## Seminar information archive

Seminar information archive ～02/18｜Today's seminar 02/19 | Future seminars 02/20～

### 2007/06/06

#### Seminar on Probability and Statistics

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

非正則な位置尺度母数分布族における位置母数の逐次点推定について

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/01.html

**小池 健一**(筑波大学大学院数理物質科学研究科)非正則な位置尺度母数分布族における位置母数の逐次点推定について

[ Abstract ]

有界な台をもつ非正則な位置尺度母数分布族に対して,その位置母数の逐次点推定を考える.ここでは,平均二乗誤差に費用も加えてリスクを考える.レンジに基づく停止則を提案し,これが漸近有効であることを示す.また,良く知られているRobbinsの逐次推定方式との比較を行い,密度関数の台の端点で密度関数が急激に変化する場合には,提案する逐次推定方式が標本数やリスクの意味で優れていることを示す.この結果は,逐次区間推定に関するKoike (2007)のものと同様であることが分かる

[ Reference URL ]有界な台をもつ非正則な位置尺度母数分布族に対して,その位置母数の逐次点推定を考える.ここでは,平均二乗誤差に費用も加えてリスクを考える.レンジに基づく停止則を提案し,これが漸近有効であることを示す.また,良く知られているRobbinsの逐次推定方式との比較を行い,密度関数の台の端点で密度関数が急激に変化する場合には,提案する逐次推定方式が標本数やリスクの意味で優れていることを示す.この結果は,逐次区間推定に関するKoike (2007)のものと同様であることが分かる

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/01.html

### 2007/06/05

#### Tuesday Seminar on Topology

17:00-18:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Symplectic mapping classes and fillings

**Emmanuel Giroux**(ENS Lyon)Symplectic mapping classes and fillings

[ Abstract ]

We will describe a joint work in progress with Paul Biran in

which contact geometry is combined with properties of Lagrangian manifolds

in subcritical Stein domains to obtain nontrivaility results for symplectic

mapping classes.

We will describe a joint work in progress with Paul Biran in

which contact geometry is combined with properties of Lagrangian manifolds

in subcritical Stein domains to obtain nontrivaility results for symplectic

mapping classes.

### 2007/06/04

#### Seminar on Geometric Complex Analysis

10:45-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)

有理楕円曲面上の微分方程式

**坂井秀隆**(東京大学)有理楕円曲面上の微分方程式

### 2007/06/02

#### Mathematical Finance

17:30-19:00 Room #128 (Graduate School of Math. Sci. Bldg.)

分布が Fat tail を持つ i.i.d. 確率変数の和に関して

**楠岡 成雄**(東京大)分布が Fat tail を持つ i.i.d. 確率変数の和に関して

### 2007/05/30

#### Mathematical Finance

17:30-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)

非対称関数上の最適ヘッジ戦略

**新井 拓児**(慶応大)非対称関数上の最適ヘッジ戦略

### 2007/05/29

#### Operator Algebra Seminars

15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Galois groups and an obstruction to principal graphs of subfactors

**Marta Asaeda**(UC Riverside)Galois groups and an obstruction to principal graphs of subfactors

#### Lie Groups and Representation Theory

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

A host algebra for the regular representations of the canonical commutation relations

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070529neeb

**Karl-Hermann Neeb**(Technische Universität Darmstadt)A host algebra for the regular representations of the canonical commutation relations

[ Abstract ]

We report on joint work with H. Grundling (Sydney).

The concept of a host algebra generalises that of a group $C^*$-algebra to groups which are not locally compact in the sense that its non-degenerate representations are in one-to-one correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a non-zero central character.

[ Reference URL ]We report on joint work with H. Grundling (Sydney).

The concept of a host algebra generalises that of a group $C^*$-algebra to groups which are not locally compact in the sense that its non-degenerate representations are in one-to-one correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a non-zero central character.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070529neeb

### 2007/05/26

#### Infinite Analysis Seminar Tokyo

13:00-16:30 Room #117 (Graduate School of Math. Sci. Bldg.)

