過去の記録

過去の記録 ~02/23本日 02/24 | 今後の予定 02/25~

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
坊向伸隆 氏 (大阪市立大学)
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.
[ 講演参考URL ]
http://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
金行壮二 氏 (上智大学名誉教授)
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 $M$.
[ 講演参考URL ]
http://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
沖本 竜義 氏 (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
[ 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.
[ 講演参考URL ]
http://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
甲斐千舟 氏 (九州大学)
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.
[ 講演参考URL ]
http://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
厚地淳 氏 (慶応大学)
熱核を用いたNevanlinna理論 --- Gauss mapへの試み

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
小川朋宏 氏 (東大数理)
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
真野元 氏 (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)
[ 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.
[ 講演参考URL ]
http://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
宮尾 忠宏 氏 (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

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
渡邉 忠之 氏 (京都大学数理解析研究所)
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
戸松玲治 氏 (東大数理)
自己準同型の収束と近似的内部性

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
宮崎 直 氏 (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
森山 哲裕 氏 (東京大学大学院数理科学研究科)
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。
荒川知幸 氏 (奈良女子大学)
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.
[ 講演参考URL ]
http://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
辻 元 氏 (上智大学)
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
謝啓鴻(Xie Qihong) 氏 (東大・数理)
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
長谷川 泰子 氏 (東京大学大学院数理科学研究科)
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
下村 明洋 氏 (学習院大理学部)
非線型シュレディンガー方程式の解の長時間挙動について

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
飯田正敏 氏 (城西大学)
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.
[ 講演参考URL ]
http://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
公田 藏 氏 (立教大学名誉教授)
明治前期の日本において学ばれたユークリッド幾何学
[ 講演参考URL ]
http://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
緒方芳子 氏 (東大数理)
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
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
Localized Characteristic Class and Swan Class

2007年04月24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
五味 清紀 氏 (東京大学大学院数理科学研究科)
Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators
[ 講演概要 ]
A problem in twisted $K$-theory is to realize twisted $K$-groups generally by means of finite-dimensional geometric objects, like vector bundles. I would like to talk about an approach toward the problem by means of Mikio Furuta's generalized vector bundles. By using a twisted version of the generalized vector bundle and a finite-dimensional approximation of Fredholm operators, I construct a group into which there exists a natural injection from the twisted $K$-group twisted by any third integral cohomology class.

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
Taro Yoshino (吉野太郎) 氏 (University of Tokyo)
Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds

[ 講演概要 ]
The existence problem of compact Clifford-Klein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its `infinitesimal' homogeneous space.
This homogeneous space is easier to consider the existence problem of compact Clifford-Klein forms.
In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact Clifford-Klein forms to certain algebraic problem, which was already studied from other motivation.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino

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