## Seminar information archive

Seminar information archive ～10/21｜Today's seminar 10/22 | Future seminars 10/23～

### 2010/04/19

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

制限型体積と因子的ザリスキー分解

**松村 慎一**(東大数理)制限型体積と因子的ザリスキー分解

[ Abstract ]

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

#### Lectures

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

**Cyrill Muratov**(New Jersey Institute of Technology)Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

[ Abstract ]

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Loewner's theory on complex manifolds (ENGLISH)

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**Filippo Bracci**(Universita di Roma, ``Tor Vergata'')Loewner's theory on complex manifolds (ENGLISH)

[ Abstract ]

Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

[ Reference URL ]Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

#### Mathematical Biology Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

**Horoshi HAENO**(Memorial Sloan-Kettering Cancer Center)骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

### 2010/04/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

**MIYAZAKI Tadashi**(Tokyo Univ. of agr. and indus.) 13:30-14:30Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

**HARASHITA Shushi**(Yokohama National Univ.) 15:00-16:00A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

### 2010/04/15

#### Lie Groups and Representation Theory

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Generalized hypergeometric systems (ENGLISH)

**Uuganbayar Zunderiya**(Nagoya University)Generalized hypergeometric systems (ENGLISH)

[ Abstract ]

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Long-time behaviour of solutions of a forward-backward parabolic equation

**Alberto Tesei**(University of Rome 1)Long-time behaviour of solutions of a forward-backward parabolic equation

[ Abstract ]

We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.

We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.

#### Classical Analysis

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

The Galois group of projectively isomonodromic deformations (ENGLISH)

**Claude Mitschi**(Univ. de Strasbourg)The Galois group of projectively isomonodromic deformations (ENGLISH)

[ Abstract ]

Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.

Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.

### 2010/04/14

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The cohomological weighted fundamental lemma

**Gerard Laumon**(CNRS, Universite Paris XI - Orsay)The cohomological weighted fundamental lemma

[ Abstract ]

Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.

(本講演は「東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とIHESとの双方向同時中継で行います。)

Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.

(本講演は「東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とIHESとの双方向同時中継で行います。)

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

**Etsuro Yokoyama**(Gakushuin University)Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

### 2010/04/13

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Torsors in non-commutative geometry (ENGLISH)

**Christian Kassel**(CNRS, Univ. de Strasbourg)Torsors in non-commutative geometry (ENGLISH)

[ Abstract ]

G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.

G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Strichartz estimates and the Isozaki-Kitada parametrix

on asymptotically hyperbolic manifolds (ENGLISH)

**Jean-Marc Bouclet**(Toulouse University, France)Strichartz estimates and the Isozaki-Kitada parametrix

on asymptotically hyperbolic manifolds (ENGLISH)

### 2010/04/12

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**千葉 優作**(東大数理)Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/04/06

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On the characters of tempered modules of affine Hecke

algebras of classical type

**加藤周**(京都大学)On the characters of tempered modules of affine Hecke

algebras of classical type

[ Abstract ]

We present an inductive algorithm to compute the characters

of tempered modules of an affine Hecke algebras of classical

types, based on a new class of representations which we call

"tempered delimits". They have some geometric origin in the

eDL correspondence.

Our new algorithm has some advantage to the Lusztig-Shoji

algorithm (which also describes the characters of tempered

modules via generalized Green functions) in the sense it

enables us to tell how the characters of tempered modules

changes as the parameters vary.

This is a joint work with Dan Ciubotaru at Utah.

We present an inductive algorithm to compute the characters

of tempered modules of an affine Hecke algebras of classical

types, based on a new class of representations which we call

"tempered delimits". They have some geometric origin in the

eDL correspondence.

Our new algorithm has some advantage to the Lusztig-Shoji

algorithm (which also describes the characters of tempered

modules via generalized Green functions) in the sense it

enables us to tell how the characters of tempered modules

changes as the parameters vary.

This is a joint work with Dan Ciubotaru at Utah.

### 2010/04/05

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

From Lang's Conjecture to finiteness properties of Torelli groups

**Alexandru Dimca**(Université Nice-Sophia Antipolis)From Lang's Conjecture to finiteness properties of Torelli groups

[ Abstract ]

First we recall one of Lang's conjectures in diophantine geometry

on the interplay between subvarieties and translated subgroups in a

commutative algebraic group

(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,

a powerful tool in the study of fundamental groups of algebraic varieties.

Finally, using the two ingredients above, we show that the Torelli

groups $T_g$

have some surprising finiteness properties for $g>3$.

In particular, we show that for any subgroup $N$ in $T_g$ containing

the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$

is finite dimensional.

All the details are available in our joint preprint with S. Papadima

arXiv:1002.0673.

