## Seminar information archive

#### Lectures

17:30-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
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.

#### Lectures

17:30-18:30   Room #122 (Graduate School of Math. Sci. Bldg.)
Antonio Degasperis (La Sapienza, University of Rome)
Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)
[ Abstract ]
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.

#### Lectures

09:45-10:45   Room #123 (Graduate School of Math. Sci. Bldg.)
Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

#### Lectures

11:00-12:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Gerardo Morsella (Univ. Roma II)
Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

#### Lectures

13:30-14:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Joav Orovitz (Ben-Gurion Univ.)
Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

#### Lectures

14:45-15:45   Room #118 (Graduate School of Math. Sci. Bldg.)
Nicola Watson (Univ. Toronto)
Noncommutative covering dimension (ENGLISH)

#### Lectures

16:00-17:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. G\"ottingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)

#### Lectures

17:15-18:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroki Asano (Univ. Tokyo)
Group actions with Rohlin property (ENGLISH)

#### GCOE Seminars

16:00-17:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Marcel Bischoff (Univ. Göttingen)
Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-3.htm

### 2013/01/28

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Taiji MARUGAME (MS U-Tokyo)
Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)

#### Seminar on Probability and Statistics

13:00-14:10   Room #006 (Graduate School of Math. Sci. Bldg.)
Ernst August Frhr. v. Hammerstein (Albert-Ludwigs-Universität Freiburg)
Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)
[ Abstract ]
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
[ Reference 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 Seminars

16:00-17:00   Room #270 (Graduate School of Math. Sci. Bldg.)
The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)
[ Abstract ]
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.

### 2013/01/26

#### Harmonic Analysis Komaba Seminar

13:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Guorong, Hu
(Tokyo Univesity) 13:30-15:00
On Triebel-Lizorkin spaces on Stratified Lie groups
(ENGLISH)
[ Abstract ]
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 $G$,