過去の記録 ~09/27本日 09/28 | 今後の予定 09/29~


17:30-18:30   数理科学研究科棟(駒場) 122号室
Antonio Degasperis 氏 (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ 講演概要 ]
A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.


09:45-10:45   数理科学研究科棟(駒場) 123号室
Marzieh Forough 氏 (Ferdowsi Univ. Mashhad)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)


11:00-12:00   数理科学研究科棟(駒場) 123号室
Gerardo Morsella 氏 (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)


13:30-14:30   数理科学研究科棟(駒場) 123号室
Joav Orovitz 氏 (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)


14:45-15:45   数理科学研究科棟(駒場) 118号室
Nicola Watson 氏 (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)


16:00-17:00   数理科学研究科棟(駒場) 118号室
Marcel Bischoff 氏 (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)


17:15-18:15   数理科学研究科棟(駒場) 118号室
浅野裕樹 氏 (東大数理)
Group actions with Rohlin property (ENGLISH)


16:00-17:00   数理科学研究科棟(駒場) 118号室
このセミナーはMiniworkshop on Operator Algebras IIIの一環として行われます
Marcel Bischoff 氏 (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ 参考URL ]



10:30-12:00   数理科学研究科棟(駒場) 126号室
丸亀 泰二 氏 (東大数理)
完備Kaehler-Einstein計量に対する繰り込みGauss-Bonnet公式 (JAPANESE)
[ 講演概要 ]


13:00-14:10   数理科学研究科棟(駒場) 006号室
FMSP共催.参加をご希望される方は鎌谷 (阪大基礎工); kamatani at sigmath.es.osaka-u.ac.jpまでご連絡ください.
Ernst August Frhr. v. Hammerstein 氏 (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
[ 講演概要 ]
A fundamental problem in mathematical finance is the explicit computation of expectations which arise as prices of derivatives. Closed formulas that can easily be evaluated are typically only available in models driven by a Brownian motion. If one considers more sophisticated jump-type Levy processes as drivers, the problem quickly becomes rather nontrivial and complicated. Starting with the paper of Carr and Madan (1999) and the PhD thesis of Raible (2000), Laplace and Fourier based methods have been used to derive option pricing formulas that can be evaluated very efficiently numerically. In this talk we review the initial idea of Raible (2000), show how it can be generalized and discuss under which precise mathematical assumptions the Laplace and Fourier approach work. We then give several examples of specific options and Levy models to which the general framework can be applied to. In the last part, we present some formulas for pricing options on the supremum and infimum of the asset price process that use the Wiener-Hopf factorization.

FMSP Lectures
[ 参考URL ]



16:00-17:00   数理科学研究科棟(駒場) 270号室
Bernadette Miara 氏 (Universite Paris-Est)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
[ 講演概要 ]
This lecture is twofold.
In the first part we recall the difference between the three-dimensional unilateral contact problem (the so-called Signorini problem) and its two-dimensional limit (the obstacle problem) in the case of an elastic shell as it was considered in [1] and [2].
In the second part we consider a simplified set of equations which describe the equilibrium equations of a shallow membrane (as justified in [3]) in contact with a plane obstacle and we study the stability of the contact zone with respect to small changes of the applied force, which amounts to studying the variation of the boundary of this contact zone. This kind of stability was first established in the scalar case for the Laplacian operator [4] then for the biharmonic operator [5]. The interest of the vectorial case considered here is due to the coupling effects between the in-plane and the transverse components of the displacement field in the framework of linearized Marguerre-von K´arm´an shell model.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.



13:30-18:00   数理科学研究科棟(駒場) 128号室
胡 国栄
(東京大学) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
[ 講演概要 ]
We introduce the notion of Triebel-Lizorkin spaces
$\\dot{F}^{s}_{p,q}(G)$ on a stratified Lie group $G$
in terms of a Littlewood-Paley-type decomposition
with respect to a sub-Laplacian $\\mathscr{L}$ of $G$,
for $s \\in \\mathbb{R}$, $0

We show that the scale of these spaces is actually independent of
the precise choice of the sub-Laplacian
and the Littlewood-Paley-type decomposition.
As we shall see, many properties of the classical
Triebel-Lizorkin spaces on $\\mathbb{R}^{n}$, e.g.,
lifting property, embeddings and dual property,
can be extended to the setting of stratified Lie groups
without too much effort.
We then study the boundedness of convolution operators
on these spaces and finally,
we obtain a Hormander type spectral multipliers theorem.

