第4回数学総合若手研究集会
〜他分野との学際的交流を目指して〜
- The 4th COE Conference for Young Researchers -
アブストラクト：プログラム
森本 光太郎（首都大学東京大学院理工学研究科）
- タイトル：Construction of a solution to the Gierer-Meinhardt system with saturation（サチュレーション効果のあるGierer-Meinhardt 系の解の構成）
- アブストラクト：
- We are concerned with stationary solutions to the
Gierer-Meinhardt system with saturation. In this lecture, we study about
the following. What is saturation effect? What is different from in no
saturation case? How to construct of solutions.
長尾 健太郎（京都大学大学院理学研究科）
- タイトル：Higher q-Fock spaces and fusion products
- アブストラクト：
- Quiver varieties involve rich mathematical structures.
For example, thier torus equivariant K-groups have actions of quantum
loop algebras. On the other hand, q-Fock spaces play important roles in
many areas of representation theory. In particular, bases so called
"canonical bases" of q-Fock spaces sometimes mediate misteriously
between completely different-looking objects. In this talk, we will
intruduce isomorphisms between equivariant K-groups of quiver varieties
of affine A type and q-Fock spaces. We will also discuss what would be
expected beyond these isomorphisms.
曽我 幸平（早稲田大学理工学術院）
- タイトル：On the KAM theory
- アブストラクト：
- We review the KAM theory. Next, we give a new approach
to the theory: We consider initial value problems for nearly integrable
Hamiltonian systems. We formulate a sufficient condition for each
initial value to admit the quasi-periodic solution with a Diophantine
frequency, without any nondegeneracy of the integrable part. We
reconstruct the KAM theory, as a theory of the measure estimate for the
initial values satisfying this sufficient condition. Our version is of
the form closely analogous to the corresponding arguments for the
integrable case.
米田 剛（東京大学大学院数理科学研究科）
- タイトル：On the Navier-Stokes equations with spatially almost periodic data
- アブストラクト：
- We consider the Navier-Stokes equations when initial
data may not decrease at spatial infinity so that Fourier sum of the
form $\sum_{\lambda\in\Lambda}c_\lambda e^{i\lambda x}$ is allowed. It
is proved that the local-in-time solution is almost periodic function
and the frequency set is preserved in time. To solve this problem,
uniformly $L^p$ local spaces, Besov spaces, modulation spaces and FM
spaces are used.
岡 康之（上智大学大学院理工学研究科）
- タイトル：A characterization of Gel'fand-Shilov space $S^r_r$ and
$(S^r_r)^{\prime}$ by Weyl transform
- アブストラクト：
- We give a characterization of Gel'fand-Shilov space
$S^r_r$ and its dual space ($S^r_r$)^{\prime} by Weyl transform.
梅田 陽子（北海道大学大学院理学院）
- タイトル：On the turning point of the second kind of the Noumi-Yamada
system $NY_{2m+1}$ （野海山田系方程式NY奇数系の第2種変わり点について）
- アブストラクト：
- The Noumi-Yamada system $NY_{l}$ is one of the
Painlev$\acute{e}$ hierarchies. The structure of $NY_{l}$ depends on the
parity of $l$. In this talk, we have the result concerning the number of
the turning points of the second kind of $NY_{l}$ in the case of $l = 2m+1$.
瀧 真語（名古屋大学大学院多元数理科学研究科）
- タイトル：Classification of non-symplectic automorphisms of order 3 on
$K3$ surfaces
- アブストラクト：
- We study non-symplectic automorphisms of order 3 on
algebraic $K3$ surface over $\mathbb{C}$ which act trivially on the
N\'{e}ron-Severi lattice. In particular we shall characterize their
fixed locus in terms of the invariants of 3-elementary lattices.
上田 好寛（九州大学大学院数理学府）
- タイトル：Asymptotic stability of planar stationary waves for damped
wave equations in multi-dimensional half space
- アブストラクト：
- We consider the large-time behavior of solutions to the
initial and boundary value problem for damped wave equations with a
nonlinear convection term in the multi-dimensional half space. We show
that solutions to the problem converge to the corresponding planar
stationary wave as time tends to infinity under the smallness condition
on the initial perturbation. Moreover, the algebraic convergence rate is
obtained by assuming that the initial perturbation decays algebraically
in the normal direction.
