## Seminar information archive

Seminar information archive ～12/01｜Today's seminar 12/02 | Future seminars 12/03～

### 2006/01/18

#### PDE Real Analysis Seminar

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

Analyticity of the interface of the classical two-phase Stefan problem

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Juergen Saal**(TU Darmstadt)Analyticity of the interface of the classical two-phase Stefan problem

[ Abstract ]

The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.

The strong formulation of this model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.

We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.

The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.

[ Reference URL ]The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.

The strong formulation of this model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.

We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.

The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006/01/11

#### PDE Real Analysis Seminar

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

On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

Local and Global Exact Controllability of Evolution Equations

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**伊東 一文**(North Carolina State University) 10:30-11:30On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem

[ Abstract ]

The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control problem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out

that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.

[ Reference URL ]The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control problem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out

that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Oleg Yu. Imanuvilov**(Colorado State University) 11:45-12:45Local and Global Exact Controllability of Evolution Equations

[ Abstract ]

We discuss rcent global and local controlability results for the Navier-Stokes system and Bousinesq system. The control is acting on the part of the boundary or locally distributed over subdomain.

[ Reference URL ]We discuss rcent global and local controlability results for the Navier-Stokes system and Bousinesq system. The control is acting on the part of the boundary or locally distributed over subdomain.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/12/05

#### Seminar on Geometric Complex Analysis

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

Positive cones of hyper-Keahler manifold

**Sebastien Boucksom**(ParisVII / Univ. of Tokyo)Positive cones of hyper-Keahler manifold

### 2005/11/28

#### Seminar on Geometric Complex Analysis

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

Schroeder equation and Abel equation

**上田哲生**(京都大学)Schroeder equation and Abel equation

### 2005/11/22

#### Seminar on Mathematics for various disciplines

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

Mathematics in the epidemiology and control of infectious diseases

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Hans Heesterbeek**(University of Utrecht)Mathematics in the epidemiology and control of infectious diseases

[ Abstract ]

In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.

[ Reference URL ]In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005/11/21

#### Seminar on Geometric Complex Analysis

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

On CR-invariant differential operators

**Andreas Cap**(Univ. of Vienna)On CR-invariant differential operators

[ Abstract ]

My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.

Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.

My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.

Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.

### 2005/11/14

#### Seminar on Geometric Complex Analysis

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

New invariants for CR and contact manifolds

**Raphael Pong**(Ohio State Univ)New invariants for CR and contact manifolds

[ Abstract ]

In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.

In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.

### 2005/11/09

#### PDE Real Analysis Seminar

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

Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**藤田安啓**(富山大学)Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations

[ Abstract ]

In this talk, we consider the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_t + \\alpha x\\cdot Du + H(Du) =f(x)$ in ${\\rm I}\\!{\\rm R}^N \\times (0,\\infty)$, where $\\alpha$ is a positive constant and $H$ is a convex function on ${\\rm I} \\!{\\rm R}^N$. We show that, under some assumptions, $u(x,t) - ct - v(x)$ converges to $0$ locally uniformly in ${\\rm I}\\!{\\rm R}^N$ as $t \\to \\infty$, where $c$ is a constant and $v$ is a viscosity solution of the Hamilton-Jacobi equation $c + \\alpha x\\cdot Dv + H(Dv) = f(x)$ in ${\\rm I}\\!{\\rm R}^N$. A set in ${\\rm I}\\!{\\rm R}^N$, which is called the {\\it Aubry set}, gives a concrete representation of the viscosity solution $v$. We also discuss convergence rates of this asymptotic behavior. This is a joint work with Professors H. Ishii and P. Loreti.

