# - The 3rd COE Conference for Young Researchers -

### アブストラクト：プログラム

タイトル：The characterizations of weighted function spaces by wavelets and scaling functions
アブストラクト:
We explain the basic theory of wavelets associated with a multiresolution analysis and some classes of weights. We also state some interesting results on the characterizations of weighted function spaces by means of wavelets and scaling functions with suitable properties.

タイトル：Word theory and its applications to knots and plane curves
アブストラクト:
V.Turaev in math.CO/0503683 introduced 'word'. He describes there "Every word has its own personality and should be treated with the same respect and attention as say, a polyhedron or a manifold." I'd like to speak the following three points. Firstly, I explained how the 'word' is defined. Secondly, we think what position we can give this theory in knot theory. Thirdly, I'll try to apply the word theory to plane curves.

タイトル：The dynamics of a holomorphic map in some small neighborhood of a fixed point
アブストラクト:
In this talk we survey the dynamics of a holomorphic map in some small neighborhood of a fixed point. It is known that the first derivative at a fixed point plays an important role in the dynamics near the point. Thus we can classify the dynamics near the point into cases using the derivative. Most cases are now well understood, but a few cases still present extremely difficult problems. We introduce a topological technique which can be used to study these cases.

タイトル：he lower bound of the w-indices of surface links via quandle cocycle invariants
アブストラクト:
The minimal number of triple points of a surface braid S is called the w-index of S. The minimal number of the w-indices of surface braids whose closure is equivalent to a surface link F is called the w-index of F. In this talk, we will prove that there exists a surface link F of any genus such that the w-index of F is 6.

タイトル：Geometry of toric stacks
アブストラクト:
In my talk, I shall discuss toric geometry from the stack-theoretic point of view. Main subjects to be discussed are toric stacks introduced by myself. I'll present my recent results on their categorical aspects, intersection theory on them and etc., and explain how they govern the geometry of simplicial toric varieties.

タイトル：Asymptotic stability of stationary waves for viscous gases
アブストラクト:
We are conserned with the asymptotic stability of stationary waves for viscous gases in the half space. We discuss the following three cases: (1) nondegenerate stationary waves for damped wave equations with nonlinear convection, (2) degenerate stationary waves for viscous conservation laws, and (3) degenerate stationary waves for damped wave equations with nonlinear convection. In each case, we show that the solution converges to the corresponding stationary waves.

タイトル：Global existence of the solution to the system for a spherically symmetric viscous gaseous star with rigid core
アブストラクト:
We consider a system of equations describing a motion of the three-dimensional spherically symmetric gaseous star with free-boundary on the surface and rigid core in the centre. We also take into account the radiative effect and reacting process. Based on the fundamental local-in-time existence result, we construct a classical unique global-in-time solution.

タイトル：Asymptotic expansions of solutions to heat equations with generalized functions initial value
アブストラクト:
We will drive the asymptotic expansions of solutions of the heat equation with generalized functions initial data.

タイトル：Classification of behavior induced by noise in a spatio-temporal intermittency model
アブストラクト:
It has been reported that a spatially extended model of the van der Pol oscillator shows spatio-temporal intermittency. Recently the influence of external additive noise on this model was investigated, where a re-entrant phenomenon was observed. In this study, we calculate a phase diagram of this model to show whether the re-entrant behavior is observed in a wide range of the parameter space.

タイトル：Homotopy nilpotency in localized Lie groups
アブストラクト:
Homotopical nilpotency of topological groups is an important homotopy invariant. We studied homotopical nilpotency of $G_{(p)}$, a compact connected simple Lie group localized at a prime $p$. Suppose that the highest degree generator of $H^*(G;\mathbb{Q})$ has degree $2n_l-1$. Then $G_{(p)}$ is homotopy nilpotent of class $2$ if $\frac{3}{2}n_l<p<2n_l$ and of class $3$ if $n_l \le p \le \frac{3}{2}n_l$ except for several cases of exceptional Lie groups.

タイトル：On the congruence in a finite group
アブストラクト:In the study on the congruence on the number of the solution of the equation on the finite group, there is a long history. We call the congruence on the number of the solution of the equation on the finite group Frobenius type cougruence. In this lecture, Iwasaki's theorem and the enhancing are described from among Frobenius type congruence.
ボルディジャール　カルマール(Boldizsar Kalmar) [九州大学大学院数理学研究院数学部門]
タイトル：Cobordism of fold maps
アブストラクト:
Cobordism is an equivalence relation which can be generalized to singular maps as well. In the talk we give results about the description of cobordism classes of fold maps. We show relations between the geometry and topology of the source and the image of a fold map and its cobordism class.

