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過去の記録
過去の記録 ～07/26｜本日 07/27 | 今後の予定 07/28～
2010年10月21日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
Benoit Collins 氏 (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)
Benoit Collins 氏 (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)
2010年10月20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
北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)までの情報が掲載されております。
小川 直久 氏 (北海道工業大学)
厚みのある2次元曲面での粒子の拡散 (JAPANESE)
北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)までの情報が掲載されております。
小川 直久 氏 (北海道工業大学)
厚みのある2次元曲面での粒子の拡散 (JAPANESE)
[ 講演概要 ]
3次元空間に埋め込まれた、厚みのある2次元曲面での粒子の拡散を考察する。
このとき通常の拡散流に加えて、面の厚さ:ε展開において、
曲率依存性をもった拡散流が現れる。
例として、楕円柱の表面での拡散を考えると、
曲率の効果はすべて拡散係数に繰り込むことができることを示す。
さらに、3次元に埋め込まれた1次元の場合(チューブ)を考察し、
曲率の効果の物理的な意味を検証する。
3次元空間に埋め込まれた、厚みのある2次元曲面での粒子の拡散を考察する。
このとき通常の拡散流に加えて、面の厚さ:ε展開において、
曲率依存性をもった拡散流が現れる。
例として、楕円柱の表面での拡散を考えると、
曲率の効果はすべて拡散係数に繰り込むことができることを示す。
さらに、3次元に埋め込まれた1次元の場合(チューブ)を考察し、
曲率の効果の物理的な意味を検証する。
2010年10月19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) 002号室
Tea: 16:00 - 16:30 コモンルーム
Jinseok Cho 氏 (早稲田大学)
Optimistic limits of colored Jones invariants (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Jinseok Cho 氏 (早稲田大学)
Optimistic limits of colored Jones invariants (ENGLISH)
[ 講演概要 ]
Yokota made a wonderful theory on the optimistic limit of Kashaev
invariant of a hyperbolic knot
that the limit determines the hyperbolic volume and the Chern-Simons
invariant of the knot.
Especially, his theory enables us to calculate the volume of a knot
combinatorially from its diagram for many cases.
We will briefly discuss Yokota theory, and then move to the optimistic
limit of colored Jones invariant.
We will explain a parallel version of Yokota theory based on the
optimistic limit of colored Jones invariant.
Especially, we will show the optimistic limit of colored Jones
invariant coincides with that of Kashaev invariant modulo 2\\pi^2.
This implies the optimistic limit of colored Jones invariant also
determines the volume and Chern-Simons invariant of the knot, and
probably more information.
This is a joint-work with Jun Murakami of Waseda University.
Yokota made a wonderful theory on the optimistic limit of Kashaev
invariant of a hyperbolic knot
that the limit determines the hyperbolic volume and the Chern-Simons
invariant of the knot.
Especially, his theory enables us to calculate the volume of a knot
combinatorially from its diagram for many cases.
We will briefly discuss Yokota theory, and then move to the optimistic
limit of colored Jones invariant.
We will explain a parallel version of Yokota theory based on the
optimistic limit of colored Jones invariant.
Especially, we will show the optimistic limit of colored Jones
invariant coincides with that of Kashaev invariant modulo 2\\pi^2.
This implies the optimistic limit of colored Jones invariant also
determines the volume and Chern-Simons invariant of the knot, and
probably more information.
This is a joint-work with Jun Murakami of Waseda University.
2010年10月18日(月)
複素解析幾何セミナー
10:30-11:30 数理科学研究科棟(駒場) 128号室
Sergey Ivashkovitch 氏 (Univ. de Lille)
Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)
Sergey Ivashkovitch 氏 (Univ. de Lille)
Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)
[ 講演概要 ]
The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.
The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.