[ Reference URL ]In this talk, we consider the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_t + \\alpha x\\cdot Du + H(Du) =f(x)$ in ${\\rm I}\\!{\\rm R}^N \\times (0,\\infty)$, where $\\alpha$ is a positive constant and $H$ is a convex function on ${\\rm I} \\!{\\rm R}^N$. We show that, under some assumptions, $u(x,t) - ct - v(x)$ converges to $0$ locally uniformly in ${\\rm I}\\!{\\rm R}^N$ as $t \\to \\infty$, where $c$ is a constant and $v$ is a viscosity solution of the Hamilton-Jacobi equation $c + \\alpha x\\cdot Dv + H(Dv) = f(x)$ in ${\\rm I}\\!{\\rm R}^N$. A set in ${\\rm I}\\!{\\rm R}^N$, which is called the {\\it Aubry set}, gives a concrete representation of the viscosity solution $v$. We also discuss convergence rates of this asymptotic behavior. This is a joint work with Professors H. Ishii and P. Loreti.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/11/07

#### Seminar on Geometric Complex Analysis

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

Moduli of Galois coverings of the complex projective line

**難波誠**(追手門学院大学)Moduli of Galois coverings of the complex projective line

### 2005/10/26

#### PDE Real Analysis Seminar

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

On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**利根川吉廣**(北海道大学)On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems

[ Abstract ]

The Cahn-Hilliard equation and its variants have been widely used in materials science community to model coarse graining phenomena in mesoscopic scale. The equation has a parameter corresponding the order of thickness of phase boundaries. When the parameter is close to zero, the phase boundary and the chemical potential field are known to evolve by the so-called Mullins-Sekerka problem. The rigorous justification for the latter statement is known only for short-time so far. I describe some recent progress as well as some difficulties on the long-time case, relateing my recent works and those by M. Roeger and R. Schaetzle.

[ Reference URL ]The Cahn-Hilliard equation and its variants have been widely used in materials science community to model coarse graining phenomena in mesoscopic scale. The equation has a parameter corresponding the order of thickness of phase boundaries. When the parameter is close to zero, the phase boundary and the chemical potential field are known to evolve by the so-called Mullins-Sekerka problem. The rigorous justification for the latter statement is known only for short-time so far. I describe some recent progress as well as some difficulties on the long-time case, relateing my recent works and those by M. Roeger and R. Schaetzle.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/10/24

#### Seminar on Geometric Complex Analysis

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

Ambient metrics for even dimensional conformal structures

**平地健吾**(東大数理)Ambient metrics for even dimensional conformal structures

### 2005/10/18

#### Seminar on Mathematics for various disciplines

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

Hybrid methods for inverse boundary problems

[ Reference URL ]

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Rainer Kress**(Goettingen 大学)Hybrid methods for inverse boundary problems

[ Reference URL ]

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005/10/17

#### Seminar on Geometric Complex Analysis

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

On the discriminant of certain K3 surfaces

**吉川謙一**(東大数理)On the discriminant of certain K3 surfaces

### 2005/09/28

#### PDE Real Analysis Seminar

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

The Navier-Stokes flow in the exterior of a rotating obstacle

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Matthias Geissert**(ダルムシュタット工科大学)The Navier-Stokes flow in the exterior of a rotating obstacle

[ Abstract ]

We show the existence of solutions of the Navier-Stokes flow in the exterior of a rotating obstacle. In the first step we transform the Navier-Stokes equations to a problem in a time independent domain. In this talk we present two different change of coordinates to do this. Finally, we discuss the advantages of both approaches and show the local existence and uniqueness of mild and strong $L^p$ solutions.

[ Reference URL ]We show the existence of solutions of the Navier-Stokes flow in the exterior of a rotating obstacle. In the first step we transform the Navier-Stokes equations to a problem in a time independent domain. In this talk we present two different change of coordinates to do this. Finally, we discuss the advantages of both approaches and show the local existence and uniqueness of mild and strong $L^p$ solutions.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/07/22

#### Seminar on Geometric Complex Analysis

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

Szegö kernel の構成について

**倉西正武**(コロンビア大学)Szegö kernel の構成について

#### Seminar on Geometric Complex Analysis

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Effective Local Finite Generation of Multiplier Ideal Sheaves

**Dan Popovici**(JSPS, 名古屋大学多元数理)Effective Local Finite Generation of Multiplier Ideal Sheaves

### 2005/07/20

#### PDE Real Analysis Seminar

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

Equivalence between the boundary Harnack principle and the Carleson estimate

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**相川弘明**(島根大学)Equivalence between the boundary Harnack principle and the Carleson estimate

[ Abstract ]

Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this talk is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.

