## 過去の記録

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 117号室
2講演です
Vincent Maillot 氏 (Jussieu/京大数理研) 16:30-17:30
New applications of the arithmetic Riemann-Roch theorem
Don Blasius 氏 (UCLA) 17:45-18:45
Zariski Closures of Automorphic Galois Representations

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Stefano IACUS 氏 (Department of Economics Business and Statistics, University of Milan, Italy)
Inference problems for the standard and geometric telegraph process
[ 講演概要 ]
The telegraph process {X(t), t>0}, has been introduced (see Goldstein, 1951) as an alternative model to the Brownian motion B(t). This process describes a motion of a particle on the real line which alternates its velocity, at Poissonian times, from +v to -v. The density of the distribution of the position of the particle at time t solves the hyperbolic differential equation called telegraph equation and hence the name of the process. Contrary to B(t) the process X(t) has finite variation and continuous and differentiable paths. At the same time it is mathematically challenging to handle.

In this talk we will discuss inference problems for the estimation of the intensity of the Poisson process, either homogeneous and non homogeneous, from continuous and discrete time observations of X(t). We further discuss estimation problems for the geometric telegraph process S(t) = S(0) * exp{m - 0.5 * s^2) * t + s X(t)} where m is a known constant and s>0 and the intensity of the underlying Poisson process are two parameter of interest to be estimated. The geometric telegraph process has been recently introduced in Mathematical Finance to describe the dynamics of assets as an alternative to the usual geometric Brownian motion.

For discrete time observations we consider the "high frequency" approach, which means that data are collected at n+1 equidistant time points Ti=i * Dn, i=0,1,..., n, n*Dn = T, T fixed and such that Dn shrinks to 0 as n increases.

The process X(t) in non Markovian, non stationary and not ergodic thus we use approximation arguments to derive estimators. Given the complexity of the equations involved only estimators on the standard telegraph process can be studied analytically. We will also present a Monte Carlo study on the performance of the estimators for small sample size, i.e. Dn not shrinking to 0.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/16.html

### 2006年12月04日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Professor Burt Totaro

(University of Cambridge)

When does a curve move on a surface, especially over a finite field?

#### 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

Invariant CR-Laplacian type operator on the Silov boundary of a Siegel domain of rank one

### 2006年12月02日(土)

#### 東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 117号室

Spin Hall effect in metals and in insulators
[ 講演概要 ]
We theoretically predicted that by applying an electric field
to a nonmagnetic system, a spin current is induced in a transverse
direction [1,2]. This is called a spin Hall effect. After its
theoretical predictions on semiconductors [1,2], it has been
extensively studied theoretically and experimentally, partly due
to a potential application to spintronics devices.
In particular, one of the topics of interest is quantum spin
Hall systems, which are spin analogues of the quantum Hall systems.
These systems are insulators in bulk, and have gapless edge states
which carry a spin current. These edge states are characterized
by a Z_2 topological number [3] of a bulk Hamiltonian.
If the topological number is odd, there appear gapless edge states
which carry spin current. In my talk I will briefly review the
spin Hall effect including its experimental results and present
understanding. Then I will focus on the quantum spin Hall systems,
and explain various properties of the Z_2 topological number and
its relation to edge states.
[1] S. Murakami, N. Nagaosa, and S.-C. Zhang, Science 301, 1348 (2003).
[2] J. Sinova et al., Phys. Rev. Lett. 92, 126603 (2004)
[3] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802, 226801 (2005)

#### 東京無限可積分系セミナー

15:00-16:00   数理科学研究科棟(駒場) 117号室
Yshai Avishai 氏 (Ben-Gurion Univ. , 東大物工)
Disorder in Quantum Spin Hall Systems
[ 講演概要 ]
The quantum spin Hall phase is a novel state of matter with
topological properties. It might be realized in graphene and
probably also in type III semiconductors quantum wells.
Most recent theoretical treatments of this phase discuss its
occurrence in clean systems with perfect crystal symmetry.
In this seminar I will report on a recent work (in collaboration
with N. Nagaosa and M. Onoda) on disordered quantum spin Hall
systems. Following a brief introduction and background I will
discuss the persistence of topological terms also in disordered
systems (following a recent work of Sheng and Haldane) and
then present our results on the localization problem in two
dimensional systems. Due to spin-orbit interaction, there
is a metallic phase as is well known
for the symplectic ensemble. Together with the existence of
a topological term it leads to some surprising results regarding
the scaling theory of localization.

