## 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

Rigid local systemとその切断の積分表示,および接続係数
[ 講演概要 ]
A local system on $CP^1-\\{finite points\\}$ is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory.

### 2007年06月18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

An intrinsic characterization of the unit polydisc

### 2007年06月16日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

Lie theoretic structures for the generalized symmetric groups
[ 講演概要 ]

modular表現論とKac-Moody Lie環/量子群といったLie theoreticな対象との関係が研究
されて来た。このうち対称群のmodular表現論については、

(1) 標数p>0において、対称群\\mathfrak{S}_nの(有限次元)表現のGrothendieck群の
(nを走らせた)直和には、Kac-Moody Lie環g(A^{1}_{p-1})のレベル1基本既約最高
weight表現の構造を入れることが出来る。

(2) 対称群の既約表現の同型類の直和には、量子群U_q(g(A^{1}_{p-1}))の
レベル1基本既約最高weight表現に付随する(Kashiwaraの意味での)結晶構造を

と、その関係をまとめることが出来る。

に付随する量子群との関係を示唆する結果を得たので、まずはそれを解説したい。

なお、G(m,1,n)の群環のq-変形と考えられているcyclotomic Hecke algebraにおいて、
qが1でない1の羃根の場合は既に(1),(2)の対応物が知られているので、時間が許せば
それとの比較についても解説したい。

Wirtinger 積分の構造について
[ 講演概要 ]
Wirtinger はガウスの超幾何函数 $_2F_1$ を一意化する目的でこれを
テータ函数の冪積の積分で表わす表示を1902年に得た.Wirtinger の発見以降,
この積分に関する組織的な研究は講演者の調べた限りではほとんど無いのであるが,
この積分を講演者は前述に因んで Wirtinger 積分と呼んでいる.
この積分は実質的には超幾何函数なのであるが,あえてこの事実を忘れテータ函数の

できれば,それはテータ函数論の観点からのガウスの超幾何函数論の再構成と

ことである.

### 2007年06月15日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)

[ 講演概要 ]
21世紀はバイオの時代と言われて10年が経過しようとしている。ゲノムプロジェクトによってヒトのDNA配列は決定され、一塩基多型、コピー数解析とゲノム上での変化と遺伝子の発現、および疾患との関連性も調べられてきた。最近ではエピゲノムといわれるDNAのメチル化などゲノム配列以外の効果によっても、遺伝子発現が制御されるメカニズムが次第に明らかにされつつある。確かに、実験手法の急速な進歩によって大量のデータが得られ、知識も急増している。さらに、IT、データベース技術によって、オリジナルデータやそこから得られた情報なども容易に入手可能である。しかし生命現象で最も基本的でしかも応用上最も最優先で解明すべき遺伝子の転写機構でさえも、様々なモデルが提唱され定説もまだないのが現状である。我々は、データマイニングの観点からデータ処理を進める一方、文献から遺伝子や蛋白質の相互作用を自然言語処理で抽出し、マイクロアレイの解析に適用しいくつかの結果を得た。しかし、実験から得られるデータはますます大規模化が進み、新たな情報処理が必要になってきている。そこで、我々の解析のアプローチといくつかの問題点、さらには今後の解決の方向性について、演者自身が過去にいくつかの分野で採用してきたアプローチについても触れながら考察してみたい。また、生命科学の発展が期待されている領域である臨床研究でのイノベーションとも関連付け、今後の新しい数理解析への期待について述べてみたい。

### 2007年06月13日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Walter Strauss 氏 (Brown University)
[ 講演概要 ]
Consider a classical 2D water wave under the influence of gravity with an arbitrary vorticity function. Assume such a wave is traveling at a constant speed over a flat bed. Then there exist many families of such waves of large amplitude. The proof is based on elliptic PDEs, bifurcation and degree theory. I will also exhibit some recent numerical computations. If the vorticity is sufficiently large, the first stagnation point occurs not at the crest (as with irrotational flows) but on the bed directly below the crest. For variable vorticity the first stagnation point can occur in the interior of the fluid.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

#### 数理人口学・数理生物学セミナー

14:40-15:40   数理科学研究科棟(駒場) 123号室
Alex Cook 氏 (Actuarial Mathematics and Statistics,
School of Mathematical and Computer Sciences,
Heriot-Watt University)
Return of the Giant Hogweed: modelling the invasion of Britain by a dangerous alien plant
[ 講演概要 ]
As a result of changing climate and land use, as well as due to human intervention, increasingly species are moving to new abitats. We wish to understand the risk of invasive species entering new areas, and as an example consider the spread of Giant Hogweed (Heracleum mantegazzianum) from SW Asia in Great Britain, a species that has been damaging Britain's biodiversity since it was introduced in the 19th C and which is dangerous to human health. We construct a spatio-temporal stochastic model for its spread (both local and at distance) that takes account of covariates such as the heterogeneous land-cover and climate of the island. We then fit the model directly to observed data. Fitting the model was non-trivial and involved the use of Markov chain Monte Carlo techniques. The approach taken allows spatio-temporal predictions of the future spread of the weed can be made, consistent with the invasion history; it also allows the effect of varying habitats and climate to be understood. The approach we have taken can be generalised to other biological systems exhibiting stochastic variability, and there are clear parallels to epidemic models for the spread of disease within heterogeneous host populations.
[ 講演参考URL ]
http://www.ma.hw.ac.uk/~alexc/

### 2007年06月12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
Tian-Jun Li 氏 (University of Minnesota)
The Kodaira dimension of symplectic 4-manifolds
[ 講演概要 ]
Various results and questions about symplectic4-manifolds can be
formulated in terms of the notion of the Kodaira dimension. In particular,
we will discuss the classification and the geography problems. It is interesting
to understand how it behaves undersome basic constructions.Time permitting
we will discuss the symplectic birational aspect of this notion and speculate
how to extend it to higher dimensional manifolds.

### 2007年06月07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

Affine holonomy foliations

### 2007年06月06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

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/01.html

### 2007年06月05日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 117号室
Tea: 16:40 - 17:00 コモンルーム
Emmanuel Giroux 氏 (ENS Lyon)
Symplectic mapping classes and fillings
[ 講演概要 ]
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年06月04日(月)

#### 複素解析幾何セミナー

10:45-12:15   数理科学研究科棟(駒場) 128号室

### 2007年06月02日(土)

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 128号室

### 2007年05月30日(水)

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 118号室

### 2007年05月29日(火)

#### 作用素環セミナー

15:00-16:30   数理科学研究科棟(駒場) 002号室
Marta Asaeda 氏 (UC Riverside)
Galois groups and an obstruction to principal graphs of subfactors

#### 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.
[ 講演参考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.
[ 講演参考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 $M$.
[ 講演参考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.
[ 講演参考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.
[ 講演参考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.
[ 講演参考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