## 過去の記録

#### 統計数学セミナー

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
http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html
[ 参考URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/13.html

http://faculty.ms.u-tokyo.ac.jp/~fmsp/jpn/conferences/fmsp.html

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 270号室
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.

### 2013年01月26日(土)

#### 調和解析駒場セミナー

13:30-18:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.

(東京大学) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
[ 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 (JAPANESE) [ 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 infinity. This work extends previous results obtained by other authors to the general case. ### 2013年01月25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) 002号室 旧記録は、上記セミナーURLにあります。 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。 ### 2013年01月24日(木) #### GCOEセミナー 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. #### GCOEセミナー 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. ### 2013年01月23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 北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)までの情報が掲載されております。 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. #### 作用素環セミナー 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) #### GCOEセミナー 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 ] https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm #### GCOEセミナー 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. ### 2013年01月22日(火) #### Lie群論・表現論セミナー 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). #### トポロジー火曜セミナー 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. ### 2013年01月21日(月) #### トポロジー火曜セミナー 16:30-17:30 数理科学研究科棟(駒場) 002号室 日時と場所がいつもとは違います。 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 ] リー$\\mathfrak{g}$-葉層構造が与えられたとき,それに付随した構造リー環と呼 ばれる$\\mathfrak{g}$の部分リー環$\\mathfrak{h}$が定まる.本講演ではその逆, すなわち,リー環$\\mathfrak{g}$とその部分リー環$\\mathfrak{h}$が与えられた とき構造リー環が$\\mathfrak{h}$となるリー$\\mathfrak{g}$-葉層構造が存在す るかという問題についてて,$\\mathfrak{g}$がベキ零リー環の場合に説明をする. #### トポロジー火曜セミナー 17:30-18:30 数理科学研究科棟(駒場) 002号室 日時と場所がいつもとは違います。 石田 智彦 氏 (東京大学大学院数理科学研究科) Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE) [ 講演概要 ] Gambaudo and Ghys constructed linearly independent countably many quasi- morphisms on the group of area-preserving diffeomorphisms of the 2-disk from quasi-morphisms on braid groups. In this talk, we will explain that their construction is injective as a homomorphism between vector spaces of quasi-morphisms. If time permits, we introduce an application by Brandenbursky and K\\c{e} dra. #### 複素解析幾何セミナー 10:30-12:00 数理科学研究科棟(駒場) 126号室 雨宮 卓史 氏 (東大数理) コンパクト複素多様体への有理型写像の値分布について (JAPANESE) [ 講演概要 ] In a late paper of J. Noguchi and J. Winkelmann they showed the condition of being Kähler or non-Kähler of the image space to make a difference in the value distribution theory of meromorphic mappings into compact complex manifolds. In the present talk, we will discuss the order of meromorphic mappings to a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface (they are non-Kähler surfaces). For a general Hopf surface$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$. ### 2013年01月16日(水) #### 幾何コロキウム 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. #### 代数学コロキウム 18:00-19:00 数理科学研究科棟(駒場) 002号室 大久保俊 氏 (東京大学数理科学研究科) On differential modules associated to de Rham representations in the imperfect residue field case (ENGLISH) [ 講演概要 ] Let K be a CDVF of mixed characteristic (0,p) and G the absolute Galois group of K. When the residue field of K is perfect, Laurent Berger constructed a p-adic differential equation N_dR(V) for any de Rham representation V of G. In this talk, we will generalize his construction when the residue field of K is not perfect. We also explain some ramification properties of our N_dR, which are due to Adriano Marmora in the perfect residue field case. (本講演は「東京北京パリ数論幾何セミナー」として、インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.) #### 講演会 10:00-11:00 数理科学研究科棟(駒場) 123号室 R\'emi Boutonnet 氏 (ENS Lyon)$W^*$-superrigidity of mixing Gaussian actions of rigid groups (ENGLISH) #### 講演会 11:30-12:30 数理科学研究科棟(駒場) 123号室 Tim de Laat 氏 (University of Copenhagen) The Approximation Property for Lie groups (ENGLISH) #### 講演会 14:40-15:40 数理科学研究科棟(駒場) 118号室 Arnaud Brothier 氏 (KU Leuven) Unique Cartan decomposition for II$_1$factors arising from cross section equivalence relations (ENGLISH) #### 講演会 15:55-16:55 数理科学研究科棟(駒場) 118号室 Michael Hartglass 氏 (UC Berkeley) Rigid$C^*$tensor categories of bimodules over interpolated free group factors (ENGLISH) #### 講演会 17:10-18:10 数理科学研究科棟(駒場) 118号室 James Tener 氏 (UC Berkeley) Manifestly unitary conformal field theory (ENGLISH) #### GCOEセミナー 14:40-15:40 数理科学研究科棟(駒場) 118号室 このセミナーはMiniworkshop on Operator Algebras IIの一環として行われます Arnaud Brothier 氏 (KU Leuven) Unique Cartan decomposition for II$_1\$ factors arising from cross section equivalence relations (ENGLISH)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOEセミナー

15:55-16:55   数理科学研究科棟(駒場) 118号室
このセミナーはMiniworkshop on Operator Algebras IIの一環として行われます
Michael Hartglass 氏 (UC Berkeley)
TBA (ENGLISH)
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOEセミナー

16:00-17:00   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State University)
3-D Calderon's Problem with partial Dirichlet-to Neumann map (ENGLISH)
[ 講演概要 ]
We present new results for the uniqueness of recovery of a potential in three dimensional Calderon's problem with partial Dirichlet-to-Neumann map.
The proof is based on complex geometric optics solutions and the Radon transform.