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過去の記録 ～05/01｜本日 05/02 | 今後の予定 05/03～
応用解析セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
倉田 和浩 氏 (首都大学東京・理工学研究科・数理情報科学専攻)
弱い飽和効果をもったGierer-Meinhardt systemにおける軸対称領域上での多重ピーク解の構成と漸近挙動について
倉田 和浩 氏 (首都大学東京・理工学研究科・数理情報科学専攻)
弱い飽和効果をもったGierer-Meinhardt systemにおける軸対称領域上での多重ピーク解の構成と漸近挙動について
[ 講演概要 ]
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).
We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\\epsilon^2 \\Delta A-A+A^2/(H(1+kA^2), A>0,$
$\\tau H_t=D\\Delta H-H+A2, H>0,$
where $\\epsilon >0$, $\\tau \\geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\\Omega$ is an $x_N$-axially symmetric domain and $2\\leq N\\leq 5$, for sufficiently small $\\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\\partial \\Omega$, under the condition that $k\\epsilon^{-2N}$ converges to some $k_0\\in[0,\\infty)$ as $\\epsilon \\to 0$.
In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).
We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\\epsilon^2 \\Delta A-A+A^2/(H(1+kA^2), A>0,$
$\\tau H_t=D\\Delta H-H+A2, H>0,$
where $\\epsilon >0$, $\\tau \\geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\\Omega$ is an $x_N$-axially symmetric domain and $2\\leq N\\leq 5$, for sufficiently small $\\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\\partial \\Omega$, under the condition that $k\\epsilon^{-2N}$ converges to some $k_0\\in[0,\\infty)$ as $\\epsilon \\to 0$.
In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.
2007年11月07日(水)
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 122号室
鎌谷 研吾 氏 (東京大学大学院数理科学研究科)
ハプロタイプ関連解析:EMアルゴリズムによるアプローチ
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html
鎌谷 研吾 氏 (東京大学大学院数理科学研究科)
ハプロタイプ関連解析:EMアルゴリズムによるアプローチ
[ 講演概要 ]
最尤推定量の計算法である, EMアルゴリズムについて考察する. EMアルゴリズムのグローバルな観点の収束を示すことは容易でない事が多い. 一方で局所的な収束は容易に示すことができて, 一次漸近有効な推定量を 構成できる. その構成法とハプロタイプ関連解析への応用を考える. 時間があれば, ベイズ推定量の近似である, MCMCによる統計量の漸近有効性にも触れる.
[ 参考URL ]最尤推定量の計算法である, EMアルゴリズムについて考察する. EMアルゴリズムのグローバルな観点の収束を示すことは容易でない事が多い. 一方で局所的な収束は容易に示すことができて, 一次漸近有効な推定量を 構成できる. その構成法とハプロタイプ関連解析への応用を考える. 時間があれば, ベイズ推定量の近似である, MCMCによる統計量の漸近有効性にも触れる.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html
2007年11月06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
児玉 大樹 氏 (東京大学大学院数理科学研究科)
Thustion's inequality and open book foliations
Tea: 16:00 - 16:30 コモンルーム
児玉 大樹 氏 (東京大学大学院数理科学研究科)
Thustion's inequality and open book foliations
[ 講演概要 ]
We will study codimension 1 foliations on 3-manifolds.
Thurston's inequality, which implies convexity of the foliation in
some sense, folds for Reebless foliations [Th]. We will discuss
whether the inequality holds or not for open book foliations.
[Th] W. Thurston: Norm on the homology of 3-manifolds, Memoirs of the
AMS, 339 (1986), 99--130.
We will study codimension 1 foliations on 3-manifolds.
Thurston's inequality, which implies convexity of the foliation in
some sense, folds for Reebless foliations [Th]. We will discuss
whether the inequality holds or not for open book foliations.
[Th] W. Thurston: Norm on the homology of 3-manifolds, Memoirs of the
AMS, 339 (1986), 99--130.
