## Seminar information archive

### 2007/06/27

#### Seminar on Probability and Statistics

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

Empirical likelihood method for time series analysis
[ Abstract ]
For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Stephen Lichtenbaum (Brown University)
The conjecture of Birch and Swinnerton-Dyer is misleading
[ Abstract ]
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.

#### Mathematical Finance

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

Selection and Performance Analysis of Asia-Pacific Hedge Funds

### 2007/06/25

#### Seminar on Geometric Complex Analysis

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

### 2007/06/22

#### Algebraic Geometry Seminar

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Qi Zhang (Missouri大学)
Projective varieties with nef anti-canonical divisors
[ Abstract ]
Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.

### 2007/06/21

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Richard D. Burstein (UC Berkeley)
Subfactors Arising from Symmetric Commuting Squares (following Jones/Sunder)

### 2007/06/20

#### Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

LeBrun-Mason 対応とその簡約について
[ Abstract ]
LeBrun と Mason は近年,正則円板の族に関するツイスター型の対応を発見した.彼らは次元の異なる二つのタイプの対応を示しているが,どちらも Penrose や Hitchin による解析的・局所的な理論の,非解析的・大域的な version とみなすことができる.一方 Penrose らの枠組みにおいては,次元の異なるツイスター型対応を関連づける次元簡約という現象が生じることが,Dunajski などによって最近研究されている.この講演では,LeBrun らの大域的な状況で簡約理論を展開しようとするときに生じる問題点を示し,ある種の特異性を導入することでこれを解決できることを説明したい.論文:math.DG/0701116

Deformations of generalized Kahler and Calabi-Yau structures
[ Abstract ]

#### Lectures

15:00-16:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Y.S. Chow (台湾中央研究院数学研究所)
On evolution games with local interaction and mutation

### 2007/06/19

#### Tuesday Seminar of Analysis

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

Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\\"odinger equation

#### Lie Groups and Representation Theory

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

Rigid local systemとその切断の積分表示,および接続係数
[ Abstract ]
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.

### 2007/06/18

#### Seminar on Geometric Complex Analysis

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

An intrinsic characterization of the unit polydisc

### 2007/06/16

#### Infinite Analysis Seminar Tokyo

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

Lie theoretic structures for the generalized symmetric groups
[ Abstract ]

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
[ Abstract ]
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.

### 2007/06/15

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
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。

### 2007/06/13

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Walter Strauss (Brown University)
[ Abstract ]
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.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

#### Mathematical Biology Seminar

14:40-15:40   Room #123 (Graduate School of Math. Sci. Bldg.)
Alex Cook (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
[ Abstract ]
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.
[ Reference URL ]
http://www.ma.hw.ac.uk/~alexc/

### 2007/06/12

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tian-Jun Li (University of Minnesota)
The Kodaira dimension of symplectic 4-manifolds
[ Abstract ]
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.

### 2007/06/07

#### Operator Algebra Seminars

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

Affine holonomy foliations

### 2007/06/06

#### Seminar on Probability and Statistics

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

[ Abstract ]

[ Reference URL ]
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.)
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.

### 2007/06/04

#### Seminar on Geometric Complex Analysis

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

### 2007/06/02

#### Mathematical Finance

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

### 2007/05/30

#### Mathematical Finance

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

### 2007/05/29

#### Operator Algebra Seminars

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

[ Abstract ]

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
[ Abstract ]

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、