鈴木 章斗（北海道大学大学院理学院）
- タイトル：Physical states of quantum electrodynamics with an indefinite
metric
- アブストラクト：
- We consider the quantized electromagnetic field interacting with an external source. We construct the quantized radiation field on an indefinite metric space. According to the Bleular-Gupta formalism we can choose the physical state space from the indefinite metric space in the case where the external source is infrared regular. If, however, the external source is infrared sigular, the physical state space is trivial.
冨江 雅也（筑波大学大学院数理物質科学研究科）
- タイトル：Poset transformations and Quasi symmetric functions
- アブストラクト：
- The quasi symmetric function is an algebraic invariant
which encodes the flag f vector of a poset. Sometimes a transformation
of a poset induces the corresponding transformation of the quasi
symmetric function. There are explicit expressions for how the quasi
symmetric function changes after applying operations, for example
cartesian product, pyramid, prism. In this talk we will calculate more
complicated cases.
深谷 友宏（京都大学大学院理学研究科）
- タイトル：Application of non-commutative Groebner basis to a free
resolution of a module over the Steenrod algebra
- アブストラクト：
- Groebner basis gives us an algorithm of computing some
homotopy invariants. Adams spectral sequence is a powerful method to
compute the homotopy set of maps, for example, homotopy groups. The E_2
terms of Adams spectral sequence is given by Ext, which can be computed
by a free resolution of a module over the Steenrod algebra. I will
explain how to compute that free resolution using non commutative
Groebner basis.
近藤 信太郎（慶應義塾大学大学院理工学研究科）
- タイトル：Initial boundary value problem for the Hasegawa-Wakatani equations
- アブストラクト：
- The Hasegawa-Wakatani equations are the nonlinear
equations which describe the resistive drift wave turbulence in Tokamak.
I proved the existence and uniqueness of a local strong solution for the
initial boundary value problem for the Hasegawa-Wakatani equations. In
this talk, I shall explain Tokamak and the Hasegawa-Wakatani equations
and present my result.
鹿野 豊（東京工業大学大学院理工学研究科）
- タイトル：Optimal covariant measurement of momentum on a half line in
quantum mechanics
- アブストラクト：
- We cannot perform the projective measurement of a
momentum on a half line since it is not an observable. Nevertheless, we
would like to obtain some physical information of the momentum on a half
line. We define an optimality for measurement as minimizing the variance
between an inferred outcome of the measured system before a measuring
process and a measurement outcome of the probe system after the
measuring process, restricting our attention to the covariant
measurement studied by Holevo. Extending the domain of the momentum
operator on a half line by introducing a two dimensional Hilbert space
to be tensored, we make it self-adjoint and explicitly construct a model
Hamiltonian for the measured and probe systems. By taking the partial
trace over the newly introduced Hilbert space, the optimal covariant
positive operator valued measure (POVM) of a momentum on a half line is
reproduced. We physically describe the measuring process to optimally
evaluate the momentum of a particle on a half line.
阿部 拓郎（北海道大学大学院理学研究院）・縫田 光司（産業技術総合研究
所）・沼田 泰英（北海道大学大学院理学研究院）
- タイトル：Bicolor-eliminable multiplicities on the braid arrangement
- アブストラクト：
- A mutiarrangement consists of a finite collection of
linear hyperplanes with a multiplicity function on it. We can associate
a reflexive module, called logarithmic vector fields, to a
multiarrangement, and to consider its freeness is an important problem.
We consider multiplicities induced from graphs with two-colored edges on
the braid arrangement, and characterize their freeness by giving a
generalization of the theory of eliminable, or chordal graphs which were
originally introduced by Stanley.
作道 直幸（京都大学大学院理学研究院）
- タイトル：Study of quark confinement with Hodge decomposition approach
- アブストラクト：
- The quark confinement mechanism is one of the most
important problems in particle physics, and is listed as the 7 difficult
mathematical problems of the New Millennium by Cray Mathematics
Institute. In this problem, it is suggested that the monopole
singularity of the Yang-Mills field plays a crucial role. To extract the
singularity, we introduce the Hodge decomposition of the Yang-Mills
field, and numerically study the role of the singularity for confinement
in the lattice gauge theory.