タイトル：Value distribution of the hyperbolic Gauss map of costant mean curvature one surfaces
アブストラクト:
In this talk, we shall give a kind of ramification estimates for the hyperbolic Gauss map of complete surfaces of constant mean curvature 1 (CMC-1) in hyperbolic 3-spaces with constant curvature -1 and reveal the geometric meaning behind it.

タイトル：Anisotropic and weighted total variation for image restration
アブストラクト:
To remove noise from a corrupted digital image without blurring edges, we introduce the anisotropic and weighted ROF model. Our approach is to minimize: \\ \hspace*{20mm}$\frac{\|u-g\|^2}{2\lambda}+J(u)$\ \ ,\ \ $u\in R^{N\times N}$\ \ \ \ ,\ \ \ $\displaystyle{J(u):=\sum_{i,j}^N \alpha_{i,j}\phi(\nabla u)_{i,j}}$ \\ where $\phi$ is an anisotropic function and $\alpha$ is a weighted function.
フェリペ　カンペロ(Felipe Campelo) [北海道大学 大学院情報科学研究科情報科学研究科システム情報科学専攻]
タイトル：Properties of Additive Models in Multiobjective Optimization Problems
アブストラクト:
In this paper we discuss the ability of additive models to adequately map the full nondominated set in multiobjective optimization problems. Traditional techniques such as the Weighted Sum (WS)approach and the Epsilon-Constrained (EC)method present severe limitations when the nondominated set is non-convex or non-connected. These limitations are presented, discussed, and compared with the Compromise Programming(CP) technique, which is able to find solutions on concave regions of the nondominated set, as well as effectively exploring non-connected sets. The CP technique is then coupled with a stochastic optimization algorithm for the parallel search for multiple solutions of the multiobjective problem. This hybrid approach is tested on analytical and numerical problems for demonstrating its effectiveness.

タイトル：Stability of standing waves for Schrodinger-Poisson-Slater equation
アブストラクト:
We consider the stability of standing waves for the Schrodinger-Poisson-Slater equation. By a standing wave, we mean a solution of the form $u(t,x)=e^{i\omega t}\phi_{\omega}(x)$, where$\omega$ is constant. We say that standing wave is stable, if the initial data is close to the standing wave, then the solution remains close. We show that standintg wave, which is obtained by the mountain pass theorem, is stable.

タイトル：サブリーマン多様体上の測地線（Geodesics on Sub-Riemannian manifolds）
アブストラクト:
A Sub-Riemannian manifold (M,D,g) is a differential manifold M endowed with a subbundle D of the tangent bundle TM and a Riemannian metric g on D. In this talk we will treat the problem of length-minimizing paths in Sub-Riemannian geomerty.

タイトル：$M$-matrices of the ternary Golay code and the Mathieu group $M_{12}$
アブストラクト:
We shall define $M$-matrices of the ternary Golay code and build a fundamental properties the ternary Golay code on $M$-matrices. Moreover, using four $M$-matrices of the ternary Golay code, we give order three elements, in the Mathieu group $M_{12}$, which generate $M_{11}$ and $M_{12}$.

タイトル：トーラス多様体上の余次元０または１の軌道を持つコンパクト群作用の分類。(英訳：Classification of compact group actions on torus manifolds which have codimension 0 or 1 orbits.）
アブストラクト:
The torus manifold was defined by Hattori-Masuda in 2003 as a topological generalized object of the smooth toric variety in the algebraic geometry. The torus manifold is a 2n-dimensional manifold M and has some n-dimensional torus T acion. In this talk we study the question of what torus manifolds (M,T) can have an extension (M,G) with codimension zero (transitive) or codimension one principal orbits and classify such (M,G), where G is a compact Lie group which has T as a maximal toral subgroup.

タイトル：MathML-Lirary for Ruby, and its applications
アブストラクト:
My MathML-Library, math_ml.rb, provide convert-method from LaTeX expressions to MatML. It can recoganize macro with "newcommand" and "newenvironment". Programmers can add new command and environment by ruby-script, and develop software quickly including MathML for example Blog, Wiki, BBS, and so on.

タイトル：Gasussian-BGK Boltzmann方程式に基づく相変化現象に対するアプローチ（An Approache for Phase Change Phenomena Based on the Gaussian-BGK Boltzmann Equation）
アブストラクト:
The Gaussian-BGK Boltzmann equation is capable of describing the vapor flow of polyatomic molecules induced by evaporation and condensation processes at a vapor-liquid interface. In this research, interfacial phenomena accompanied with condensation is investigated by combining the numerical analysis of the Gaussian-BGK Boltzmann equation and shock tube experiment.

