過去の記録

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.
[ 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.
[ 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
[ 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.
[ 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.
[ 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.
[ 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.
[ 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.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2005年06月08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

Weighted Hardy spaces on an interval and Jacobi series
[ 講演概要 ]
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.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2005年06月06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

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

2005年06月01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
Jong-Shenq-Guo 氏 (国立台湾師範大学)
Annihilation of wave fronts of a reaction-diffusion equation
[ 講演概要 ]
We shall present some recent results on the existence and uniqueness of 2-front entire solutions of a reaction-diffusion equation. These entire solutions behave as two opposite wave fronts approaching each other from both sides of the x-axis and then annihilating in a finite time.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2005年05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

2005年05月25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
Vincenzo Vespri 氏 (Dipartimento di Matematica Ulisse Dini Viale Morgagni) 10:30-11:30
Some regularity results for Stefan equation
[ 講演概要 ]
We consider the eqation $\\beta (u)_t = A(u)$ where $A$ is an elliptic operator and $\\beta$ is a maximal graph. Under suitable hypothesis on $\\beta$ and $A$ we prove the continuity of local solutions extendind some techniques introduced in the 80's.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Paolo Marcellini 氏 (Università degli Studi di Firenze) 11:45-12:45
Nonlinear elliptic systems with general growth
[ 講演概要 ]
We prove \\textit{local Lipschitz-continuity} and, as a consequence, $C^{k}$%\\textit{\\ and }$C^{\\infty }$\\textit{\\ regularity} of \\textit{weak} solutions $u$ for a class of \\textit{nonlinear elliptic differential systems} of the form $\\sum_{i=1}^{n}\\frac{\\partial }{\\partial x_{i}}a_{i}^{\\alpha}(Du)=0,\\;\\alpha =1,2\\dots m$. The \\textit{growth conditions} on the dependence of functions $a_{i}^{\\alpha }(\\cdot )$ on the gradient $Du$ are so mild to allow us to embrace growths between the \\textit{linear} and the \\textit{exponential} cases, and they are more general than those known in the literature.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2005年05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

A-branes from CR-geometry

2005年05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

A model of damage evolution in viscous locking material.
[ 講演概要 ]
A model problem, describing the damage evolution for instance in some composite materials, is considered. The model is a system of nonlinear PDEs, which are kinetic equations for the displacement and damage quantity in the material. They are both heavily nonlinear parabolic equations, and one of them is of degenerate type. In this talk, the existence of a global in time solution is shown with some key ideas.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2005年05月16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

Algebraic degeneracy of holomorphic curves