## 過去の記録

#### 講演会

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.

#### 講演会

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)

#### 講演会

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)

#### 講演会

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)

#### 講演会

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)

#### 講演会

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)

#### 講演会

17:15-18:15   数理科学研究科棟(駒場) 118号室

Group actions with Rohlin property (ENGLISH)

#### GCOEセミナー

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 ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm

### 2013年01月28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) 126号室

[ 講演概要 ]

#### 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 $G$,

### 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

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.