小野寺 有紹
(九州大学) 15:30-17:00
Profiles of solutions to an integral system related to
the weighted Hardy-Littlewood-Sobolev inequality
[ 講演概要 ]
We study the Euler-Lagrange system for a variational problem
associated with the weighted Hardy-Littlewood-Sobolev inequality of
Stein and Weiss.
We show that all the nonnegative solutions to the system are radially
symmetric and have particular profiles around the origin and the
This work extends previous results obtained by other authors to the
general case.



16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。

中尾充宏 氏 (佐世保工業高等専門学校(校長)・九州大学名誉教授)
偏微分方程式の解に対する数値的検証の現状と動向 (JAPANESE)
[ 講演概要 ]
本講演では、非線形偏微分方程式の解に対する 数値的検証法(精度保証付き数値計算法)について、現在までの研究の状況を概観し、今後の研究動向を考察する。特に、講演者らによってこれまでに得られた楕円型方程式を中心とする結果を総括し、最近の発展方程式に関する拡張についてもその現状と展望を述べる。さらに近年の力学系研究グループによる偏微分方程式に対する結果にも言及しその動向を探る。



14:00-15:00   数理科学研究科棟(駒場) 056号室
Leevan Ling 氏 (Hong Kong Baptist University)
Global radial basis functions method and some adaptive techniques (ENGLISH)
[ 講演概要 ]
It is now commonly agreed that the global radial basis functions method is an attractive approach for approximating smooth functions. This superiority does not come free; one must find ways to circumvent the associated problem of ill-conditioning and the high computational cost for solving dense matrix systems.
In this talk, we will overview different variants of adaptive methods for selecting proper trial subspaces so that the instability caused by inappropriately shaped parameters were minimized.


15:00-16:00   数理科学研究科棟(駒場) 056号室
Christian Clason 氏 (Graz University)
Parameter identification problems with non-Gaussian noise (ENGLISH)
[ 講演概要 ]
For inverse problems subject to non-Gaussian (such as impulsive or uniform) noise, other data fitting terms than the standard L^2 norm are statistically appropriate and more robust. However, these formulations typically lead to non-differentiable problems which are challenging to solve numerically. This talk presents an approach that combines an iterative smoothing procedure with a semismooth Newton method, which can be applied to parameter identification problems for partial differential equations. The efficiency of this approach is illustrated for the inverse potential problem.



10:30-11:30   数理科学研究科棟(駒場) 056号室
Chun Liu 氏 (Pennsylvania State University)
Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)
[ 講演概要 ]
The problems of distribution and transport of charged particles and ionic fluids are ubiquitous in our daily life and crucial in physical and biological applications. The multiscale and multiphysics nature of these problems provides major challenges and motivations.
In this talk, I will present the derivation of the continuum models such as Poisson-Nerest-Planck (PNP) system from the kinetic formulations.
Our focus is on the multiple species solutions and the corresponding boundary conditions for bounded containers.


16:30-18:00   数理科学研究科棟(駒場) 118号室
David Evans 氏 (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)


16:30-18:00   数理科学研究科棟(駒場) 118号室
David Evans 氏 (Cardiff University)
Exotic subfactors and conformal field theories (ENGLISH)
[ 参考URL ]


17:15-18:15   数理科学研究科棟(駒場) 370号室
Volker Schulz 氏 (Trier University)
Shape and topology optimization in application (ENGLISH)
[ 講演概要 ]
Shape and topology optimization currently is of high interest for applications but also from a theoretical point of view. Recently, new developments in the shape calculus and in a related calculus for topology have enabled successful solutions of challenging optimization problems. This talk specifically reports on parameter free shape optimization in aerodynamics, thermoelastics and acoustics. Furthermore, novel results for the elastic topology optimization of the interior of wings are presented. We will try to give insight into the challenges in this field as well as the numerical solution approaches.



16:30-18:00   数理科学研究科棟(駒場) 126号室
Simon Goodwin 氏 (Birmingham University)
Representation theory of finite W-algebras (ENGLISH)
[ 講演概要 ]
There has been a great deal of recent research interest in finite W-algebras motivated by important connection with primitive ideals of universal enveloping algebras and applications in mathematical physics.
There have been significant breakthroughs in the rerpesentation theory of finite W-algebras due to the research of a variety of mathematicians.
In this talk, we will give an overview of the representation theory of finite W-algebras focussing on W-algebras associated to classical Lie algebras (joint with J. Brown) and W-algebras associated to general linear Lie superalgebras (joint with J. Brown and J. Brundan).


