## Seminar information archive

Seminar information archive ～05/23｜Today's seminar 05/24 | Future seminars 05/25～

#### 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.

#### Operator Algebra Seminars

**David Evans**(Cardiff University)

Exotic subfactors and conformal field theories (ENGLISH)

#### GCOE Seminars

**David Evans**(Cardiff University)

Exotic subfactors and conformal field theories (ENGLISH)

[ Reference URL ]

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

#### GCOE Seminars

**Volker Schulz**(Trier University)

Shape and topology optimization in application (ENGLISH)

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.

### 2013/01/22

#### Lie Groups and Representation Theory

**Simon Goodwin**(Birmingham University)

Representation theory of finite W-algebras (ENGLISH)

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).

#### Tuesday Seminar on Topology

**Jarek Kedra**(University of Aberdeen)

On the autonomous metric of the area preserving diffeomorphism

of the two dimensional disc. (ENGLISH)

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.

### 2013/01/21

#### Tuesday Seminar on Topology

**Naoki Kato**(The University of Tokyo

)

Lie foliations transversely modeled on nilpotent Lie

algebras

(JAPANESE)

To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra

$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the

structure Lie algabra. In this talk, we will explain the inverse problem,

that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a

Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}

$, under the assumption that $\\mathfrak{g}$ is nilpotent.

#### Tuesday Seminar on Topology

**Tomohiko Ishida**(The University of Tokyo)

Quasi-morphisms on the group of area-preserving diffeomorphisms of

the 2-disk

(JAPANESE)

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.

#### Seminar on Geometric Complex Analysis

**Takushi AMEMIYA**(MS U-Tokyo)

Value distribution of meromorphic mappings to compact complex manifolds (JAPANESE)

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 $\rho_{f}\geq 2$.

### 2013/01/16

#### Geometry Colloquium

**Yuuji Tanaka**(Kyoto University)

A construction of Spin(7)-instantons (JAPANESE)

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.

#### Number Theory Seminar

**Shun Ohkubo**(University of Tokyo)

On differential modules associated to de Rham representations in the imperfect residue field case (ENGLISH)

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.

#### Lectures

**R\'emi Boutonnet**(ENS Lyon)

$W^*$-superrigidity of mixing Gaussian actions of rigid groups (ENGLISH)

#### Lectures

**Tim de Laat**(University of Copenhagen)

The Approximation Property for Lie groups (ENGLISH)

#### Lectures

**Arnaud Brothier**(KU Leuven)

Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

#### Lectures

**Michael Hartglass**(UC Berkeley)

Rigid $C^*$ tensor categories of bimodules over interpolated

free group factors (ENGLISH)

#### Lectures

**James Tener**(UC Berkeley)

Manifestly unitary conformal field theory (ENGLISH)

#### GCOE Seminars

**Arnaud Brothier**(KU Leuven)

Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOE Seminars

**Michael Hartglass**(UC Berkeley)

TBA (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOE Seminars

**Oleg Emanouilov**(Colorado State University)

3-D Calderon's Problem with partial Dirichlet-to Neumann map (ENGLISH)

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.

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