弦理論対応における可積分性

AdS/CFT 対応における $a$-maximization について

**酒井一博**(慶応大経済) 13:00-14:30弦理論対応における可積分性

[ Abstract ]

概要:N=4超対称ゲージ理論と反ド・ジッター時空を背景とする弦理論の等価性を主

張するAdS/CFT対応は、ここ十年弦理論の分野でもっとも活発に研究されてい

るテーマのひとつである。この枠組の中で、伝統的な一次元量子可積分系や二

次元古典可積分系と同種の可積分構造が発見され、近年飛躍的な研究の進展が

続いている。この流れは、既存の可積分系の知識の単なる応用にとどまらず、

一次元Hubbard模型の可積分性の背景にある代数構造を明らかにするなど、可

積分系の分野へのフィードバックをももたらしている。本講演では、ゲージ理

論・弦理論双方で可積分性がどのように現れるかを概観しながら、この分野の

研究の最前線を紹介する。

概要:N=4超対称ゲージ理論と反ド・ジッター時空を背景とする弦理論の等価性を主

張するAdS/CFT対応は、ここ十年弦理論の分野でもっとも活発に研究されてい

るテーマのひとつである。この枠組の中で、伝統的な一次元量子可積分系や二

次元古典可積分系と同種の可積分構造が発見され、近年飛躍的な研究の進展が

続いている。この流れは、既存の可積分系の知識の単なる応用にとどまらず、

一次元Hubbard模型の可積分性の背景にある代数構造を明らかにするなど、可

積分系の分野へのフィードバックをももたらしている。本講演では、ゲージ理

論・弦理論双方で可積分性がどのように現れるかを概観しながら、この分野の

研究の最前線を紹介する。

**加藤晃史**(東大数理) 15:00-16:30AdS/CFT 対応における $a$-maximization について

[ Abstract ]

弦双対性の一つである AdS/CFT 対応において、$a$-maximization

と呼ばれる変分問題が4次元超対称共形場理論のスペクトルの決定に

重要な働きをするがわかってきた。本講演では非専門家向けに

$a$-maximization の基本的な構造を説明するとともに、

関連するいくつかの話題を紹介したい。

弦双対性の一つである AdS/CFT 対応において、$a$-maximization

と呼ばれる変分問題が4次元超対称共形場理論のスペクトルの決定に

重要な働きをするがわかってきた。本講演では非専門家向けに

$a$-maximization の基本的な構造を説明するとともに、

関連するいくつかの話題を紹介したい。

### 2007/05/25

#### Lie Groups and Representation Theory

14:30-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

The classification of simple irreducible pseudo-Hermitian symmetric spaces: from a view of elliptic orbits

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525boumuki

**坊向伸隆**(大阪市立大学)The classification of simple irreducible pseudo-Hermitian symmetric spaces: from a view of elliptic orbits

[ Abstract ]

In this talk, we call a special elliptic element an Spr-element, we create an equivalence relation on the set of Spr-elements of a real form of a complex simple Lie algebra, and we classify Spr-elements of each real form of all complex simple Lie algebras under our equivalence relation. Besides, we demonstrate that the classification of Spr-elements under our equivalence relation corresponds to that of simple irreducible pseudo-Hermitian symmetric Lie algebras under Berger's equivalence relation. In terms of the correspondence, we achieve the classification of simple irreducible pseudo-Hermitian symmetric Lie algebras without Berger's classification.

[ Reference URL ]In this talk, we call a special elliptic element an Spr-element, we create an equivalence relation on the set of Spr-elements of a real form of a complex simple Lie algebra, and we classify Spr-elements of each real form of all complex simple Lie algebras under our equivalence relation. Besides, we demonstrate that the classification of Spr-elements under our equivalence relation corresponds to that of simple irreducible pseudo-Hermitian symmetric Lie algebras under Berger's equivalence relation. In terms of the correspondence, we achieve the classification of simple irreducible pseudo-Hermitian symmetric Lie algebras without Berger's classification.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525boumuki

#### Lie Groups and Representation Theory

16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Causalities, G-structures and symmetric spaces

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki

**金行壮二**(上智大学名誉教授)Causalities, G-structures and symmetric spaces

[ Abstract ]

Let M be an $n$-dimensional smooth manifold, $F(M)$ the frame bundle of $M$, and let $G$ be a Lie subgroup of $GL(n,\\mathbb R)$. We say that $M$ has a $G$-structure, if there exists a principal subbundle $Q$ of $F(M)$ with structure group $G$. Let $C$ be a causal cone in $\\mathbb R^n$, and let $Aut C$ denote the automorphism group of $C$.