タイトル：Lorenz chaotic system and unstable periodic orbits
アブストラクト:
Infinite number of unstable periodic orbits are embedded in a chaotic system. Recently researches on unstable periodic orbits have attracted much attention from the point of view of both basic aspects and applications such as fluid turbulence and economics, although there are difficulties in extracting unstable periodic orbits even numerically. In this talk, several properties of famous Lorenz system are discussed through focusing on more than one thousand of unstable periodic orbits detected numerically.

タイトル：Hyperscaling in the Ising lattice model on a surface with constant negative curvature
アブストラクト:
We have numerically studied critical phenomena of the ferromagnetic Ising lattice model defined on a surface with constant negative curvature. When the Ising model is assigned on a curved surface, its critical properties may be affected by non-Euclidean property of the surface. In fact, our numerical simulations have reveled that several critical exponents of the Ising model on the curved surface distinct from those for the planar Ising model, whereas they still satisfy the Hyperscaling relations. These findings indicate that the Ising model assigned on the curved surface belongs to a novel universality class distinct from that of the planar Ising model.

タイトル：分数積分作用素の有界性に関して(On the boundedness of the fractional integral operators)
アブストラクト:
This speech is oriented to presenting two things. One is an introduction to harmonic analysis and the other is a brief introduction of my research. Fractional integral operators are frequently used in various fields of mathematics. In this present lecture I shall give a whole proof of its typical boundedness.

タイトル：O(1)-loop models and the sum rule: affine Temperley-Lieb/Hecke algebra and qKZ equation
アブストラクト:
We briefly review the Razumov-Stroganov (RS) conjecture which relates the O(1)-loop model to alternating sign matrices. Then, we will discuss the A_{k} generalization of the O(1)-loop model on a cylinder by using representation theory of the Affine Hecke algebra and the qKZ equation. The RS sum rule for the A_{k} model and the relation with the spin chain model are also discussed.

タイトル：境界要素法を用いた核融合プラズマ平衡解析 (Boundary element method applied to the equilibrium analyses of nuclear fusion plasma)
アブストラクト:
The boundary element method has been applied to solve the Grad-Shafranov equation that governs the magnetohydrodynamic quilibrium in Tokamak Plasma. The above equation is transformed into two types of boundary integral equations (BIE), i.e., the standard and the hyper-singular ones, respectively with the fundamental solution and its derivative at a singular point. Numerical calculations demonstrate the high accuracy of magnetic flux solutions attained by the formulation for these two BIEs.

タイトル：Logarithmic derivatives of urvature of curves and isometric immersions
アブストラクト:
We characterize isotropic immersions by a condition which logarithmic derivatives of curvature of curves are preserved. As an application of this we characterize veroneseembeddings among Kaehler isometricimmersions.

タイトル：ヘリオトロン型核融合装置における粒子軌道解析 (Particle Orbit Analysis in Heliotron Type Fusion Device)
アブストラクト:
The charged-particle orbits are analyzed in the Large Helical Device that is the largest heliotron type fusion device in the world. Particle orbit characteristics are clarified in two types of magnetic field. One is a vacuum magnetic field (plasma pressure = 0). The other is the plasma equilibrium magnetic field which configuration has been changed by the finite plasma pressure. The particle orbit characteristics are almost the same between these two types of magnetic fields. The charge-exchange between the charged particles and the neutral ones in the peripheral region is investigated. The number of the charge-exchange reactions in the plasma equilibrium magnetic field is larger than that in the vacuum magnetic field.

タイトル：The Schr\"odinger equation of a quantum system embedded on a curved surface
アブストラクト:
The present work focuses on the Schr\"odinger equation that describes the motion of a quantum particle confined in a cylindrical surface with a variable diameter. The quantum confinement normal to the curved surface causes an effective potential whose magnitude depends on the Gaussian curvature of the surface of interest. This curvature-induced potential strongly affects the nature of the quantum system, which implies the possibility of developing a novel type of quantum-mechanical devices.