複素解析幾何セミナー
13:00-14:00 数理科学研究科棟(駒場) 128号室
Philippe Eyssidieux 氏 (Institut Fourier, Grenoble)
Degenerate complex Monge-Ampere equations (ENGLISH)
Philippe Eyssidieux 氏 (Institut Fourier, Grenoble)
Degenerate complex Monge-Ampere equations (ENGLISH)
Kavli IPMU Komaba Seminar
16:30-18:00 数理科学研究科棟(駒場) 002号室
Todor Milanov 氏 (IPMU)
Quasi-modular forms and Gromov--Witten theory of elliptic orbifold $\\mathbb{P}^1$ (ENGLISH)
Todor Milanov 氏 (IPMU)
Quasi-modular forms and Gromov--Witten theory of elliptic orbifold $\\mathbb{P}^1$ (ENGLISH)
[ 講演概要 ]
This talk is based on my current work with Y. Ruan. Our project is part of the so called Landau--Ginzburg/Calabi-Yau correspondence. The latter is a conjecture, due to Ruan, that describes the relation between the $W$-spin invariants of a Landau-Ginzburg potential $W$ and the Gromov--Witten invariants of a certain Calabi--Yau orbifold. I am planning first to explain the higher-genus reconstruction formalism of Givental. This formalism together with the work of M. Krawitz and Y. Shen allows us to express the Gromov--Witten invariants of the orbifold $\\mathbb{P}^1$'s with weights $(3,3,3)$, $(2,4,4)$, and $(2,3,6)$ in terms of Saito's Frobenius structure associated with the simple elliptic singularities $P_8$, $X_9$, and $J_{10}$ respectively. After explaining Givental's formalism, my goal would be to discuss the Saito's flat structure, and to explain how its modular behavior fits in the Givental's formalism. This allows us to prove that the Gromov--Witten invariants are quasi-modular forms on an appropriate modular group.
This talk is based on my current work with Y. Ruan. Our project is part of the so called Landau--Ginzburg/Calabi-Yau correspondence. The latter is a conjecture, due to Ruan, that describes the relation between the $W$-spin invariants of a Landau-Ginzburg potential $W$ and the Gromov--Witten invariants of a certain Calabi--Yau orbifold. I am planning first to explain the higher-genus reconstruction formalism of Givental. This formalism together with the work of M. Krawitz and Y. Shen allows us to express the Gromov--Witten invariants of the orbifold $\\mathbb{P}^1$'s with weights $(3,3,3)$, $(2,4,4)$, and $(2,3,6)$ in terms of Saito's Frobenius structure associated with the simple elliptic singularities $P_8$, $X_9$, and $J_{10}$ respectively. After explaining Givental's formalism, my goal would be to discuss the Saito's flat structure, and to explain how its modular behavior fits in the Givental's formalism. This allows us to prove that the Gromov--Witten invariants are quasi-modular forms on an appropriate modular group.
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
三内 顕義 氏 (東大数理)
ガロア拡大と局所コホモロジー間の写像について (JAPANESE)
三内 顕義 氏 (東大数理)
ガロア拡大と局所コホモロジー間の写像について (JAPANESE)
[ 講演概要 ]
正則環に線型簡約群が作用するとき、その不変式環がコーエンマコーレー環になるという直和因子予想は正標数、等標数の場合にHochster, Hunekeらによってビッグコーエンマコーレー代数の存在定理を用いることで解決された。この存在定理の証明は大変複雑なものであったが2007年にHuneke, Lyubeznikらによって有限環拡大の局所コホモロジー間の射の計算に帰着された。
今回はその定理を強めた結果とそれによってできる新しいビッグコーエンマコーレー代数の存在について解説する。
正則環に線型簡約群が作用するとき、その不変式環がコーエンマコーレー環になるという直和因子予想は正標数、等標数の場合にHochster, Hunekeらによってビッグコーエンマコーレー代数の存在定理を用いることで解決された。この存在定理の証明は大変複雑なものであったが2007年にHuneke, Lyubeznikらによって有限環拡大の局所コホモロジー間の射の計算に帰着された。
今回はその定理を強めた結果とそれによってできる新しいビッグコーエンマコーレー代数の存在について解説する。
2010年10月14日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 122号室
河東泰之 氏 (東大数理)
Nonstandard analysis for operator algebraists (JAPANESE)
河東泰之 氏 (東大数理)
Nonstandard analysis for operator algebraists (JAPANESE)
2010年10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
Andrei Pajitnov 氏 (Univ. de Nantes, 東京大学大学院数理科学研究科)
Asymptotics of Morse numbers of finite coverings of manifolds (ENGLISH)
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes, 東京大学大学院数理科学研究科)
Asymptotics of Morse numbers of finite coverings of manifolds (ENGLISH)
[ 講演概要 ]
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.
In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?
It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.
In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?
It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.