Starting from a causal structure $\\mathcal{C}$ on $M$ with model cone $C$, we construct an $Aut C$-structure $Q(\\mathcal{C})$. Several concepts on causal structures can be interpreted as those on $Aut C$-structures. As an example, the causal automorphism group $Aut(M,\\mathcal{C})$ of $M$ coincides with the automorphism group $Aut(M,Q(\\mathcal{C}))$ of the $Aut C$-structure.

As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space $M$ to the global causal automorphism of the compactification of $M$.

[ Reference URL ]Let M be an $n$-dimensional smooth manifold, $F(M)$ the frame bundle of $M$, and let $G$ be a Lie subgroup of $GL(n,\\mathbb R)$. We say that $M$ has a $G$-structure, if there exists a principal subbundle $Q$ of $F(M)$ with structure group $G$. Let $C$ be a causal cone in $\\mathbb R^n$, and let $Aut C$ denote the automorphism group of $C$.

Starting from a causal structure $\\mathcal{C}$ on $M$ with model cone $C$, we construct an $Aut C$-structure $Q(\\mathcal{C})$. Several concepts on causal structures can be interpreted as those on $Aut C$-structures. As an example, the causal automorphism group $Aut(M,\\mathcal{C})$ of $M$ coincides with the automorphism group $Aut(M,Q(\\mathcal{C}))$ of the $Aut C$-structure.

As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space $M$ to the global causal automorphism of the compactification of $M$.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki

### 2007/05/23

#### Seminar on Probability and Statistics

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

New Evidence of Asymmetric Dependence Structures in International Equity Markets

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/00.html

**沖本 竜義**(横浜国立大学経済学部・大学院国際社会科学研究科)New Evidence of Asymmetric Dependence Structures in International Equity Markets

[ Abstract ]

A number of recent studies found two asymmetries in dependence structures in international equity markets; specifically, dependence tends to be high in (1) highly volatile markets and (2) bear markets. In this paper, a further investigation on asymmetric dependence structures in international equity markets is performed under the use of the Markov switching model and copula theory. Combining these two theories enables us to model dependence structures with sufficient flexibility. Using this flexible framework we indeed found that there are two distinct regimes in the US-UK market. We also showed that, for the US-UK market, the bear regime is better described by an asymmetric copula with lower tail dependence with clear rejection of the Markov switching multivariate Normal model. In addition, we showed ignorance of this further asymmetry in bear markets is very costly for risk management. Lastly, we conducted similar analysis for other G7 countries, where we found other c ases where the use of a Markov switching multivariate Normal model would be inappropriate.

[ Reference URL ]A number of recent studies found two asymmetries in dependence structures in international equity markets; specifically, dependence tends to be high in (1) highly volatile markets and (2) bear markets. In this paper, a further investigation on asymmetric dependence structures in international equity markets is performed under the use of the Markov switching model and copula theory. Combining these two theories enables us to model dependence structures with sufficient flexibility. Using this flexible framework we indeed found that there are two distinct regimes in the US-UK market. We also showed that, for the US-UK market, the bear regime is better described by an asymmetric copula with lower tail dependence with clear rejection of the Markov switching multivariate Normal model. In addition, we showed ignorance of this further asymmetry in bear markets is very costly for risk management. Lastly, we conducted similar analysis for other G7 countries, where we found other c ases where the use of a Markov switching multivariate Normal model would be inappropriate.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/00.html

### 2007/05/22

#### Lie Groups and Representation Theory

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

A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps

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

**甲斐千舟**(九州大学)A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps

[ Abstract ]

When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order.