タイトル：C1 Approximation of Vector Fields on the Renormalization Group Method and its Applications
アブストラクト:
The renormalization group (RG) method for differential equations is one of the perturbation methods for obtaining solutions which are approximate to exact solutions uniformly in time. It is shown that for a given vector field on arbitrary manifold, approximate solutions obtained on the RG method define a vector field which is close to an original vector field in C1 topology. Furthermore, some topological properties of the approximate vector field, for instance, the existence of an invariant manifold and its stability, are inherited from the RG equation.
チャンゲンユ(Genryu Zhang) [東京工業大学大学院理工学研究科]
タイトル：crosscap numbers of knots and links
アブストラクト:
The crosscap number of a knot (or a link) is defined to be the minimum first Betti number of non-orientable surfaces bounding the knot (or the link). We will review the known work on crosscap numbers of knots and links first. Then we define the concordance crosscap number of a knot as the minimum crosscap number among all the knots concordant to the knot, and study the gap between the concordance crosscap number and 4-dimensional one of a knot.

タイトル：Ergodic theorems for random sequences
アブストラクト:
In this talk, we study some properties of Martin-L\"{o}f random sequences. We show some extensions of two ergodic theorems, Shannon-McMillan-Breiman theorem and Wyner-Ziv recurrence time theorem, to individual Martin-L\"{o}f random sequences. Moreover, in the case of finite-order Markov processes, we have the ultimate extensions of these theorems.

タイトル：>Classical and Quantum isomonodromic deformation with affine Weyl group symmetry of type $C_l^{(1)}$
アブストラクト:
>I construct classical Integrable systems with affine Weyl group symmetries of type C, using Lax formalism. Hamiltonians are $z$'s coefficients of trace of some power of Lax operators. I show that they are mutually commuting and each Hamiltonian flow has affine Weyl group symmetry of type C. Moreover, I quantize these classical systems, by replacing the poisson bracket with the commutator.

タイトル：On perfect isometries
アブストラクト:
In the representation theory of finite groups, there are some problems which deserve attention. They are some conjectures on characters and Sylow p-subgroups. In this talk, we consider correspondences of irreducible characters which is called "perfect isometry". A perfect isometry is a reflection at the level of character theory of an equivalence of the derived categories of two block algebras as triangulated categries.

タイトル：フラットバンド不規則電子系における局在−非局在転移 (Localization-delocalization transition in a flat band disordered electronic system)
アブストラクト:
We propose a disorder-induced localization-delocalization transition of one-electron states. We first make a highly degenerated localized states by constructing a three-dimensional periodic system possessing only flat dispersion relations. When we introduce a disorder into it, a finite-size scaling of the level statistics shows localization-delocalization-localization transition for a wide range of the energy, with increasing the degree of disorder.

タイトル：Equivalence problem of differential equations
アブストラクト:
The equivalence problem is studied deeply by Sophus Lie and Elie Cartan and many other authors. In this talk, we first review an equivalence problem for second order ODE. Moreover, we study an equivalence problem for second order PDE with respect to two variables one-unknown function.

タイトル：Configuration of the central streams in the moduli of abelian varieties.
アブストラクト:
We study the structure of the moduli space of principally polarized abelian varieties in positive characteristic. Oort defined the central streams in the moduli space. We determine the configuration of the central streams. As a corollary of our proof we obtain a new proof of the dimension formula of the central streams.

タイトル：Groebner basis and cohomology of oriented Grassmann manifolds with application of LS-category
アブストラクト:
The cohomology of oriented Grassmann manifold has the sub ring which is isomorphic to a quotient ring of a polynomial ring by an ideal. We consider the Groebner basis of that ideal. We apply it to the estimation of LS-category.

タイトル：The earlier-on successions of the constructions of the solutions on the Navier-Stokes equations
アブストラクト:
We indtroduce the successions of the constructions of the solutions on the Navier-Stokes equations earlier on in the history until 1950s, summarizing with the following 4 types of these successions :
1) for the classical solutions, to formulate the Navier-Stokes equations by Newton,Bernoulli,d’Alembert,Euler,Navier,
2) for the fundamental solutions, owing to Newton’s potential theory, to construct the invariant tensor tij by Poisson,Cauchy,Green,Stokes,Oseen,Lichtenstein,Odqvist,Leray,Ladyzhenskaya,
3) for the Cauchy problem/turbulent solution/weak solutions to define and construct the conception/notion of the solution by Cauchy,Kovalevskaya,Hadamar,Leray,Hopf, and
4) for the generalized solutions/strong solutions, in using the functional analysis, especially, directly the Sobolev’s tools, to construct the proof and regurality by Sobolev,Keselev,Ladyzhenskaya,Prodi,J.L.Lions,Serrin.

