## Seminar information archive

Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～

#### thesis presentations

**Makoto MIURA**(Guraduate School of Mathematical Sciences the University of Tokyo)

Hibi toric varieties and mirror symmetry (JAPANESE)

#### thesis presentations

**Tomohiko ISHIDA**(Guraduate School of Mathematical Sciences the University of Tokyo)

Quasi-morphisms on the group of area-preserving diffeomorphisms of the 2-disk (JAPANESE)

#### GCOE Seminars

**Asaf Iskandarov**(Lenkaran State University)

Identification of quantum potentials in the Schrodinger equation (ENGLISH)

In this lecture I will consider the identification problem of determining the unknown time-dependent coefficients of nonlinear Schrodinger equation.We applied the variational method and studied the correctness of direct and identification problems. We find a necessary condition of the solution and give a stable methed for solution.

#### Seminar on Probability and Statistics

**Stefano M. Iacus**(Dipartimento di Economia, Managemente Metodi Quantitativi Universita' di Milano)

On L^p model selection for discretely observed diffusion processes (JAPANESE)

The LASSO is a widely used L^2 statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. In the first part of the seminar, we introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. In the second part of the seminar we present general L^p approach for stochastic differential equations with small diffusion noise. Finally, we present simulated and real data analysis to provide some evidence on the applicability of this method.

FMSP Lectures

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

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/14.html

### 2013/02/05

#### Lie Groups and Representation Theory

**Nizar Demni**(Université de Rennes 1)

Dunkl processes assciated with dihedral systems, II (ENGLISH)

I'll focus on dihedral systems and its semi group density. I'll show how one can write down this density using probabilistic techniques and give some interpretation using spherical harmonics. I'll also present some results attempting to get a close formula for the density: the main difficulty comes then from the inversion (in composition sense) of Tchebycheff polynomials of the first kind in some neighborhood. Finally, I'll display expressions through known special functions for even dihedral groups, and the unexplained connection between the obtained formulas and those of Ben Said-Kobayashi-Orsted.

### 2013/02/04

#### Lie Groups and Representation Theory

**Nizar Demni**(Université de Rennes 1)

Dunkl processes assciated with dihedral systems, I (ENGLISH)

I'll first give a brief and needed account on root systems and finite reflection groups. Then, I'll introduce Dunkl operators and give some properties. Once I'll do, I'll introduce Dunkl processes and their continuous components, so-called radial Dunkl processes. The latter generalize eigenvalues processes of some matrix-valued processes and reduces to reflected Brownian motion in Weyl chambers. Besides, Brownian motion in Weyl chambers corresponds to all multiplicity values equal one are constructed from a Brownian motion killed when it first hits the boundary of the Weyl chamber using the unique positive harmonic function (up to a constant) on the Weyl chamber. In the analytic side, determinantal formulas appear and are related to harmonic analysis on the Gelfand pair (Gl(n,C), U(n)). This is in agreement on the one side with the so-called reflection principle in stochastic processes theory and matches on the other side the so-called shift principle introduced by E. Opdam. Finally, I'll discuss the spectacular result of Biane-Bougerol-O'connell yielding to a Duistermaat-Heckman distribution for non crystallographic systems.

### 2013/01/30

#### Geometry Colloquium

**Ryoichi Kobayashi**(Nagoya University)

Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)

We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.

The idea of the proof is :

- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,

and then :

- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.

#### Lectures

**Antonio Degasperis**(La Sapienza, University of Rome)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

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

**Antonio Degasperis**(La Sapienza, University of Rome)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

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

**Antonio Degasperis**(La Sapienza, University of Rome)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

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

**Marzieh Forough**(Ferdowsi Univ. Mashhad)

Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

#### Lectures

**Gerardo Morsella**(Univ. Roma II)

Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

#### Lectures

**Joav Orovitz**(Ben-Gurion Univ.)

Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

#### Lectures

**Nicola Watson**(Univ. Toronto)

Noncommutative covering dimension (ENGLISH)

#### Lectures

**Marcel Bischoff**(Univ. G\"ottingen)

Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)

#### Lectures

**Hiroki Asano**(Univ. Tokyo)

Group actions with Rohlin property (ENGLISH)

#### GCOE Seminars

**Marcel Bischoff**(Univ. Göttingen)

Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)

[ Reference URL ]

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

### 2013/01/28

#### Seminar on Geometric Complex Analysis

**Taiji MARUGAME**(MS U-Tokyo)

Renormalized Chern-Gauss-Bonnet formula for complete Kaehler-Einstein metrics (JAPANESE)

#### Seminar on Probability and Statistics

**Ernst August Frhr. v. Hammerstein**(Albert-Ludwigs-Universität Freiburg)

Laplace and Fourier based valuation methods in exponential Levy models (JAPANESE)

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

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

**Bernadette Miara**(Universite Paris-Est)

The obstacle problem for a shallow membrane-Justification and stability (ENGLISH)

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

**Guorong, Hu**

(Tokyo Univesity) 13:30-15:00

On Triebel-Lizorkin spaces on Stratified Lie groups

(ENGLISH)

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.

**Michiaki, Onodera**(Kyushu University) 15:30-17:00

Profiles of solutions to an integral system related to

the weighted Hardy-Littlewood-Sobolev inequality

(JAPANESE)

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.

### 2013/01/25

#### Colloquium

**Mitsuhiro T. Nakao**(Sasebo National College of Technology)

State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)

### 2013/01/24

#### GCOE Seminars

**Leevan Ling**(Hong Kong Baptist University)

Global radial basis functions method and some adaptive techniques (ENGLISH)

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 Seminars

**Christian Clason**(Graz University)

Parameter identification problems with non-Gaussian noise (ENGLISH)

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.

### 2013/01/23

#### Seminar on Mathematics for various disciplines

**Chun Liu**(Pennsylvania State University)

Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)

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.

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