[ Reference URL ]Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this talk is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/07/13

#### PDE Real Analysis Seminar

10:30-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

On classical solutions of the compressible Navier-Stokes equation with nonnegative density

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**Yonggeun Cho**(北海道大学)On classical solutions of the compressible Navier-Stokes equation with nonnegative density

[ Abstract ]

In this talk, we discuss a recent progress on the regularity of solution of compressible Navier-Stokes equations with nonnegative density. The nonnegativity of density cauases a problem in using the usual parabolicity of momentum equations and hence in general makes it hard to gain a regularity of solution. To overcome the difficulty, we develop a natural compatibility condition. Then observing a smoothing effect for positive time, we obtain classical solutions of the compressible Navier-Stokes equations.

[ Reference URL ]In this talk, we discuss a recent progress on the regularity of solution of compressible Navier-Stokes equations with nonnegative density. The nonnegativity of density cauases a problem in using the usual parabolicity of momentum equations and hence in general makes it hard to gain a regularity of solution. To overcome the difficulty, we develop a natural compatibility condition. Then observing a smoothing effect for positive time, we obtain classical solutions of the compressible Navier-Stokes equations.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/07/11

#### Seminar on Geometric Complex Analysis

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

学習理論のゼータ関数と特異点解消

**青柳美輝**(上智大理工)学習理論のゼータ関数と特異点解消

### 2005/07/04

#### Seminar on Geometric Complex Analysis

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

Variation of Bergman kernel of projective manifolds

**辻 元**(上智大理工)Variation of Bergman kernel of projective manifolds

### 2005/06/27

#### Seminar on Geometric Complex Analysis

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

Uniqueness problem of analytic coverng spaces

**相原義弘**(沼津高専)Uniqueness problem of analytic coverng spaces

### 2005/06/22

#### Seminar on Mathematics for various disciplines

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Threshold Dynamics for the Piecewise Constant

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Y. H. Richard Tsai**(University of Texas)Threshold Dynamics for the Piecewise Constant

[ Abstract ]

We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding. We discuss our current work of extending this line of work to higher order accuracy and to applications involving Willmore flow.

[ Reference URL ]We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding. We discuss our current work of extending this line of work to higher order accuracy and to applications involving Willmore flow.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005/06/15

#### PDE Real Analysis Seminar

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

Singular and fractional integral operators on function spaces related to Morrey spaces

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**中井英一**(大阪教育大学)Singular and fractional integral operators on function spaces related to Morrey spaces

[ Abstract ]

It is known that the Hardy-Littlewood maximal operator, singular integral operators and fractional integral operators are bounded on L^p spaces and Morrey spaces. We extend the boundedness to generalized Morrey spaces, Orlicz-Morrey spaces, etc.

[ Reference URL ]It is known that the Hardy-Littlewood maximal operator, singular integral operators and fractional integral operators are bounded on L^p spaces and Morrey spaces. We extend the boundedness to generalized Morrey spaces, Orlicz-Morrey spaces, etc.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/06/08

#### PDE Real Analysis Seminar

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

Weighted Hardy spaces on an interval and Jacobi series

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

**宮地晶彦**(東京女子大学)Weighted Hardy spaces on an interval and Jacobi series

[ Abstract ]

For the classical Hardy class consisting of functions holomorphic in the unit disc, the Burkholder-Gundy-Silverstein theorem gives a characterization of the class in terms of certain maximal functions. We give a variant of this theorem related to weighted Hardy spaces on the interval(0,$\\pi$) and generalized holomorphic functions efined through ultraspherical (Gegenbauer) polynomials.

[ Reference URL ]For the classical Hardy class consisting of functions holomorphic in the unit disc, the Burkholder-Gundy-Silverstein theorem gives a characterization of the class in terms of certain maximal functions. We give a variant of this theorem related to weighted Hardy spaces on the interval(0,$\\pi$) and generalized holomorphic functions efined through ultraspherical (Gegenbauer) polynomials.

http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005/06/06

#### Seminar on Geometric Complex Analysis

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

Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds

**大沢健夫**(名大多元数理)Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds

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