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
Jarek Kedra 氏 (University of Aberdeen)
On the autonomous metric of the area preserving diffeomorphism
of the two dimensional disc. (ENGLISH)
[ 講演概要 ]
Let D be the open unit disc in the Euclidean plane and let
G:=Diff(D, area) be the group of smooth compactly supported
area-preserving diffeomorphisms of D. A diffeomorphism is called
autonomous if it is the time one map of the flow of a time independent
vector field. Every diffeomorphism in G is a composition of a number
of autonomous diffeomorphisms. The least amount of such
diffeomorphisms defines a norm on G. In the talk I will investigate
geometric properties of such a norm.

In particular I will construct a bi-Lipschitz embedding of the free
abelian group of arbitrary rank to G. I will also show that the space
of homogeneous quasi-morphisms vanishing on all autonomous
diffeomorphisms in G is infinite dimensional.

This is a joint work with Michael Brandenbursky.



16:30-17:30   数理科学研究科棟(駒場) 002号室
加藤 直樹 氏 (東京大学大学院数理科学研究科)
ベキ零リー環を横断構造に持つリー葉層構造について (JAPANESE)
[ 講演概要 ]


17:30-18:30   数理科学研究科棟(駒場) 002号室
石田 智彦 氏 (東京大学大学院数理科学研究科)
Quasi-morphisms on the group of area-preserving diffeomorphisms of
the 2-disk
[ 講演概要 ]
Gambaudo and Ghys constructed linearly independent countably many quasi-
morphisms on the group of area-preserving diffeomorphisms of the 2-disk
from quasi-morphisms on braid groups.
In this talk, we will explain that their construction is injective as a
homomorphism between vector spaces of quasi-morphisms.
If time permits, we introduce an application by Brandenbursky and K\\c{e}


10:30-12:00   数理科学研究科棟(駒場) 126号室
雨宮 卓史 氏 (東大数理)
コンパクト複素多様体への有理型写像の値分布について (JAPANESE)
[ 講演概要 ]
In a late paper of J. Noguchi and J. Winkelmann they showed the condition of being Kähler or non-Kähler of the image space to make a difference in the value distribution theory of meromorphic mappings into compact complex manifolds. In the present talk, we will discuss the order of meromorphic mappings to a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface (they are non-Kähler surfaces). For a general Hopf surface $S$, we prove that there exists a differentiably non-degenerate holomorphic mapping $f:\mathbf{C}^2 \to S$ whose order satisfies $\rho_{f}\leq 1$. For an Inoue surface $S'$, we prove that every non-constant meromorphic mapping $f:\mathbf{C}^n \to S'$ is holomorphic and its order satisfies $\rho_{f}\geq 2$.



10:30-12:00   数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
田中祐二 氏 (京都大学)
A construction of Spin(7)-instantons (JAPANESE)
[ 講演概要 ]
Spin(7)-instantons are elliptic gauge fields on 8-dimensional Spin(7)-manifolds, which minimize the Yang-Mills action. Analytic properties of Spin(7)-instantons have been studied by Gang Tian and others, but little was known about the existence of examples of Spin(7)-instantons other than an Oxford Ph.D thesis by Christopher Lewis in 1998.
There are two known constructions of compact Spin(7)-manifolds both obtained by Dominic Joyce. The first one begins with a torus orbifold of a special kind with non-isolated singularities. The Spin(7)-manifold is obtained by resolving the singularities with the aid of algebraic geometry techniques. The second one begins with a Calabi-Yau four-orbifold with isolated singular points of a special kind and an anti-holomorphic involution fixing only the singular points. The Spin(7)-manifold is obtained by gluing ALE Spin(7)-manifolds with anti-holomorphic involutions fixing only the origins to each singular point.
Christopher Lewis studied the problem of constructing Spin(7)-instantons on Spin(7)-manifolds coming from Joyce's first construction.
This talk describes a general construction of Spin(7)-instantons on examples of compact Spin(7)-manifolds coming from Joyce's second construction. Starting with certain Hermitian-Einstein connections on the Calabi-Yau four-orbifold and on ALE Spin(7)-manifolds, we glue them together simultaneously with the underlying pieces to make a Spin(7)-instanton on the compact Spin(7)-manifold by Joyce.

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