### 2006年12月01日(金)

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 126号室

von Neumann 環上の群作用
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm

#### 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)
James McKernan 氏 (UC Santa Barbara)
Finite generation of the canonical ring
[ 講演概要 ]
One of the most fundamental invariants of any smooth projective variety is the canonical ring, the graded ring of all global pluricanonical holomorphic n-forms. We explain some of the recent ideas behind the proof of finite generation of the canonical ring and its connection with the programme of Iitaka and Mori in the classification of algebraic varieties.

### 2006年11月30日(木)

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 126号室

von Neumann 環上の群作用
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm

### 2006年11月29日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Atomistic view of InAs quantum dot self-assembly from inside the growth chamber
[ 講演概要 ]
A 'quantum dot' is a tiny region of a solid, typically just nanometres in each direction, in which electrons can be confined. Semiconductor quantum dots are the focus of intense research geared towards exploiting this property for electronic devices. The most economical method of producing quantum dots is by self-assembly, where billions of dots can be grown simultaneously. The precise mechanism of self-assembly is not understood and is hampering efforts to control the characteristics of the dots. We have used a unique microscope to directly image semiconductor quantum dots as they are growing, which is a unique scanning tunnelling microscope placed within the molecular beam epitaxy growth chamber. The images elucidate the mechanism of InAs quantum dot nucleation on GaAs(001) substrate, demonstrating directly that not all deposited In is initially incorporated into the lattice, hence providing a large supply of material to rapidly form quantum dots via islands containing tens of atoms. kinetic Monte Carlo simulations based on first-principles calculations show that alloy fluctuations in the InGaAs wetting layer prior to are crucial in determining nucleation sites.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 122号室

von Neumann 環上の群作用
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm

#### 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

Gaussian K-Scheme について

### 2006年11月28日(火)

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 122号室

von Neumann 環上の群作用
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム

The Yamabe constants of infinite coverings and a positive mass theorem
[ 講演概要 ]
The {\\it Yamabe constant} $Y(M, C)$ of a given closed conformal manifold
$(M, C)$ is defined by the infimum of
the normalized total-scalar-curavarure functional $E$
among all metrics in $C$.
The study of the second variation of this functional $E$ led O.Kobayashi and Schoen
to independently introduce a natural differential-topological invariant $Y(M)$,
which is obtained by taking the supremum of $Y(M, C)$ over the space of all conformal classes.
This invariant $Y(M)$ is called the {\\it Yamabe invariant} of $M$.
For the study of the Yamabe invariant,
the relationship between $Y(M, C)$ and those of its conformal coverings
is important, the case when $Y(M, C)> 0$ particularly.
When $Y(M, C) \\leq 0$, by the uniqueness of unit-volume constant scalar curvature metrics in $C$,
the desired relation is clear.
When $Y(M, C) > 0$, such a uniqueness does not hold.
However, Aubin proved that $Y(M, C)$ is strictly less than
the Yamabe constant of any of its non-trivial {\\it finite} conformal coverings,
called {\\it Aubin's Lemma}.
In this talk, we generalize this lemma to the one for the Yamabe constant of
any $(M_{\\infty}, C_{\\infty})$ of its {\\it infinite} conformal coverings,
under a certain topological condition on the relation between $\\pi_1(M)$ and $\\pi_1(M_{\\infty})$.
For the proof of this, we aslo establish a version of positive mass theorem
for a specific class of asymptotically flat manifolds with singularities.

#### 代数解析火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室

[ 講演概要 ]

[ 参考URL ]
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html

### 2006年11月27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
Aleksandr G. Aleksandrov 氏 (Institute for Control Sciences, Moscow)
Logarithmic connections along Saito free divisors
[ 講演概要 ]
We develop an approach to the study of meromorphic connections with logarithmic poles along a Saito free divisor. In particular, basic properties of Christoffel symbols of such connections are established. We also compute the set of all integrable meromorphic connections with logarithmic poles and describe the corresponding spaces of horizontal sections for some examples of Saito free divisors including the discriminants of the minimal versal deformations of $A_2$- and of $A_3$-singularities, and a divisor in $\mathbf{C}^3$ which appeared in a work of M. Sato in the context of the theory of prehomogeneous spaces.

