## Seminar information archive

#### Mathematical Finance

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

Gaussian K-Scheme について

### 2006/11/28

#### Lectures

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

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

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

The Yamabe constants of infinite coverings and a positive mass theorem
[ Abstract ]
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.

#### Tuesday Seminar of Algebraic Analysis

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

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

### 2006/11/27

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Aleksandr G. Aleksandrov (Institute for Control Sciences, Moscow)
Logarithmic connections along Saito free divisors
[ Abstract ]
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.

#### Lectures

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

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

### 2006/11/24

#### Colloquium

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

ゆらぎをめぐる風景
[ Abstract ]
「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。

### 2006/11/22

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

A Note on Haplotype Estimation
[ Abstract ]
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.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/15.html

### 2006/11/21

#### Applied Analysis

16:30-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Henrik SHAHGHOLIAN (王立工科大学、ストックホルム)
Composite membrane and the structure of the singular set
[ Abstract ]
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.

### 2006/11/20

#### Seminar on Geometric Complex Analysis

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

Advances and examples in the value distribution theory

### 2006/11/18

#### Seminar for Mathematical Past of Asia

16:30-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)

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─
[ Abstract ]
『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。

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

#### Infinite Analysis Seminar Tokyo

13:30-14:30   Room #117 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

#### Infinite Analysis Seminar Tokyo

15:00-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
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。

### 2006/11/17

#### Seminar on Probability and Statistics

15:00-16:10   Room #118 (Graduate School of Math. Sci. Bldg.)

Functional estimation of L'evy measure for jump-type processes
[ Abstract ]
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.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html

### 2006/11/16

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

The large time behavior of graphical surfaces in the mean curvature flow
[ Abstract ]
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.

#### Operator Algebra Seminars

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

### 2006/11/15

#### Lectures

16:30-18:00   Room #117 (Graduate School of Math. Sci. Bldg.)
Pierre Berthelot (Rennes大学)
Crystalline complexes and D-modules

#### Mathematical Finance

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

### 2006/11/14

#### Tuesday Seminar on Topology

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

[ Abstract ]
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.

### 2006/11/13

#### Seminar on Geometric Complex Analysis

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

Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds

#### Algebraic Geometry Seminar

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

Hom stacks and Picard stacks

### 2006/11/10

#### Geometry Seminar

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

#### Tuesday Seminar on Topology

17:40-19:00   Room #118 (Graduate School of Math. Sci. Bldg.)

WRT invariant for Seifert manifolds and modular forms
[ Abstract ]
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.

### 2006/11/09

#### Operator Algebra Seminars

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

Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)