タイトル：An Elliptic Analogue of the Generalized Dedekind-Rademacher Sums
アブストラクト:
We introduce an elliptic analogue of the generalized Dedekind-Rademacher sums which satisfy reciprocity laws. In these sums, Kronecker’s double series play a role of elliptic Bernoulli functions. We also mention a relation between the generating function of Kronecker’s double series and that of the (Debye) elliptic polylogarithms studied by A. Levin.

タイトル：Asymptotic solutions of Hamilton-Jacobi equations with state constraints
アブストラクト:
We study the solvability of Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition and establish a general convergence result for solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.

タイトル：Universal lexsegment ideals
アブストラクト:
After Macaulay characterized the Hilbert function of all homogeneous ideals in the polynomial ring, lexsegment ideals have played an important role in the theory of Hilbert functions. Universal lexsegment ideals, which were introduced by Babson et al., are lexsegment ideals that behave nicely under ring extensions. In this talk, I will talk about some extreme properties of universal lexsegment ideals on Hilbert functions and Hilbert polynomials.

タイトル：ナノ液滴の蒸発・凝縮に関する分子動力学的研究（Molecular Dynamics Study of Evaporation and Condensation of Nanodroplets）
アブストラクト：
Evaporation coefficients for interfaces between argon vapor and its droplets at 85 K are investigated by molecular dynamics simulations of liquid-vapor equilibrium state and evaporation into virtual vacuum for a droplet radii ranging from 10 A to 40 A. The result shows that evaporation coefficient becomes small as the droplet radius does small.

タイトル：Exotic rational elliptic surfaces without 1-handles
アブストラクト:
Harer, Kas and Kirby conjectured that every handle decomposition of the Dolgachev surface $E(1)_{2,3}$ requires both 1- and 3-handles. In this talk, we construct a smooth 4-manifold which has the same Seiberg-Witten invariant as $E(1)_{2,3}$ and has neither 1- nor 3-handles in a handle decomposition.

タイトル：On Hamiltonian deformation of loops
アブストラクト:
A problem we consider in this talk is when two embedded loops in a symplectic manifold are deformed into each other by a Hamiltonian flow. In particular, we will exposit the case that the dimension of the manifold is two, because this case is related to Lagrangian intersection theory.

タイトル：リーマンゼータ関数、ベルヌーイ多項式と ソボレフ不等式の最良定数 (Riemann zeta function, Bernoulli polynomials and the best constant of Sobolev inequality)
アブストラクト:
Green function for periodic boundary value problem of $2M$-th order ordinary differential equation is found by symmetric orthogonalization method under a suitable solvability condition. As an application, the best constants and the best functions of the Sobolev inequalities in a certain series of Hilbert spaces are found and expressed by means of the well-known Bernoulli polynomials. This result has clarified the variational meaning of the special values $\ \zeta(2M)\ (M=1,2,3,\cdots)\$ of Riemann zeta function $\zeta(z)$.

タイトル：ダイマーとコアメーバ、ホモロ ジカルミラー対称性 (Dimer, Coamoeba and Homological Mirror Symmetry)
アブストラクト:
Amoeba is an interesting object and has intimate relation with various topics such as tropical geometry and real algebraic geometry. Recently, physicists defined its cousin, known as coamoeba, and clarified its relation with dimer model (a.k.a. brane tiling). Our work (in collaboration with Kazushi Ueda) has shown that coamoeba has beautiful application to homological mirror symmetry.

タイトル：Singular fibers and Characteristic classes
アブストラクト:
In this talk, we represent characteristic classes in terms of the singular fibers of differentiable maps.

タイトル：核融合プラズマ解析へのニューラル ネットワークの適用 （Application of neural network to the fusion plasma analysis）
アブストラクト:
A neoclassical transport database, DCOM/NNW, has been constructed using the neural network (NNW) method to analyze the plasma in Large Helical Device (LHD). As the "training data" used in the "learning" for the NNW, the mono-energetic neoclassical transport coefficients were evaluated using a Monte Calro code, DCOM. The database has been prepared for two typical magnetic field configurations in LHD: the standard and the inward shifted configurations. The neoclassical transport coefficients for the thermal plasma can now be given quickly by the DCOM/NNW.

タイトル：Cyclic sum of multiple zeta values (joint work with Y.Ohno)
アブストラクト:
We will talk on a new class of relations among the multiple zeta-star values (MZSVs), which we call the cyclic sum identities. MZSVs are real numbers defined by convergent series. (These numbers were first considered by Euler.) The cyclic sum identities are generalization of the sum formula for MZSVs, and give new relations between a sum of MZSVs and the Riemann zeta value.