## Seminar information archive

### 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
[ 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 ]
https://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
[ 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 ]
https://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
[ 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 ]
https://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
[ 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 ]
https://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.)

### 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

#### 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)
[ 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 ]
https://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.)
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).

#### Tuesday Seminar of Analysis

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

#### 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
[ 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.

### 2007/05/14

#### Seminar on Geometric Complex Analysis

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

### 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 $Sp(3,R)$

### 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
[ 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.

#### Lie Groups and Representation Theory

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

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 ]
https://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

#### Algebraic Geometry Seminar

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

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.

### 2007/05/02

#### Number Theory Seminar

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

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

### 2007/05/01

#### Tuesday Seminar of Analysis

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

#### Lie Groups and Representation Theory

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

Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$
[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007/04/26

#### Seminar for Mathematical Past of Asia

17:00-18:30   Room #123 (Graduate School of Math. Sci. Bldg.)

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

#### Operator Algebra Seminars

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

Nonequilibrium steady states in quantum systems

### 2007/04/25

#### Number Theory Seminar

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

Localized Characteristic Class and Swan Class

### 2007/04/24

#### Tuesday Seminar on Topology

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

Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators
[ Abstract ]
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 Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Taro Yoshino (吉野太郎) (University of Tokyo)
Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds

[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino