込みを帰納的に繰り返すことで超幾何層を定義し、この局所系を中間次数(偶数次数のときはup to 代数的サイクル)に持つようなU上のカラビヤウ多様体の族の構成とその各ファイバーの潜在的保型性やUnit root formula など数論への応用を述べる。以上は都築暢夫氏(東北大学)との共同研究である。
2010年05月12日(水)
講演会
15:30-17:00 数理科学研究科棟(駒場) 123号室
3回連続の最終回です。前2回より開始時間が早いのでご注意ください。
教室を変更しましたのでご注意ください。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
3回連続の最終回です。前2回より開始時間が早いのでご注意ください。
教室を変更しましたのでご注意ください。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
松本 眞 氏 (東京大学数理科学研究科)
Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
松本 眞 氏 (東京大学数理科学研究科)
Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
[ 講演概要 ]
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
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。
Jean-Pierre Puel 氏 (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (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。
Jean-Pierre Puel 氏 (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (ENGLISH)
[ 講演概要 ]
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.
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
荻田武史 氏 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
http://www.infsup.jp/utnas/
荻田武史 氏 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ 講演概要 ]
与えられた行列の条件数が非常に大きい場合,基本精度(倍精度演算など)による演算で通常の行列分解アルゴリズム(LU分解,固有値分解など)を実行しても,精度の良い結果を得ることはできない.本講演では,そのような行列に対しても,基本精度による演算だけを用いて精度の良い結果を得ることができるロバストなアルゴリズムを紹介する.
[ 参考URL ]与えられた行列の条件数が非常に大きい場合,基本精度(倍精度演算など)による演算で通常の行列分解アルゴリズム(LU分解,固有値分解など)を実行しても,精度の良い結果を得ることはできない.本講演では,そのような行列に対しても,基本精度による演算だけを用いて精度の良い結果を得ることができるロバストなアルゴリズムを紹介する.
http://www.infsup.jp/utnas/
GCOEセミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
数値解析セミナー#002
荻田 武史 氏 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
http://www.infsup.jp/utnas/
数値解析セミナー#002
荻田 武史 氏 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ 講演概要 ]
与えられた行列の条件数が非常に大きい場合,基本精度(倍精度演算など)による演算で通常の行列分解アルゴリズム(LU分解,固有値分解など)を実行しても,精度の良い結果を得ることはできない.本講演では,そのような行列に対しても,基本精度による演算だけを用いて精度の良い結果を得ることができるロバストなアルゴリズムを紹介する.
[ 参考URL ]与えられた行列の条件数が非常に大きい場合,基本精度(倍精度演算など)による演算で通常の行列分解アルゴリズム(LU分解,固有値分解など)を実行しても,精度の良い結果を得ることはできない.本講演では,そのような行列に対しても,基本精度による演算だけを用いて精度の良い結果を得ることができるロバストなアルゴリズムを紹介する.
http://www.infsup.jp/utnas/
2010年05月11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
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The logarithms of Dehn twists (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
河澄 響矢 氏 (東京大学大学院数理科学研究科)
The logarithms of Dehn twists (JAPANESE)
[ 講演概要 ]
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).
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
松本久義 氏 (東京大学)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
松本久義 氏 (東京大学)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
[ 講演概要 ]
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
2010年05月10日(月)
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
三浦 真人 氏 (東大数理)
Grassmann多様体のトーリック退化とミラー対称性 (JAPANESE)
三浦 真人 氏 (東大数理)
Grassmann多様体のトーリック退化とミラー対称性 (JAPANESE)
[ 講演概要 ]
Grassmann多様体のトーリック退化と、
それを用いたGrassmann多様体の完全交叉カラビ・ヤウ多様体に対するミラー構
成について説明する。
とくに、項順序によるトーリック退化に着目すれば、
座標環が一様斉次なsagbi基底を持つように項順序を選ぶ必要がある。
A型Grassmann多様体やスピノル多様体などの例に関してこの条件を考察する。
Grassmann多様体のトーリック退化と、
それを用いたGrassmann多様体の完全交叉カラビ・ヤウ多様体に対するミラー構
成について説明する。
とくに、項順序によるトーリック退化に着目すれば、
座標環が一様斉次なsagbi基底を持つように項順序を選ぶ必要がある。
A型Grassmann多様体やスピノル多様体などの例に関してこの条件を考察する。
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
松本 佳彦 氏 (東大数理)
ACH-Einstein計量の漸近展開と半可積分概CR多様体上のある不変テンソル場 (JAPANESE)
松本 佳彦 氏 (東大数理)
ACH-Einstein計量の漸近展開と半可積分概CR多様体上のある不変テンソル場 (JAPANESE)
[ 講演概要 ]
強擬凸な半可積分(partially-integrable)概CR多様体を非コンパクト完備Riemann空間の無限遠境界ととらえて調べるため、ACH-Einstein方程式を考察する。その解は、境界に沿った(空間の次元によって決まる)あるオーダーのジェットとしては、境界を保つ微分同相の作用による任意性を除き一意的に存在する。さらに高次の解を対数特異性を含まない範囲で構成するにあたっては一般には障害があり、それは境界上のある局所不変テンソル場を与えることを説明する。その不変テンソル場の持つ性質についても触れる。
強擬凸な半可積分(partially-integrable)概CR多様体を非コンパクト完備Riemann空間の無限遠境界ととらえて調べるため、ACH-Einstein方程式を考察する。その解は、境界に沿った(空間の次元によって決まる)あるオーダーのジェットとしては、境界を保つ微分同相の作用による任意性を除き一意的に存在する。さらに高次の解を対数特異性を含まない範囲で構成するにあたっては一般には障害があり、それは境界上のある局所不変テンソル場を与えることを説明する。その不変テンソル場の持つ性質についても触れる。
2010年05月07日(金)
講演会
16:00-17:30 数理科学研究科棟(駒場) 056号室
3回連続の第2回です。最終回は、5月12日(水)3時半から5時で、部屋は同じく056です。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
3回連続の第2回です。最終回は、5月12日(水)3時半から5時で、部屋は同じく056です。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
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)。
Jean-Pierre Puel 氏 (The University of Tokyo, Universite de Versailles Saint-Quentin)
Why to study controllability problems and the mathematical tools involved (ENGLISH)
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
Jean-Pierre Puel 氏 (The University of Tokyo, Universite de Versailles Saint-Quentin)
Why to study controllability problems and the mathematical tools involved (ENGLISH)
[ 講演概要 ]
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.
