## 過去の記録

### 2006年01月30日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Compact non-kaehler threefolds associated to hyperbolic 3-manifolds

### 2006年01月23日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Stochastic processes and Besov spaces on local field

### 2006年01月18日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Analyticity of the interface of the classical two-phase Stefan problem
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006年01月11日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Oleg Yu. Imanuvilov 氏 (Colorado State University) 11:45-12:45
Local and Global Exact Controllability of Evolution Equations
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年12月05日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Sebastien Boucksom 氏 (ParisVII / Univ. of Tokyo)
Positive cones of hyper-Keahler manifold

### 2005年11月28日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Schroeder equation and Abel equation

### 2005年11月22日(火)

#### 諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 128号室
Hans Heesterbeek 氏 (University of Utrecht)
Mathematics in the epidemiology and control of infectious diseases
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005年11月21日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Andreas Cap 氏 (Univ. of Vienna)
On CR-invariant differential operators
[ 講演概要 ]
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年11月14日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Raphael Pong 氏 (Ohio State Univ)
New invariants for CR and contact manifolds
[ 講演概要 ]
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年11月09日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年11月07日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Moduli of Galois coverings of the complex projective line

### 2005年10月26日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年10月24日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Ambient metrics for even dimensional conformal structures

### 2005年10月18日(火)

#### 諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 128号室
Rainer Kress 氏 (Goettingen 大学)
Hybrid methods for inverse boundary problems
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005年10月17日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

On the discriminant of certain K3 surfaces

### 2005年09月28日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Matthias Geissert 氏 (ダルムシュタット工科大学)
The Navier-Stokes flow in the exterior of a rotating obstacle
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年07月22日(金)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Szegö kernel の構成について

#### 複素解析幾何セミナー

15:30-17:00   数理科学研究科棟(駒場) 128号室
Dan Popovici 氏 (JSPS, 名古屋大学多元数理)
Effective Local Finite Generation of Multiplier Ideal Sheaves

### 2005年07月20日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Equivalence between the boundary Harnack principle and the Carleson estimate
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年07月13日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 122号室
Yonggeun Cho 氏 (北海道大学)
On classical solutions of the compressible Navier-Stokes equation with nonnegative density
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2005年07月11日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

### 2005年07月04日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Variation of Bergman kernel of projective manifolds

### 2005年06月27日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

Uniqueness problem of analytic coverng spaces

### 2005年06月22日(水)

#### 諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 056号室
Y. H. Richard Tsai 氏 (University of Texas)
Threshold Dynamics for the Piecewise Constant
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2005年06月15日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Singular and fractional integral operators on function spaces related to Morrey spaces
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html