Lie群論・表現論セミナー
15:00-16:30 数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. IV
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. IV
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
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
森脇政泰 氏 (広島大学)
Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
森脇政泰 氏 (広島大学)
Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007年11月01日(木)
Lie群論・表現論セミナー
16:30-18:00 数理科学研究科棟(駒場) 052号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. III
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. III
[ 講演概要 ]
Kontsevich's formality theorem and applications in Representation theory.
We shall first give an explicit construction of an associative star-product on an arbitrary smooth finite-dimensional Poisson manifold.
As application, we will consider in details the crucial example of the dual of a finite-dimensional Lie algebra and will sketch a generalization of the Duflo isomorphism describing the set of infinitesimal characters of irreducible unitary representations of the corresponding Lie group.
[ 参考URL ]Kontsevich's formality theorem and applications in Representation theory.
We shall first give an explicit construction of an associative star-product on an arbitrary smooth finite-dimensional Poisson manifold.
As application, we will consider in details the crucial example of the dual of a finite-dimensional Lie algebra and will sketch a generalization of the Duflo isomorphism describing the set of infinitesimal characters of irreducible unitary representations of the corresponding Lie group.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007年10月31日(水)
統計数学セミナー
16:20-17:30 数理科学研究科棟(駒場) 122号室
深澤 正彰 氏 (東京大学大学院数理科学研究科)
最尤推定量の漸近展開とその応用:とくに拡散過程の場合について
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html
深澤 正彰 氏 (東京大学大学院数理科学研究科)
最尤推定量の漸近展開とその応用:とくに拡散過程の場合について
[ 講演概要 ]
最尤推定量とそのスチューデント化統計量の漸近展開公式について、 スキューネス修正の観点から考察し、AR過程や、あるクラスの拡散過程モデルへの応用について述べる。 一般の対称拡散過程モデルにおける最尤推定量のバイアス推定量、 スキューネス推定量も提案する。
[ 参考URL ]最尤推定量とそのスチューデント化統計量の漸近展開公式について、 スキューネス修正の観点から考察し、AR過程や、あるクラスの拡散過程モデルへの応用について述べる。 一般の対称拡散過程モデルにおける最尤推定量のバイアス推定量、 スキューネス推定量も提案する。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html
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
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)
2007年10月30日(火)
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 (東京大学大学院数理科学研究科)
On Weyl groups for parabolic subalgebras
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
松本久義 氏 (東京大学大学院数理科学研究科)
On Weyl groups for parabolic subalgebras
[ 講演概要 ]
Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
[ 参考URL ]Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Lie群論・表現論セミナー
15:00-16:30 数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. II
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. II
[ 講演概要 ]
Back to Mathematics. Two methods of quantization.
We will start with a discussion on
-Weyl symbolic calculus on a symplectic vector space
and its asymptotic behavior.
In the second part, as a consequence of previous considerations, we will define the notion of deformation quantization.
[ 参考URL ]Back to Mathematics. Two methods of quantization.
We will start with a discussion on
-Weyl symbolic calculus on a symplectic vector space
and its asymptotic behavior.
In the second part, as a consequence of previous considerations, we will define the notion of deformation quantization.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
代数幾何学セミナー
10:00-12:00 数理科学研究科棟(駒場) 128号室
毎週火曜10時から12時の連続講演の第2回目です. 10月23日と12月4日は休講です.
第1回目の講義ノートがhttp://imperium.lenin.ru/~kaledin/math/tokyo/にあります.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in Non-commutative Geometry
毎週火曜10時から12時の連続講演の第2回目です. 10月23日と12月4日は休講です.
第1回目の講義ノートがhttp://imperium.lenin.ru/~kaledin/math/tokyo/にあります.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in Non-commutative Geometry
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
太田 啓史 氏 (名大多元数理)
$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.
Tea: 16:40 - 17:00 コモンルーム
太田 啓史 氏 (名大多元数理)
$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.