2010年05月06日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
山下 真 氏 (東大数理)
Connes-Landi Deformation of Spectral Triples (ENGLISH)
山下 真 氏 (東大数理)
Connes-Landi Deformation of Spectral Triples (ENGLISH)
[ 講演概要 ]
We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.
We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.
2010年04月28日(水)
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。
Marcus Wunsch 氏 (Kyoto University
)
GLOBAL AND SINGULAR SOLUTIONS TO SOME
HYDRODYNAMIC EVOLUTION EQUATIONS
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。
Marcus Wunsch 氏 (Kyoto University
)
GLOBAL AND SINGULAR SOLUTIONS TO SOME
HYDRODYNAMIC EVOLUTION EQUATIONS
[ 講演概要 ]
The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.
After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.
Finally, global existence in time of these weak solutions is proved.
The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.
After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.
Finally, global existence in time of these weak solutions is proved.
講演会
16:00-17:30 数理科学研究科棟(駒場) 056号室
3回連続の第1回です。2回目と3回目は、5月7日(金)4時から5時半と
5月12日(水)3時半から5時です。部屋はどちらも056です。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
3回連続の第1回です。2回目と3回目は、5月7日(金)4時から5時半と
5月12日(水)3時半から5時です。部屋はどちらも056です。
Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 002号室
加藤 昇吾 氏 (統計数理研究所)
A Markov process for circular data (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html
加藤 昇吾 氏 (統計数理研究所)
A Markov process for circular data (JAPANESE)
[ 講演概要 ]
We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.
[ 参考URL ]We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html
2010年04月27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
横田 佳之 氏 (首都大学東京)
On the complex volume of hyperbolic knots (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
横田 佳之 氏 (首都大学東京)
On the complex volume of hyperbolic knots (JAPANESE)
[ 講演概要 ]
In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.
We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds
obtained by Dehn surgeries on hyperbolic knots.
In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.
We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds
obtained by Dehn surgeries on hyperbolic knots.
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
大島芳樹 氏 (東京大学)
Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
大島芳樹 氏 (東京大学)
Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
[ 講演概要 ]
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.
2010年04月26日(月)
代数幾何学セミナー
16:40-18:10 数理科学研究科棟(駒場) 126号室
馬 昭平 氏 (東大数理)
The unirationality of the moduli spaces of 2-elementary K3
surfaces (JAPANESE)
馬 昭平 氏 (東大数理)
The unirationality of the moduli spaces of 2-elementary K3
surfaces (JAPANESE)
[ 講演概要 ]
We prove the unirationality of the moduli spaces of K3 surfaces
with non-symplectic involution. As a by-product, we describe the
configuration spaces of 5, 6, 7, 8 points in the projective plane as
arithmetic quotients of type IV.
We prove the unirationality of the moduli spaces of K3 surfaces
with non-symplectic involution. As a by-product, we describe the
configuration spaces of 5, 6, 7, 8 points in the projective plane as
arithmetic quotients of type IV.
Kavli IPMU Komaba Seminar
16:30-18:00 数理科学研究科棟(駒場) 002号室
池田 暁志 氏 (東京大学大学院数理科学研究科)
The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models (JAPANESE)
池田 暁志 氏 (東京大学大学院数理科学研究科)
The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models (JAPANESE)
[ 講演概要 ]
The number of branched coverings of closed surfaces are called Hurwitz
numbers. They constitute a Frobenius algebra structure, or
two dimensional topological field theory. On the other hand, correlation
functions of matrix models are expressed in term of ribbon graphs
(graphs embedded in closed surfaces).
In this talk, I explain how the Frobenius algebra structure of Hurwitz
numbers are described in terms of matrix models. We use the
correspondence between ribbon graphs and covering of S^2 ramified at
three points, both of which have natural symmetric group actions.
As an application I use Frobenius algebra structure to compute Hermitian
matrix models, multi-variable matrix models, and their large N
expansions. The generating function of Hurwitz numbers is also expressed
in terms of matrix models. The relation to integrable hierarchies and
random partitions is briefly discussed.
The number of branched coverings of closed surfaces are called Hurwitz
numbers. They constitute a Frobenius algebra structure, or
two dimensional topological field theory. On the other hand, correlation
functions of matrix models are expressed in term of ribbon graphs
(graphs embedded in closed surfaces).
In this talk, I explain how the Frobenius algebra structure of Hurwitz
numbers are described in terms of matrix models. We use the
correspondence between ribbon graphs and covering of S^2 ramified at
three points, both of which have natural symmetric group actions.
As an application I use Frobenius algebra structure to compute Hermitian
matrix models, multi-variable matrix models, and their large N
expansions. The generating function of Hurwitz numbers is also expressed
in terms of matrix models. The relation to integrable hierarchies and
random partitions is briefly discussed.
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