## Seminar information archive

Seminar information archive ～12/04｜Today's seminar 12/05 | Future seminars 12/06～

#### Applied Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

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**(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

[ Abstract ]

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.

### 2007/11/07

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

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**(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

[ Abstract ]

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.

[ Reference 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

### 2007/11/06

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Thustion's inequality and open book foliations

**児玉 大樹**(東京大学大学院数理科学研究科)Thustion's inequality and open book foliations

[ Abstract ]

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 Groups and Representation Theory

15:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Quantization of symmetric spaces and representation. IV

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michaël Pevzner**(Université de Reims and University of Tokyo)Quantization of symmetric spaces and representation. IV

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**森脇政泰**(広島大学)Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007/11/01

#### Lie Groups and Representation Theory

16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)

Quantization of symmetric spaces and representation. III

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michaël Pevzner**(Université de Reims and University of Tokyo)Quantization of symmetric spaces and representation. III

[ Abstract ]

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.

[ Reference 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

### 2007/10/31

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

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**(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

[ Abstract ]

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。

[ Reference 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

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

On the p-adic local Langlands correspondance for GL2(Qp)

**Pierre Colmez**(Ecole Polytechnique)On the p-adic local Langlands correspondance for GL2(Qp)

### 2007/10/30

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On Weyl groups for parabolic subalgebras

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**松本久義**(東京大学大学院数理科学研究科)On Weyl groups for parabolic subalgebras

[ Abstract ]

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.

[ Reference 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 Groups and Representation Theory

15:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Quantization of symmetric spaces and representation. II

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michaël Pevzner**(Université de Reims and University of Tokyo)Quantization of symmetric spaces and representation. II

[ Abstract ]

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.

[ Reference 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

#### Algebraic Geometry Seminar

10:00-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Homological methods in Non-commutative Geometry

**Dmitry KALEDIN**(Steklov研究所, 東大数理)Homological methods in Non-commutative Geometry

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.

**太田 啓史**(名大多元数理)$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.

[ Abstract ]

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.)

### 2007/10/29

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Some examples of triangulated and/or $A_\\infty$-categories

related to homological mirror symmetry

**Hiroshige Kajiura**(RIMS, Kyoto University)Some examples of triangulated and/or $A_\\infty$-categories

related to homological mirror symmetry

[ Abstract ]

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.

### 2007/10/25

#### Operator Algebra Seminars

16:30-18:00 Room #410 (Graduate School of Math. Sci. Bldg.)

An introduction to expander graphs

**見村万佐人**(東大数理)An introduction to expander graphs

#### Lie Groups and Representation Theory

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Quantization of symmetric spaces and representations. I

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michael Pevzner**(Universite de Reims and University of Tokyo)Quantization of symmetric spaces and representations. I

[ Abstract ]

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.

[ Reference 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

### 2007/10/24

#### Number Theory Seminar

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

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**(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

[ Abstract ]

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。

### 2007/10/23

#### Tuesday Seminar on Topology

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Spaces of subspheres and their applications

**Jun O'Hara**(首都大学東京)Spaces of subspheres and their applications

[ Abstract ]

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.

#### Tuesday Seminar of Analysis

17:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Localization for random quantum graphs (joint with K. Pankrashkin)

**Fr\'{e}d\'{e}ric Klopp**(パリ北大学)Localization for random quantum graphs (joint with K. Pankrashkin)

### 2007/10/22

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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**(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)

### 2007/10/18

#### Operator Algebra Seminars

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On the classification of Bruhat-Tits buildings

**Mikael Pichot**(学振・東大数理)On the classification of Bruhat-Tits buildings

### 2007/10/17

#### Lectures

16:00-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

The method of compensated compactness for

microscopic systems

**J. Fritz**(TU Budapest)The method of compensated compactness for

microscopic systems

### 2007/10/16

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Toric Sasaki-Einstein manifolds

**二木 昭人**(東京工業大学大学院理工学研究科)Toric Sasaki-Einstein manifolds

[ Abstract ]

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.

#### Algebraic Geometry Seminar

10:00-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Homogical methods in Non-commutative Geometry

**Dmitry KALEDIN**(Steklov研究所, 東大数理)Homogical methods in Non-commutative Geometry

[ Abstract ]

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.

### 2007/10/15

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Topics on string theory, mirror symmetry, and Gromov-Witten invariants

**Shinobu Hosono**(The University of Tokyo)Topics on string theory, mirror symmetry, and Gromov-Witten invariants

[ Abstract ]

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.

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the curvature of holomorphic foliations

**大沢健夫**(名古屋大学)On the curvature of holomorphic foliations

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