[ 講演概要 ]
I will discuss $L_{\\infty}$ actions on Lagrangian filtered
$A_{\\infty}$ algebras by cycles of the ambient symplectic
manifold. In the course of the construction,
I like to remark that the stable map compactification is not
sufficient in some case when we consider ones from genus zero
bordered Riemann surface. Also, if I have time, I like to discuss
some relation to (absolute) Gromov-Witten invariant and other
applications.
(This talk is based on my joint work with K.Fukaya, Y-G Oh and K. Ono.)
I will discuss $L_{\\infty}$ actions on Lagrangian filtered
$A_{\\infty}$ algebras by cycles of the ambient symplectic
manifold. In the course of the construction,
I like to remark that the stable map compactification is not
sufficient in some case when we consider ones from genus zero
bordered Riemann surface. Also, if I have time, I like to discuss
some relation to (absolute) Gromov-Witten invariant and other
applications.
(This talk is based on my joint work with K.Fukaya, Y-G Oh and K. Ono.)
2007年10月29日(月)
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 002号室
Hiroshige Kajiura 氏 (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry
Hiroshige Kajiura 氏 (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry
[ 講演概要 ]
In this talk, I would like to discuss on some examples of
triangulated and/or $A_\\infty$-categories associated to
manifolds with additional structures
(symplectic structure, complex structure, ...)
which can appear in the homological mirror symmetry (HMS) set-up
proposed by Kontsevich'94.
The strongest form of the HMS may be to show the equivalence
of Fukaya category on a symplectic manifold with the category
of coherent sheaves on the mirror dual complex manifold
at the level of $A_\\infty$-categories.
On the other hand, for a given $A_\\infty$-category,
there is a canonical way (due to Bondal-Kapranov, Kontsevich)
to construct an enlarged $A_\\infty$-category
whose restriction to the zero-th cohomology forms a triangulated category.
I plan to talk about the triangulated structure of categories
associated to regular systems of weights
(joint work with Kyoji Saito and Atsushi Takahashi),
and also give a realization of higher $A_\\infty$-products in
Fukaya categories from the mirror dual complex manifold
via HMS in some easy examples.
In this talk, I would like to discuss on some examples of
triangulated and/or $A_\\infty$-categories associated to
manifolds with additional structures
(symplectic structure, complex structure, ...)
which can appear in the homological mirror symmetry (HMS) set-up
proposed by Kontsevich'94.
The strongest form of the HMS may be to show the equivalence
of Fukaya category on a symplectic manifold with the category
of coherent sheaves on the mirror dual complex manifold
at the level of $A_\\infty$-categories.
On the other hand, for a given $A_\\infty$-category,
there is a canonical way (due to Bondal-Kapranov, Kontsevich)
to construct an enlarged $A_\\infty$-category
whose restriction to the zero-th cohomology forms a triangulated category.
I plan to talk about the triangulated structure of categories
associated to regular systems of weights
(joint work with Kyoji Saito and Atsushi Takahashi),
and also give a realization of higher $A_\\infty$-products in
Fukaya categories from the mirror dual complex manifold
via HMS in some easy examples.
2007年10月25日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 410号室
見村万佐人 氏 (東大数理)
An introduction to expander graphs
見村万佐人 氏 (東大数理)
An introduction to expander graphs
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
連続講義です。学生の方の参加を歓迎します。
Michael Pevzner 氏 (Universite de Reims and University of Tokyo)
Quantization of symmetric spaces and representations. I
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
連続講義です。学生の方の参加を歓迎します。
Michael Pevzner 氏 (Universite de Reims and University of Tokyo)
Quantization of symmetric spaces and representations. I
[ 講演概要 ]
The first and introductory lecture of a series of four will be devoted to the discussion of fundamental principles of the Quantum mechanics and their mathematical formulation. This part is not essential for the rest of the course but it might give a global vision of the subject to be considered.
We shall introduce the Weyl symbolic calculus, that relates classical and quantum observables, and will explain its relationship with the so-called deformation quantization of symplectic manifolds.