縫田 光司（産業技術総合研究所情報セキュリティ研究センター）
- タイトル：Mathematics in information security (情報セキュリティ分野の数学)
- アブストラクト：
- As several kinds of information-technological
applications are getting widespread, research areas concerning
information security have been wider and more various as well, so are
the mathematical theories applied there. This talk will survey how (even
advanced) mathematics is used in recent researches on information security.
高江洲 俊光（九州大学大学院数理学府）
- タイトル：The spectral analysis of the Hamiltonian with a singular perturbation in quantum fields theory
- アブストラクト：
- The GSB-Hamiltonian describes particle systems coupled
to quantum fields. In this research, the GSB-Hamiltonian with a singular
perturbation is considerd. It is proven that the Hamiltonian has a
ground state and asymptotic fields exist, where ultraviolet and infrared
cut-offs are imposed on.
松尾 信一郎（東京大学大学院数理科学研究科）
- タイトル：The approximation of instantons over an arbitrary closed oriented 4-manifold
- アブストラクト：
- A classical theorem of Runge asserts that a meromorphic
function defined on a domain in the complex plain can be approximated,
over compact subsets, by rational functions, i.e. by meromorphic
functions on the entire Riemann sphere. In this talk we shall present
two analogous results in which meromorphic functions are replaced by
instantons or pseudoholomorphic curves. They generalize Donaldson's
"Runge theorem for instantons over the four-sphere".
橋本 伊都子（大阪大学大学院情報科学研究科）
- タイトル：$L^p$ energy method for scalar viscous conservation laws on
the half line （単独粘性保存則に対するある初期・値境界値問題の解の漸近評価について）
- アブストラクト：
- We study the $L^p$ energy method of the solution to an
initial boundary value problem on the half line for scalar viscous
conservation law. In t his talk, it is proved that even for a wideｒ
class of flux functions which are not necessarily convex, such the
superposition of the stationary solution and the rarefaction wave have
the same decay rate as the flux is convex, provided the rarefaction wave
is weak.
鍛冶 静雄（京都大学大学院理学研究科）
- タイトル：Chow rings of complex algebraic groups
- アブストラクト：
- The Chow ring is a certain invariant for a variety
similar to the cohomology ring. In fact, in some cases it can be
calculated from the cohomology ring, which is extensively studied by
algebraic topologists. Combining the results on the cohomology of flag
varieties with a tool from Schubert calculus, we determined the Chow
ring of simple, simply-connected complex algebraic groups (joint with M.Nakagawa).
川見 将広（大阪市立大学数学研究所）
- タイトル：Pin structures and spin structures on surfaces
- アブストラクト：
- For a closed orientable$($resp. non-orientable$)$ surface, we can always give finite numbers of spin$($resp. pin$^{\pm})$ structures.
And it is known that there are some algebraic or geometric counterpartsfor them. In this talk and article, we see their relationships and discuss some applications.
片方 江（島根大学大学院総合理工学研究科）
- タイトル：Siegel disks with bounded type rotation number
- アブストラクト：
- A Siegel disk is a rotation domain in the Riemann
sphere. We consider the topology and geometry of the boundary of Siegel
disks. A Siegel disk of some polynomial with bounded type rotation
number has the quasicircle boundary containing its critical point. In
order to construct such a Siegel disk not of a polynomial but of a
rational function, we consider some Blaschke product and employ the
quasiconformal surgery.
鬼塚 政一（島根大学大学院総合理工学研究科）
- タイトル：Non-uniform asymptotic stability for linear time-varying second-order differential equations
- アブストラクト：
- We obtain sufficient conditions that the equilibrium of
second-order differential equation is "not"uniformly asymptotically
stable. It is known that the equilibriums of the linear equations
$$x''+\frac{1}{1+t}x'+x=0, \qquad x''+\frac{1}{1+t}x'+\frac{1}{1+t}x=0$$
are asymptotically stable respectively. We discuss that they are
uniformly asymptotically stable or not.
岡崎 亮太（大阪大学大学院情報科学研究科）
- タイトル：On toric face rings
- アブストラクト：
- A toric face ring is a generalization of Stanley-Reisner
ring and affine semigroup rings, which was defined by Stanley, and
recently is more generated by Bruns, Koch and R\"omer. In this talk, we
will introduce this notion, and present some results obtained in joint
work with Kohji Yanagawa.