2010年10月08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
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)。
佐々木 隆 氏 (京都大学基礎物理学研究所)
$3+¥ell$ ($¥ell=1,2,¥ldots$) 個の確定特異点を持つ
Schroedinger (Sturm-Liouville)方程式の解としての例外Jacobi多項式 (JAPANESE)
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)。
佐々木 隆 氏 (京都大学基礎物理学研究所)
$3+¥ell$ ($¥ell=1,2,¥ldots$) 個の確定特異点を持つ
Schroedinger (Sturm-Liouville)方程式の解としての例外Jacobi多項式 (JAPANESE)
[ 講演概要 ]
3個(超幾何),4個(Heun)より多くの確定特異点を持つFuchs型微分方程式の大域解は,今までほとんど知られていない.この話では,$3+¥ell$ ($¥ell=1,2,¥ldots$)個の確定特異点を持つSchroedinger (Sturm-Liouville)方程式の解の完全系の具体形を与える.この方程式は,次のようなHamiltonian (Schroedinger作用素)を持つ Darboux-P¥"oschl-Tellerポテンシャル¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x} ¥]の変形である.固有関数は例外 Jacobi多項式$¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, からなり,その次数はdeg($P_{¥ell,n}$)$=n+¥ell$である.従ってBochnerの定理による制約を受けない.合流型の極限から2種類の例外Laguerre多項式,$¥ell=1,2,¥ldots$が得られる. 同様の変形方法によって,例外WilsonおよびAskey-Wilson多項式,$¥ell=1,2,¥ldots$が得られる.
3個(超幾何),4個(Heun)より多くの確定特異点を持つFuchs型微分方程式の大域解は,今までほとんど知られていない.この話では,$3+¥ell$ ($¥ell=1,2,¥ldots$)個の確定特異点を持つSchroedinger (Sturm-Liouville)方程式の解の完全系の具体形を与える.この方程式は,次のようなHamiltonian (Schroedinger作用素)を持つ Darboux-P¥"oschl-Tellerポテンシャル¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x} ¥]の変形である.固有関数は例外 Jacobi多項式$¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, からなり,その次数はdeg($P_{¥ell,n}$)$=n+¥ell$である.従ってBochnerの定理による制約を受けない.合流型の極限から2種類の例外Laguerre多項式,$¥ell=1,2,¥ldots$が得られる. 同様の変形方法によって,例外WilsonおよびAskey-Wilson多項式,$¥ell=1,2,¥ldots$が得られる.
2010年10月06日(水)
東京幾何セミナー
14:45-18:00 数理科学研究科棟(駒場) 056号室
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
入江 慶 氏 (京都大学大学院理学研究科) 14:45-16:15
Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems (JAPANESE)
Mirror Symmetry for Weighted Homogeneous Polynomials (JAPANESE)
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��
入江 慶 氏 (京都大学大学院理学研究科) 14:45-16:15
Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems (JAPANESE)
[ 講演概要 ]
In this talk, the term "classical Hamiltonian systems" means special types of Hamiltonian systems, which describe solutions of classical equations of motion. The study of periodic solutions of Hamiltonian systems is an interesting problem, and for classical Hamiltonian systems, the following result is known : for any compact and regular energy surface $S$, there exists a brake orbit (a particular type of periodic solutions) on $S$. This result is first proved by S.V.Bolotin in 1978, and it is a special case of the Arnold chord conjecture. In this talk, I will explain that calculations of wrapped Floer homology (which is a variant of Lagrangian Floer homology) give a new proof of the above result.
高橋 篤史 氏 (大阪大学大学院理学研究科) 16:30-18:00In this talk, the term "classical Hamiltonian systems" means special types of Hamiltonian systems, which describe solutions of classical equations of motion. The study of periodic solutions of Hamiltonian systems is an interesting problem, and for classical Hamiltonian systems, the following result is known : for any compact and regular energy surface $S$, there exists a brake orbit (a particular type of periodic solutions) on $S$. This result is first proved by S.V.Bolotin in 1978, and it is a special case of the Arnold chord conjecture. In this talk, I will explain that calculations of wrapped Floer homology (which is a variant of Lagrangian Floer homology) give a new proof of the above result.
Mirror Symmetry for Weighted Homogeneous Polynomials (JAPANESE)
[ 講演概要 ]
First we give an overview of the algebraic and the geometric aspects of the mirror symmetry conjecture for weighted homogeneous polynomials. Then we concentrate on polynomials in three variables, and show the existence of full (strongly) exceptional collection of categories of maximally graded matrix factorizations for invertible weighted homogeneous polynomials. We will also explain how the mirror symmetry naturally explains and generalizes the Arnold's strange duality between the 14 exceptional unimodal singularities.