Afterwards, we will pay attention to a more algebraic question of formal deformation of an arbitrary smooth Poisson manifold and will define the Kontsevich star-product.
[ 参考URL ]The first and introductory lecture of a series of four will be devoted to the discussion of fundamental principles of the Quantum mechanics and their mathematical formulation. This part is not essential for the rest of the course but it might give a global vision of the subject to be considered.
We shall introduce the Weyl symbolic calculus, that relates classical and quantum observables, and will explain its relationship with the so-called deformation quantization of symplectic manifolds.
Afterwards, we will pay attention to a more algebraic question of formal deformation of an arbitrary smooth Poisson manifold and will define the Kontsevich star-product.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007年10月24日(水)
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
阿部知行 氏 (東京大学大学院数理科学研究科)
l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
阿部知行 氏 (東京大学大学院数理科学研究科)
l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
[ 講演概要 ]
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
2007年10月23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
Jun O'Hara 氏 (首都大学東京)
Spaces of subspheres and their applications
Tea: 16:00 - 16:30 コモンルーム
Jun O'Hara 氏 (首都大学東京)
Spaces of subspheres and their applications
[ 講演概要 ]
The set of q-dimensional subspheres in S^n is a Grassmann manifold which has natural pseudo-Riemannian structure, and in some cases, symplectic structure as well. Both of them are conformally invariant.
I will explain some examples of their applications to geometric aspects of knots and links.
The set of q-dimensional subspheres in S^n is a Grassmann manifold which has natural pseudo-Riemannian structure, and in some cases, symplectic structure as well. Both of them are conformally invariant.
I will explain some examples of their applications to geometric aspects of knots and links.
解析学火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 128号室
いつもと30分ずれていますのでお間違いなく.
Fr\'{e}d\'{e}ric Klopp 氏 (パリ北大学)
Localization for random quantum graphs (joint with K. Pankrashkin)
いつもと30分ずれていますのでお間違いなく.
Fr\'{e}d\'{e}ric Klopp 氏 (パリ北大学)
Localization for random quantum graphs (joint with K. Pankrashkin)
2007年10月22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
志賀弘典 氏 (千葉大学)
ガウス算術幾何平均定理の多変数化とその保型形式的解釈(小池健二氏との共同研究)
志賀弘典 氏 (千葉大学)
ガウス算術幾何平均定理の多変数化とその保型形式的解釈(小池健二氏との共同研究)
2007年10月18日(木)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Mikael Pichot 氏 (学振・東大数理)
On the classification of Bruhat-Tits buildings
Mikael Pichot 氏 (学振・東大数理)
On the classification of Bruhat-Tits buildings
2007年10月17日(水)
講演会
16:00-17:00 数理科学研究科棟(駒場) 470号室
J. Fritz 氏 (TU Budapest)
The method of compensated compactness for
microscopic systems
J. Fritz 氏 (TU Budapest)
The method of compensated compactness for
microscopic systems
2007年10月16日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム
二木 昭人 氏 (東京工業大学大学院理工学研究科)
Toric Sasaki-Einstein manifolds
Tea: 16:40 - 17:00 コモンルーム
二木 昭人 氏 (東京工業大学大学院理工学研究科)
Toric Sasaki-Einstein manifolds
[ 講演概要 ]
A compact toric Sasaki manifold admits a Sasaki-Einstein metric if and only if it is obtained by the Delzant construction from a toric diagram of a constant height. As an application we see that the canonical line bundle of a toric Fano manifold admits a complete Ricci-flat K\\"ahler metric.
A compact toric Sasaki manifold admits a Sasaki-Einstein metric if and only if it is obtained by the Delzant construction from a toric diagram of a constant height. As an application we see that the canonical line bundle of a toric Fano manifold admits a complete Ricci-flat K\\"ahler metric.
