過去の記録

過去の記録 ~02/17本日 02/18 | 今後の予定 02/19~

代数幾何学セミナー

15:00-16:25   数理科学研究科棟(駒場) 126号室
Stefan Kebekus 氏 氏 (Mathematisches Institut
Universität zu Köln
)
Rationally connected
foliations

2006年12月07日(木)

講演会

13:00-14:30   数理科学研究科棟(駒場) 056号室
大学院イニシアティブ特別講演会(平成18年度-冬)
組織委員:儀我美一(東京大学大学院数理科学研究科)連絡先:丸菱美佳 (labgiga@ms.u-tokyo.ac.jp)

Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
[ 講演概要 ]
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.

We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.

Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
[ 講演参考URL ]
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
山下真 氏 (東大数理)
An introduction to analytic endomotives (after Connes-Consani-Marcolli)

2006年12月06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
横山悦郎 氏 (学習院大学)
Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model
[ 講演概要 ]
Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.

In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

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.
[ 講演参考URL ]
http://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
伊師英之 氏 (横浜市立大学)
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
村上 修一 氏 (東大物工)
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
竹崎正道 氏 (UCLA)
von Neumann 環上の群作用
[ 講演参考URL ]
http://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
竹崎正道 氏 (UCLA)
von Neumann 環上の群作用
[ 講演参考URL ]
http://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
塚本 史郎 氏 (東京大学生産技術研究所)
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.
[ 講演参考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
竹崎正道 氏 (UCLA)
von Neumann 環上の群作用
[ 講演参考URL ]
http://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
楠岡 成雄 氏 (東京大)
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
竹崎正道 氏 (UCLA)
von Neumann 環上の群作用
[ 講演参考URL ]
http://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
芥川 和雄 氏 (東京理科大学理工学部)
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
打越 敬祐 氏 (防衛大学校)
非圧縮性完全流体の特異初期値問題
[ 講演概要 ]
題材は流体力学ですが,内容的には超局所解析の考え方を駆使する問題
[ 講演参考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
作用素環論連続講演 2006年11月27日(月)~12月1日(金)
毎日午後4時~6時 122号室(月~水),126号室(木~金)

竹崎正道 氏 (UCLA)
von Neumann 環上の群作用
[ 講演参考URL ]
http://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)
佐々真一 氏 (東京大学・大学院総合文化研究科)
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
鎌谷 研吾 氏 (東京大学大学院数理科学研究科)
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.
[ 講演参考URL ]
http://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
野口潤次郎 氏 (東大数理)
Advances and examples in the value distribution theory

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