First we give an overview of the algebraic and the geometric aspects of the mirror symmetry conjecture for weighted homogeneous polynomials. Then we concentrate on polynomials in three variables, and show the existence of full (strongly) exceptional collection of categories of maximally graded matrix factorizations for invertible weighted homogeneous polynomials. We will also explain how the mirror symmetry naturally explains and generalizes the Arnold's strange duality between the 14 exceptional unimodal singularities.
代数学コロキウム
16:30-17:30 数理科学研究科棟(駒場) 117号室
いつもと教室が異なりますのでご注意ください
Hélène Esnault 氏 (Universität Duisburg-Essen)
Finite group actions on the affine space (ENGLISH)
いつもと教室が異なりますのでご注意ください
Hélène Esnault 氏 (Universität Duisburg-Essen)
Finite group actions on the affine space (ENGLISH)
[ 講演概要 ]
If $G$ is a finite $\\ell$-group acting on an affine space $\\A^n$ over a
finite field $K$ of cardinality prime to $\\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\\ell$ divides $q-1$. To this aim, we study group actions on weak
N\\'eron models.
(Joint work with Johannes Nicaise)
If $G$ is a finite $\\ell$-group acting on an affine space $\\A^n$ over a
finite field $K$ of cardinality prime to $\\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\\ell$ divides $q-1$. To this aim, we study group actions on weak
N\\'eron models.
(Joint work with Johannes Nicaise)
統計数学セミナー
15:00-16:10 数理科学研究科棟(駒場) 000号室
鈴木 大慈 氏 (東京大学)
Elasticnet型正則化を持つMultiple Kernel Learningについて (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html
鈴木 大慈 氏 (東京大学)
Elasticnet型正則化を持つMultiple Kernel Learningについて (JAPANESE)
[ 講演概要 ]
Mutiple Kernel Learning (MKL) はGroup Lassoをカーネル法へ拡張した手法であり,
多くの候補となるカーネルの中から必要なカーネルを選びそれらの凸結合をとって
カーネルを学習する方法である.凸最適化で解ける点と多くのカーネルの結合係数
を0にさせるスパース性を有するという利点がある.しかし最近になって,一様重みで
単純にカーネルを足し合わせる方法とMKLの中間にあたるような,「中間的なスパー
スさ」が画像認識などの応用で良い性能を示すことが実験的に示されている.本発表
ではその「中間的なスパースさ」を実現する方法としてelasticnet型正則化を持つ
MKLを扱い,その効率的な計算アルゴリズムや,漸近的な収束性能について議論する.
漸近的な収束性能については,真のカーネル結合係数がスパースな場合とそうでない
場合で状況を分けて考え,minimaxレートを達成することや,普通のMKLより少し緩い
条件でスパースパターンの一致性があることなどelasticnet型MKLにはいくつかの
良い性質があることを示す.
[ 参考URL ]Mutiple Kernel Learning (MKL) はGroup Lassoをカーネル法へ拡張した手法であり,
多くの候補となるカーネルの中から必要なカーネルを選びそれらの凸結合をとって
カーネルを学習する方法である.凸最適化で解ける点と多くのカーネルの結合係数
を0にさせるスパース性を有するという利点がある.しかし最近になって,一様重みで
単純にカーネルを足し合わせる方法とMKLの中間にあたるような,「中間的なスパー
スさ」が画像認識などの応用で良い性能を示すことが実験的に示されている.本発表
ではその「中間的なスパースさ」を実現する方法としてelasticnet型正則化を持つ
MKLを扱い,その効率的な計算アルゴリズムや,漸近的な収束性能について議論する.
漸近的な収束性能については,真のカーネル結合係数がスパースな場合とそうでない
場合で状況を分けて考え,minimaxレートを達成することや,普通のMKLより少し緩い
条件でスパースパターンの一致性があることなどelasticnet型MKLにはいくつかの
良い性質があることを示す.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html
2010年10月04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
伊師 英之 氏 (名大多元数理)
The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)
伊師 英之 氏 (名大多元数理)
The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)
[ 講演概要 ]
For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.
Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.
For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.
Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.