上別府 陽（筑波大学大学院数理物質科学研究科）
- タイトル：Homotopy type of the box complexes of graphs without 4-cycles
- アブストラクト：
- For a graph G, an abstract free simplicial Z_2-complex
B(G), called the box complex of G, is defined by J. Matousek and
G.M.Ziegler. The Z_2-index of B(G) give us a lower bound for the
chromatic number of G. We are interested in the relation between the
topology of B(G) and the combinatorics of G. In this speech, the box
complexes of graphs without 4-cycles are characterized by a
1-dimensional Z_2-subcomplex of B(G).
秋元 琢磨（早稲田大学理工学術院）
- タイトル：Generalized arcsine law in an infinite measure system
- アブストラクト：
- It is known that intermittent phenomena, such as the
Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are
described by infinite measure dynamical systems. We show that the time
average of some observation functions converges to the generalized
arcsine distribution in an infinite measure dynamical system.
増田 茂（首都大学東京大学院理学研究科）
- タイトル：The modeling in the equations of fluid mechanics at the dawn or Navier{-}Stokes （黎明期における流体力学ないしはNavier{-}Stokes方程式のモデリング）
- アブストラクト：
- The original Navier-Stokes equations (NS) or Navier
equations were introduced in the prime of the second period of molecules
in 1821 and also Stokes’ in 1845 respectively. The heated arguments for
modeling in the formulations of NS, based on or not on the then current
topics on actions of molecules among the g´eom`etres about the elastic
solid/fluid, were published in the then jounals. Helmholtz and Thomson
discovered the theories of vorticies in 1850s, in not using NS.
Moreover, “until Reynold’s and Boussinesq’s studies of turbulent flow in
1880s, NS remained completely irrelevant to hydraulics” (Darrigol). We
would like to report on these modeling after fluid mechanics at the
dawn, from the three points of view : two parameters in the equations of
the elastic solid/fluid, the boundary conditions and vortices.
源 泰幸（京都大学大学院理学研究科）
- タイトル：A noncommutative algebro geometric characterization of representation type of a quiver （クイバーの表現型の非可換代数幾何学的特徴付け）
- アブストラクト：
- Let Q be a quiver and let \Pi be the preprojective
algebra of Q. We prove that the category of representations of Q and the
category \qgr\Pi are derived equivalent where \qgr\Pi is the abelian
category which is considered as the category of coherent sheaves on
noncommutative projective scheme \proj\Pi associated to \Pi.As a
corollary we obtain "a noncommutative geometric characterization of
representation type of a quiver"
巴山 竜来（大阪大学大学院理学研究科）
- タイトル：On the boundary of the moduli space of log Hodge structure
- アブストラクト：
- In recently work of Kazuya Kato and Sampei Usui, they
constructed partial compactifications of the arithmetic quotients
of Griffiths period domains by marrying the original work of Griffiths
school on degenerations of Hodge structure with the theory of log
geometry. They introduced a notion of log Hodge structure and showed
that these partial compactifions are fine moduli of polarized log Hodge
structure. I talk about some result on the boundary of this moduli spaces.
吉川 満（関西学院大学大学院経済学研究科）
- タイトル：A mathematical principle of evolutionary game theory （進化ゲーム理論の数理）
- アブストラクト：
- The basic concepts in the modern economics of today was
constructed by the great mathematician (von Neumann,
Nash, Smale, etc). In my talk, we deal with the EVOLUTIONARY GAME
THEORY, pursue the new developments. It is said that it can explain the
anomaly in the economics and it will be important field in the future.
It is formulated rigorously and rearranged
by my researches. We propose the direction of the new research
(Equilibrium Concept, etc).
柘植 直樹（広島工業大学情報学部）
- タイトル：Large time decay of solutions to isentropic gas dynamics
- アブストラクト：
- We study the large time behavior of solutions to
isentropic gas dynamics. Our goal in this talk is to derive the decay of
the $L1$ norm of pressure. To do this, we investigate approximate
solutions constructed by a difference scheme.
縄田 紀夫（九州大学大学院数理学府）
- タイトル：Irrational rotation algebras and real quadratic fields
- アブストラクト：
- Irrational rotation algebras are objects in
$C^*$-algebra theory. They are also called noncommutative tori. Y. Manin
proposed the use of noncommutative tori as geometric framework for the
study of abelian class field theory of real quadratic fields. In this
talk, we introduce $C^*$-algebra theory and explain the reason why Y.