In this talk, we investigate this order-reversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *-map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *-map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order.

[ Reference URL ]When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order.

In this talk, we investigate this order-reversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *-map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *-map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order.

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

### 2007/05/21

#### Seminar on Geometric Complex Analysis

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

熱核を用いたNevanlinna理論 --- Gauss mapへの試み

**厚地淳**(慶応大学)熱核を用いたNevanlinna理論 --- Gauss mapへの試み

### 2007/05/17

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the statistical equivalence for sets of quantum states

**小川朋宏**(東大数理)On the statistical equivalence for sets of quantum states

#### Lie Groups and Representation Theory

15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)

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

**真野元**(東京大学数理科学研究科)The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)

[ Abstract ]

The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.

This is a joint work with T. Kobayashi.

[ Reference URL ]The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.

This is a joint work with T. Kobayashi.

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

### 2007/05/15

#### Algebraic Geometry Seminar

14:30-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Riemann-Roch for determinantal gerbes and smooth manifolds

**Mikhail Kapranov**(Yale 大学)Riemann-Roch for determinantal gerbes and smooth manifolds

[ Abstract ]

A version of the Riemann-Roch theorem for curves due to Deligne, describes the determinant of the cohomology of a vector bundle E on a curve.

If one realizes E via the Krichever construction, the determinant of the cohomology becomes a Hom-space in the determinantal gerbe for the vector space over the field of power series. So one has a ``local" Riemann-Roch problem of description of this gerbe itself. The talk will present the results of a joint work with E. Vasserot describing the class of such a gerbe in a family which geometrically can be seen as a circle fibration. This can be further generalized to the case of a fibration with fibers being smooth compact manifolds of any dimension d (joint work with P. Bressler, B. Tsygan and E. Vasserot).

A version of the Riemann-Roch theorem for curves due to Deligne, describes the determinant of the cohomology of a vector bundle E on a curve.

If one realizes E via the Krichever construction, the determinant of the cohomology becomes a Hom-space in the determinantal gerbe for the vector space over the field of power series. So one has a ``local" Riemann-Roch problem of description of this gerbe itself. The talk will present the results of a joint work with E. Vasserot describing the class of such a gerbe in a family which geometrically can be seen as a circle fibration. This can be further generalized to the case of a fibration with fibers being smooth compact manifolds of any dimension d (joint work with P. Bressler, B. Tsygan and E. Vasserot).

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

量子電磁場中を運動する原子の安定性について

**宮尾 忠宏**(岡山大自然科学研究科 学振特別研究員 )量子電磁場中を運動する原子の安定性について

#### Tuesday Seminar on Topology

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

Kontsevich's characteristic classes for higher dimensional homology sphere bundles

**渡邉 忠之**(京都大学数理解析研究所)Kontsevich's characteristic classes for higher dimensional homology sphere bundles

[ Abstract ]

As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich

constructed universal characteristic classes of smooth fiber bundles with fiber

diffeomorphic to a singularly framed odd dimensional homology sphere.

In this talk, I will give a sketch proof of our result on non-triviality of the

Kontsevich classes for 7-dimensional homology sphere bundles.

As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich

constructed universal characteristic classes of smooth fiber bundles with fiber

diffeomorphic to a singularly framed odd dimensional homology sphere.

In this talk, I will give a sketch proof of our result on non-triviality of the

Kontsevich classes for 7-dimensional homology sphere bundles.

### 2007/05/14

#### Seminar on Geometric Complex Analysis

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

Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables

**Si, Quang Duc**(東大数理)Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables

### 2007/05/10

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

自己準同型の収束と近似的内部性

**戸松玲治**(東大数理)自己準同型の収束と近似的内部性

### 2007/05/09

#### Number Theory Seminar

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

$(g,K)$-module structures of principal series representations

of $Sp(3,R)$

**宮崎 直**(東京大学大学院数理科学研究科)$(g,K)$-module structures of principal series representations

of $Sp(3,R)$

### 2007/05/08

#### Tuesday Seminar on Topology

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

On the vanishing of the Rohlin invariant

**森山 哲裕**(東京大学大学院数理科学研究科)On the vanishing of the Rohlin invariant

[ Abstract ]

The vanishing of the Rohlin invariant of an amphichiral integral

homology $3$-sphere $M$ (i.e. $M \\cong -M$) is a natural consequence

of some elementary properties of the Casson invariant. In this talk, we

give a new direct (and more elementary) proof of this vanishing

property. The main idea comes from the definition of the degree 1

part of the Kontsevich-Kuperberg-Thurston invariant, and we progress

by constructing some $7$-dimensional manifolds in which $M$ is embedded.