2010年09月28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
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
Pavel Exner 氏 (Czech Academy of Sciences)
Some spectral and resonance properties of quantum graphs (ENGLISH)
[ 講演概要 ]
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
2010年09月14日(火)
東京無限可積分系セミナー
10:30-14:00 数理科学研究科棟(駒場) 117号室
柳田 伸太郎 氏 (神戸大) 10:30-11:30
AGT予想とrecursion formula (JAPANESE)
山田 裕二 氏 (立教大) 13:00-14:00
BelavinのR行列の3角極限に対する反射方程式の解の分類 (JAPANESE)
柳田 伸太郎 氏 (神戸大) 10:30-11:30
AGT予想とrecursion formula (JAPANESE)
山田 裕二 氏 (立教大) 13:00-14:00
BelavinのR行列の3角極限に対する反射方程式の解の分類 (JAPANESE)
2010年09月13日(月)
東京無限可積分系セミナー
10:30-15:30 数理科学研究科棟(駒場) 117号室
笠谷 昌弘 氏 (東大数理) 10:30-11:30
$C^¥vee C$型DAHAの多項式表現と境界付きqKZ方程式について (JAPANESE)
CFT , モノドロミー保存変形, Nekrasov関数 (JAPANESE)
Twisted de Rham theory---resonances and the non-resonance (JAPANESE)
笠谷 昌弘 氏 (東大数理) 10:30-11:30
$C^¥vee C$型DAHAの多項式表現と境界付きqKZ方程式について (JAPANESE)
[ 講演概要 ]
まずC-check-C型ダブルアフィンヘッケ代数と
その多項式表現について基本的な事柄を復習する.
次に, 多項式表現の観点から
境界付きqKZ方程式を導入しその解を構成する.
山田 泰彦 氏 (神戸大) 13:00-14:00まずC-check-C型ダブルアフィンヘッケ代数と
その多項式表現について基本的な事柄を復習する.
次に, 多項式表現の観点から
境界付きqKZ方程式を導入しその解を構成する.
CFT , モノドロミー保存変形, Nekrasov関数 (JAPANESE)
[ 講演概要 ]
共形場理論の相関関数と超対称ゲージ理論の分配関数の関係
(Alday-Gaiotto-Tachikawa予想)に関して, 微分方程式
(特に
モノドロミー保存変形)の観点から紹介する.
三町 勝久 氏 (東工大) 14:30-15:30共形場理論の相関関数と超対称ゲージ理論の分配関数の関係
(Alday-Gaiotto-Tachikawa予想)に関して, 微分方程式
(特に
モノドロミー保存変形)の観点から紹介する.
Twisted de Rham theory---resonances and the non-resonance (JAPANESE)
2010年09月12日(日)
東京無限可積分系セミナー
10:30-17:00 数理科学研究科棟(駒場) 117号室
森田 英章 氏 (室蘭工大) 10:30-11:30
マクドナルド多項式のベキ根における分解公式 (JAPANESE)
W代数と対称多項式 (JAPANESE)
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
1の巾根でのMacdonald多項式の分解公式の組合せ論的証明について (JAPANESE)
森田 英章 氏 (室蘭工大) 10:30-11:30
マクドナルド多項式のベキ根における分解公式 (JAPANESE)
[ 講演概要 ]
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
白石 潤一 氏 (東大数理) 13:00-14:00We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
W代数と対称多項式 (JAPANESE)
[ 講演概要 ]
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
長谷川 浩司 氏 (東北大) 14:30-15:30It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
Quantizing the difference Painlev¥'e VI equation (JAPANESE)
[ 講演概要 ]
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
沼田 泰英 氏 (東大情報理工) 16:00-17:00I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
1の巾根でのMacdonald多項式の分解公式の組合せ論的証明について (JAPANESE)
[ 講演概要 ]
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)
2010年09月11日(土)
東京無限可積分系セミナー
13:00-17:00 数理科学研究科棟(駒場) 117号室
伊藤 雅彦 氏 (東京電機大 未来科学部 数学系列) 13:00-14:00
$BC_n$型$q$-超幾何関数の三項間隣接関係式とその応用 (JAPANESE)
TBA (JAPANESE)
瀧 雅人 氏 (京大基礎物理学研究所) 16:00-17:00
AGT予想と幾何工学 (JAPANESE)
伊藤 雅彦 氏 (東京電機大 未来科学部 数学系列) 13:00-14:00
$BC_n$型$q$-超幾何関数の三項間隣接関係式とその応用 (JAPANESE)
[ 講演概要 ]
この講演における$BC_n$型$q$-超幾何関数とは、
ガウスの超幾何関数の積分表示のある種の$q$-類似であり、
古典的には(very-)well-poised と呼ばれるクラスの$q$-超幾何級数で、
一般には$C_n$型ワイル群対称性をもつ多重$q$-積分($q$-級数)で定義される。
この$q$-超幾何級数に含まれるパラメータの個数が6+1個の場合に、
ある対称多項式の族を定義すると(ここではBC型補間多項式と呼ぶ)、
ガウスの超幾何関数の隣接関係式に類似の三項間関係式が
成立することがわかったので紹介する。三項間関係式を繰り返し使うことにより、
