## 過去の記録

#### 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

Karl-Hermann Neeb 氏 (Technische Universität Darmstadt)
A host algebra for the regular representations of the canonical commutation relations
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070529neeb

### 2007年05月26日(土)

#### 東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

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

AdS/CFT 対応における $a$-maximization について
[ 講演概要 ]

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

$a$-maximization の基本的な構造を説明するとともに、

### 2007年05月25日(金)

#### Lie群論・表現論セミナー

14:30-16:00   数理科学研究科棟(駒場) 122号室
いつもと曜日・時刻が違います

The classification of simple irreducible pseudo-Hermitian symmetric spaces: from a view of elliptic orbits
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525boumuki

#### Lie群論・表現論セミナー

16:00-17:30   数理科学研究科棟(駒場) 122号室
いつもと曜日時刻がちがいますのでご注意ください

Causalities, G-structures and symmetric spaces
[ 講演概要 ]
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 $M$.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki

### 2007年05月23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

New Evidence of Asymmetric Dependence Structures in International Equity Markets
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/00.html

### 2007年05月22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

A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年05月21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

### 2007年05月17日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

On the statistical equivalence for sets of quantum states

#### Lie群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 002号室
いつもと、曜日・時刻・場所が違いますのでご注意ください

The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年05月15日(火)

#### 代数幾何学セミナー

14:30-16:00   数理科学研究科棟(駒場) 122号室
いつもと時間・曜日・場所が異なります。
Mikhail Kapranov 氏 (Yale 大学)
Riemann-Roch for determinantal gerbes and smooth manifolds
[ 講演概要 ]
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).

#### 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

#### 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

Kontsevich's characteristic classes for higher dimensional homology sphere bundles
[ 講演概要 ]
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年05月14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
Si, Quang Duc 氏 (東大数理)
Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables

### 2007年05月10日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

### 2007年05月09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

$(g,K)$-module structures of principal series representations
of $Sp(3,R)$

### 2007年05月08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

On the vanishing of the Rohlin invariant
[ 講演概要 ]
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群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
この週には同氏による集中講義 14:40-16:40 が行われます。セミナーの時刻はいつもと違いますのでご注意ください。

Affine W-algebras and their representations
[ 講演概要 ]
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.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年05月07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

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

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Pathologies on ruled surfaces in positive characteristic
[ 講演概要 ]
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.

### 2007年05月02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

Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields

### 2007年05月01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

#### 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

Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$
[ 講演概要 ]
Asymptotic expansion of the matrix coefficents of class-1 principal series representation was considered by Harish-Chandra. The coefficient of the leading exponent of the expansion is called the c-function which plays an important role in the harmonic analysis on the Lie group.

In this talk, we consider the Harish-Chandra expansion of the matrix coefficients of the standard representation which is the parabolic induction with respect to a non-minimal parabolic subgroup of $Sp(2,R)$.

This is the joint study with Professor T. Oda.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年04月26日(木)

#### アジア数学史セミナー

17:00-18:30   数理科学研究科棟(駒場) 123号室

[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Nonequilibrium steady states in quantum systems

### 2007年04月25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

Localized Characteristic Class and Swan Class