First we recall one of Lang's conjectures in diophantine geometry

on the interplay between subvarieties and translated subgroups in a

commutative algebraic group

(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,

a powerful tool in the study of fundamental groups of algebraic varieties.

Finally, using the two ingredients above, we show that the Torelli

groups $T_g$

have some surprising finiteness properties for $g>3$.

In particular, we show that for any subgroup $N$ in $T_g$ containing

the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$

is finite dimensional.

All the details are available in our joint preprint with S. Papadima

arXiv:1002.0673.

### 2010/03/30

#### GCOE Seminars

10:00-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)

量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)

Semismooth Newton法の理論、及び応用 (JAPANESE)

TBA (JAPANESE)

**Masahiro Yamamoto**(University of Tokyo) 10:00-10:50産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)

**Shu Nakamura**(University of Tokyo) 11:00-11:50量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)

**Kazufumi Ito**(University of Tokyo, North Carolina State University) 13:20-14:10Semismooth Newton法の理論、及び応用 (JAPANESE)

**Georg Weiss**(University of Tokyo) 14:10-15:00TBA (JAPANESE)

### 2010/03/29

#### Seminar on Probability and Statistics

13:00-14:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Inference for partially observed Markov processes and applications

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html

**Catherine Laredo**(MIA, INRA)Inference for partially observed Markov processes and applications

[ Abstract ]

We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.

We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.

[ Reference URL ]We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.

We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html

### 2010/03/25

#### Lectures

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Heuristic Choice Rules for Convex Variational Regularization

**Dr Bangti Jin**(Center for Industrial Mathematics University of Bremen, Germany)Heuristic Choice Rules for Convex Variational Regularization

[ Abstract ]

In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.

In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.

#### Lectures

16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Modern computer architectures for tsunami simulation

**M.M. Lavrentiev, Jr.**(Sobolev Institute of Mathematics, Novosibirsk, Russia)Modern computer architectures for tsunami simulation

[ Abstract ]

Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.

Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.

### 2010/03/23

#### GCOE Seminars

15:00-17:15 Room #370 (Graduate School of Math. Sci. Bldg.)

Stability estimates for the anisotropic wave and Schrodinger equations from

the Dirichlet to Neumann map

On uniqueness in inverse elastic obstacle scattering

**Mourad Bellassoued**(Univ. of Bizerte) 15:00-16:00Stability estimates for the anisotropic wave and Schrodinger equations from

the Dirichlet to Neumann map

[ Abstract ]

In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.

In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.

**Johannes Elschner**(Weierstrass Institute Berlin, Germany) 16:15-17:15On uniqueness in inverse elastic obstacle scattering

[ Abstract ]

The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.

Our approach is essentially based on a reflection principle for the Navier equation.

The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.

Our approach is essentially based on a reflection principle for the Navier equation.

### 2010/03/19

#### Lectures

11:00-12:00 Room #366 (Graduate School of Math. Sci. Bldg.)

A Regularization Parameter for Nonsmooth Tikhonov Regularization

**竹内 知哉**(North Carolina State University, USA)A Regularization Parameter for Nonsmooth Tikhonov Regularization

[ Abstract ]

We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.

We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.

### 2010/03/17

#### Lectures

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

方向依存性を持つ長距離パーコレーションの臨界曲線

**三角 淳**(東大数理)方向依存性を持つ長距離パーコレーションの臨界曲線

### 2010/03/15

#### Seminar on Probability and Statistics

15:00-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)

BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html

**Cecilia Mancini**(University of Florence)BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION

[ Abstract ]

We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.

Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.

Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.

The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.

This talk is based on Mancini and Gobbi (2009), and Mancini (2010).

[ Reference URL ]We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.

Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.

Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.

The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.

This talk is based on Mancini and Gobbi (2009), and Mancini (2010).

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html

#### Seminar on Probability and Statistics

14:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Statistical inference in the partial observation setting, in continuous time

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html

**Alexandre Brouste**(Université du Maine)Statistical inference in the partial observation setting, in continuous time

[ Abstract ]

In various fields, the {\\it signal} process, whose law depends on an unknown parameter $artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.

[ Reference URL ]In various fields, the {\\it signal} process, whose law depends on an unknown parameter $artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html

### 2010/03/12

#### Colloquium

15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)

ガルニエ系の数理

特性類と不変量を巡る旅

**岡本和夫**(東京大学大学院数理科学研究科) 15:00-16:00ガルニエ系の数理

[ Abstract ]

ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。

ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。

**森田茂之**(東京大学大学院数理科学研究科) 16:30-17:30特性類と不変量を巡る旅

[ Abstract ]

40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.

40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.

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