代数幾何学セミナー
10:00-12:00 数理科学研究科棟(駒場) 128号室
10月16日開始, 毎週火曜10時から12時の連続講演です. 10月23日と12月4日は休講です.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homogical methods in Non-commutative Geometry
10月16日開始, 毎週火曜10時から12時の連続講演です. 10月23日と12月4日は休講です.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homogical methods in Non-commutative Geometry
[ 講演概要 ]
Of all the approaches to non-commutative geometry, probably the most promising is the homological one, developed by Keller, Kontsevich, Toen and others, where non-commutative eometry is understood as "geometry of triangulated categories". Examples of "geometric" triangulated categories come from representation theory, symplectic geometry (Fukaya category) and algebraic geometry (the derived category of coherent sheaves on an algebraic variety and
various generalizations). Non-commutative point of view is expected to be helpful even in traditional questions of algebraic geometry such as the termination of flips.
We plan to give an introduction to the subject, with emphasis on homological methods (such as e.g. Hodge theory which, as it turns out, can be mostly formulated in the non-commutative setting).
No knowledge of non-commutative geometry whatsoever is assumed. However, familiarity with basic homological algebra and algebraic geometry will be helpful.
Of all the approaches to non-commutative geometry, probably the most promising is the homological one, developed by Keller, Kontsevich, Toen and others, where non-commutative eometry is understood as "geometry of triangulated categories". Examples of "geometric" triangulated categories come from representation theory, symplectic geometry (Fukaya category) and algebraic geometry (the derived category of coherent sheaves on an algebraic variety and
various generalizations). Non-commutative point of view is expected to be helpful even in traditional questions of algebraic geometry such as the termination of flips.
We plan to give an introduction to the subject, with emphasis on homological methods (such as e.g. Hodge theory which, as it turns out, can be mostly formulated in the non-commutative setting).
No knowledge of non-commutative geometry whatsoever is assumed. However, familiarity with basic homological algebra and algebraic geometry will be helpful.
2007年10月15日(月)
Kavli IPMU Komaba Seminar
17:00-18:30 数理科学研究科棟(駒場) 002号室
Shinobu Hosono 氏 (The University of Tokyo)
Topics on string theory, mirror symmetry, and Gromov-Witten invariants
Shinobu Hosono 氏 (The University of Tokyo)
Topics on string theory, mirror symmetry, and Gromov-Witten invariants
[ 講演概要 ]
Recently, some technical developments in solving BCOV
(Bershadsky-Cecotti-Ooguri-Vafa) holomorphic anomaly equation has been
made and it has become possible to predict higher genus Gromov-Witten
invariants for some class of Calabi-Yau 3 folds.
With a brief introduction to BCOV equation, I will present some
predictions for Gromov-Witten invariants of certain Calabi-Yau 3 folds,
which are not birational but derived equivalent. (This is based on
a work with Y. Konishi which appeared in mathAG/0704.2928.)
Before coming to this specific topic, I will review some recent
topics of the homological mirror symmetry focusing on
its connection to the `classical' mirror symmetry, where the
variation theory of Hodge structures (VHS) plays a central role.
The BCOV equation and its open string generalization have their grounds
on the VHS.
Recently, some technical developments in solving BCOV
(Bershadsky-Cecotti-Ooguri-Vafa) holomorphic anomaly equation has been
made and it has become possible to predict higher genus Gromov-Witten
invariants for some class of Calabi-Yau 3 folds.
With a brief introduction to BCOV equation, I will present some
predictions for Gromov-Witten invariants of certain Calabi-Yau 3 folds,
which are not birational but derived equivalent. (This is based on
a work with Y. Konishi which appeared in mathAG/0704.2928.)
Before coming to this specific topic, I will review some recent
topics of the homological mirror symmetry focusing on
its connection to the `classical' mirror symmetry, where the
variation theory of Hodge structures (VHS) plays a central role.
The BCOV equation and its open string generalization have their grounds
on the VHS.
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
大沢健夫 氏 (名古屋大学)
On the curvature of holomorphic foliations
大沢健夫 氏 (名古屋大学)
On the curvature of holomorphic foliations
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