#### 講演会

16:00-18:00   数理科学研究科棟(駒場) 122号室

von Neumann 環上の群作用
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm

### 2006年11月24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)

ゆらぎをめぐる風景
[ 講演概要 ]
「ゆらぎ」とは、決まった規則がないままにゆらゆらと漂っているさまをあわらしている。わたしたちは、明確な動きの背後には規則があると自然に信じ、その規則を探ろうとするが、「ゆらゆら」に特別の意味をみようとしないだろう。ところで、それがゆえに、「ゆらゆら」の背後に何らかの構造が埋まっていることがわかったときには、衝撃が一段と大きい。
ゆらぎから新しい構造を抜き出した例を並べると、理論物理学史のひとつの断片ができる。講演前半部分では、このなかから20世紀前半のふたりの研究成果をアレンジしながら紹介したい。そのふたりとは、アインシュタインとオンサーガである。ゆらぎと対峙することで、マクロ側の普遍的法則を抽出し、直接みることができないミクロ側の性質を暴いた。これらの成果を踏まえて、講演後半部分では、ゆらぎの背後に新しい構造を見出そうとするわたしたちの最近の試みを紹介したい。

### 2006年11月22日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

A Note on Haplotype Estimation
[ 講演概要 ]
Haplotype information is important for many analyses but it is not always possible to obtain. This work is motivated to seek haplotype information from diploid population data. We present a new approach to know the haplotype information using classical methods. We do not intend to say that our method is better than the well-known EM based approache for practical purposes, but our way is attractive in some sense.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/15.html

### 2006年11月21日(火)

#### 応用解析セミナー

16:30-17:30   数理科学研究科棟(駒場) 122号室
いつもの曜日・時間・セミナー室と違いますのでご注意ください
Henrik SHAHGHOLIAN 氏 (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
[ 講演概要 ]
In this talk we present our study of the behavior of the singular set
$\\{u=|\\nabla u| =0\\}$ for solutions $u$ to the free boundary problem
$$\\Delta u = f\\chi_{\\{u\\geq 0\\} } -g\\chi_{\\{u<0\\}},$$
where $f$ and $g$ are H\\"older continuous functions, $f$ is positive and $f+g$ is negative. Such problems arise in an eigenvalue optimization for composite membranes.
We show that if for a singular point $z$ there are $r_0>0$, and $c_0>0$ such that the density assumption
$|\\{u< 0\\}\\cap B_r(z)|\\geq c_0 r2 \\forall r< r_0$
holds, then $z$ is isolated.

### 2006年11月20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

Advances and examples in the value distribution theory

### 2006年11月18日(土)

#### アジア数学史セミナー

16:30-18:00   数理科学研究科棟(駒場) 123号室

17 世紀西洋実用幾何学の東伝と徐光啓の数学観
─『測量法義』『測量異同』『句股義』を中心として─
[ 講演概要 ]
『測量法義』『測量異同』『句股義』は、いずれも 1607 年イエズス会士宣教師マテオ・リッチ(漢名:利瑪竇)と徐光啓によって刊行された『幾何原本』に続いて刊行された測量法および句股術に関する実用数学書である。『幾何原本』が演繹論理にもとづく“度数の宗”といわれる理論書であるのに対し、これら三部作は、いずれも実用レベルの応用数学の範疇に属するものである。

(2)『測量異同』は、呉敬の『九章算法比類大全』から六つの類型の問題を抽出し、その解法を通じて西法と中法の異同を論じる小論である。
(3)『句股義』は、中法と西法の比較を経て、中法の欠点として「ただ解法を知るのみで、その義は知らない(第能言其法、不能言其義也)」ことを取り上げ、選別された 15 問について、その“義”を論じたものである。

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

#### 東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

#### 東京無限可積分系セミナー

15:00-16:00   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]
ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。

### 2006年11月17日(金)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 118号室

Functional estimation of L'evy measure for jump-type processes
[ 講演概要 ]
Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html