この$q$-超幾何級数が満たすランクn+1の一階連立$q$-差分方程式系を
具体的に表示することができる。応用として、この具体的表示から、
Gustafson の$q$-積分の無限積表示の別証明が得られるので、
それも紹介したい。
野海 正俊 氏 (神戸大) 14:30-15:30この講演における$BC_n$型$q$-超幾何関数とは、
ガウスの超幾何関数の積分表示のある種の$q$-類似であり、
古典的には(very-)well-poised と呼ばれるクラスの$q$-超幾何級数で、
一般には$C_n$型ワイル群対称性をもつ多重$q$-積分($q$-級数)で定義される。
この$q$-超幾何級数に含まれるパラメータの個数が6+1個の場合に、
ある対称多項式の族を定義すると(ここではBC型補間多項式と呼ぶ)、
ガウスの超幾何関数の隣接関係式に類似の三項間関係式が
成立することがわかったので紹介する。三項間関係式を繰り返し使うことにより、
この$q$-超幾何級数が満たすランクn+1の一階連立$q$-差分方程式系を
具体的に表示することができる。応用として、この具体的表示から、
Gustafson の$q$-積分の無限積表示の別証明が得られるので、
それも紹介したい。
TBA (JAPANESE)
瀧 雅人 氏 (京大基礎物理学研究所) 16:00-17:00
AGT予想と幾何工学 (JAPANESE)
[ 講演概要 ]
共形場理論における共形blockと超対称gauge理論の分配関数の間に成立していると考
えられている
AGT予想について議論する。
特に超対称gauge理論における表面演算子とそのAGT対応を、
位相的string理論を用いることで理解する。
その結果、局所Calabi-Yau多様体上のcurve countingから、
表面演算子に対応したramified instanton分配関数の明示公式が予想として与えられ
る。
共形場理論における共形blockと超対称gauge理論の分配関数の間に成立していると考
えられている
AGT予想について議論する。
特に超対称gauge理論における表面演算子とそのAGT対応を、
位相的string理論を用いることで理解する。
その結果、局所Calabi-Yau多様体上のcurve countingから、
表面演算子に対応したramified instanton分配関数の明示公式が予想として与えられ
る。
2010年09月09日(木)
講演会
16:30-18:00 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (3/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.
This is Part 3 of a 3-part lecture.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.
This is Part 3 of a 3-part lecture.
2010年09月06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
Prof. Remke Kloosterman 氏 (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
Prof. Remke Kloosterman 氏 (Humboldt University, Berlin)
Non-reduced components of the Noether-Lefschetz locus (ENGLISH)
[ 講演概要 ]
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\\mathbb{P}3$. Let $NL_d \\subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.
2010年09月04日(土)
講演会
09:30-11:00 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (1/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.
This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.
This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.
講演会
11:10-12:40 数理科学研究科棟(駒場) 126号室
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
Bernhard Mühlherr 氏 (Justus-Liebig-Universität Gießen)
Mini-course on Buildings (2/3) (ENGLISH)
[ 講演概要 ]
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.
This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.
This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.
2010年09月03日(金)
講演会
14:30-15:30 数理科学研究科棟(駒場) 370号室
Luc Robbiano 氏 (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
Luc Robbiano 氏 (University of Versailles)
Carleman estimates and boundary problems. (JAPANESE)
[ 講演概要 ]
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
2010年09月01日(水)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
いつもと場所が違います
Bernhard M\"uhlherr 氏 (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
いつもと場所が違います
Bernhard M\"uhlherr 氏 (Justus-Liebig-Universit\"at Giessen)
Groups of Kac-Moody type (ENGLISH)
[ 講演概要 ]
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
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