The vanishing of the Rohlin invariant of an amphichiral integral

homology $3$-sphere $M$ (i.e. $M \\cong -M$) is a natural consequence

of some elementary properties of the Casson invariant. In this talk, we

give a new direct (and more elementary) proof of this vanishing

property. The main idea comes from the definition of the degree 1

part of the Kontsevich-Kuperberg-Thurston invariant, and we progress

by constructing some $7$-dimensional manifolds in which $M$ is embedded.

#### Lie Groups and Representation Theory

17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Affine W-algebras and their representations

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

**荒川知幸**(奈良女子大学)Affine W-algebras and their representations

[ Abstract ]

The W-algebras are an interesting class of vertex algebras, which can be understood as a generalization of Virasoro algebra. It was originally introduced by Zamolodchikov in his study of conformal field theory. Later Feigin-Frenkel discovered that the W-algebras can be defined via the method of quantum BRST reduction. A few years ago this method was generalized by Kac-Roan-Wakimoto in full generality, producing many interesting vertex algebras. Almost at the same time Premet re-discovered the finite-dimensional version of W-algebras (finite W-algebras), in connection with the modular representation theory.

In the talk we quickly recall the Feigin-Frenkel theory which connects the Whittaker models of the center of $U({\\mathfrak g})$ and affine (principal) W-algebras, and discuss their representation theory. Next we recall the construction of Kac-Roan-Wakimoto and discuss the representation theory of affine W-algebras associated with general nilpotent orbits. In particular, I explain how the representation theory of finite W-algebras (=the endmorphism ring of the generalized Gelfand-Graev representation) applies to the representation of affine W-algebras.

[ Reference URL ]The W-algebras are an interesting class of vertex algebras, which can be understood as a generalization of Virasoro algebra. It was originally introduced by Zamolodchikov in his study of conformal field theory. Later Feigin-Frenkel discovered that the W-algebras can be defined via the method of quantum BRST reduction. A few years ago this method was generalized by Kac-Roan-Wakimoto in full generality, producing many interesting vertex algebras. Almost at the same time Premet re-discovered the finite-dimensional version of W-algebras (finite W-algebras), in connection with the modular representation theory.

In the talk we quickly recall the Feigin-Frenkel theory which connects the Whittaker models of the center of $U({\\mathfrak g})$ and affine (principal) W-algebras, and discuss their representation theory. Next we recall the construction of Kac-Roan-Wakimoto and discuss the representation theory of affine W-algebras associated with general nilpotent orbits. In particular, I explain how the representation theory of finite W-algebras (=the endmorphism ring of the generalized Gelfand-Graev representation) applies to the representation of affine W-algebras.

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

### 2007/05/07

#### Seminar on Geometric Complex Analysis

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

Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems

**辻 元**(上智大学)Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems

#### Algebraic Geometry Seminar

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Pathologies on ruled surfaces in positive characteristic

**謝啓鴻(Xie Qihong)**(東大・数理)Pathologies on ruled surfaces in positive characteristic

[ Abstract ]

We discuss some pathologies of log varieties in positive characteristic. Mainly, we show that on ruled surfaces there are counterexamples of several logarithmic type theorems. On the other hand, we also give a characterization of the counterexamples of the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface by means of the Tango invariant of the base curve.

We discuss some pathologies of log varieties in positive characteristic. Mainly, we show that on ruled surfaces there are counterexamples of several logarithmic type theorems. On the other hand, we also give a characterization of the counterexamples of the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface by means of the Tango invariant of the base curve.

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