Manin proposed.
若林 徳子（近畿大学大学院総合理工学研究科）
- タイトル：Generating functions for multiple zeta values with fixed weight, depth and generalized height
- アブストラクト：
- We consider multiple zeta values defined by the Euler
sums with non-strict inequalities in the summation. The notion of
i-height is introduced for every natural number i. We define generating
functions for sum of multiple zeta values with fixed weight, depth and
i-height and prove that the function can be expressed in terms of
generalized hypergeometric functions.
網谷 泰治（早稲田大学理工学術院）
- タイトル：Classification of polarized manifolds containing Castelnuovo manifolds as their hyperplane sections
- アブストラクト：
- Given a variety $A$, it is a naive problem in algebraic
geometry to determine the structures of projective varieties $X$
containing $A$ as ample divisors. The problem has been extensively
studied by many mathematicians when $A$ has some special structure. In
this conference, I would like to treat the case where $A$ is a
Castelnuovo manifold, and to announce a classification result of $X$.
Here a Castelnuovo manifold is a higher-dimensional analog of a curve of
maximal genus. Typical examples of those manifolds are Del Pezzo and
Mukai manifolds, which are Fano manifolds whose anti-canonical divisors
are high multiples of ample divisors.
北川 友美子（大阪市立大学数学研究所）
- タイトル：On sub-Riemannian manifolds（サブリーマン多様体の無限小自己同型について）
- アブストラクト：
- My subject is a sub-Riemannian geometry. A
sub-Riemannian geometry is a manifold endowed with a distribution and a
fibre inner product on the distribution. A distribution here means a
linear subbundle of the manifold. This Riemannian fibre metric is called
a Carnot Caratheodry metric, which is related an Optimal Control Theory.
Now we suppose that a distribution is bracket generating (i.e., the
collection of all vector fields generated by Lie brackets spans the
whole tangent bunndle). In this talk we study a local classification of
sub-Riemannian manifolds.
關 良輔（北海道大学大学院工学研究科）
- タイトル：Analysis of the alpha particle orbits in Heliotron type fusion
device（ヘリオトロン型核融合装置におけるα粒子の軌道解析）
- アブストラクト：
- The aim of this work is to investigate the 3.5 MeV alpha
particle orbits in the high beta plasma. It has been found that the
so-called "chaotic orbit" alpha particles are lost before they heat
fuels, i.e., their lifetimes are much shorter than the alpha-electron
relaxation time. The average lifetime of all alpha particles is
characterized mainly by the short lifetimes of the chaotic orbit alpha
particles.
田中 潤（University of California Riverside）
- タイトル：The generalized Feynman-Kac formula with a Lebesgue-Stieltjes
measure and random variables
- アブストラクト：
- This Feyman-Kac formula was obtained for an arbitrary
Borel measure. For this talk, I will concentrate on the more physically
relevant case of a measure with a finitely supported discrete measure
and for simplicity, on the case of a continuous measure + a Dirac mass
at a single time \tau. I will show that the function defined by the
function u(t) associated with the corresponding generalized Feynman-Kac
functional satisfies a suitable differential equation and integral
equation. I will then deduce that u(t) has a discontinuity at \tau. Then
I will randomize those discontinuities \tau and the Dirac mass.
中田 健二（北海道大学大学院工学研究科）
- タイトル：Boundary element analysis of tokamak plasma current profile using quasi radial basis functions with variable scaling factors
- アブストラクト：
- The Grad-Shafranov equation, which is the axisymmetric
form of the 3-DPoisson equation, has been transformed into a boundary
integral equation byintroducing the "quasi radial basis function"
expansion of itsinhomogeneous source term. It has been found that
excellent accuracy of thesolution can be realized when adopting
space-dependent scaling factors forthe above basis functions
仲田 研登（大阪大学大学院情報科学研究科）
- タイトル：Hook formulas for a generalized Young diagram
- アブストラクト：
- The number of standard Young tableaux of a given shape
is given by the classical hook formula. In this talk, we talk on a
far-reaching generalization (colored hook formula, and q-Hook formula)
for a generalized Young diagram in the sense of D.Peterson. The colored
hook formula is new even for a classical Young diagram.
沼田 泰英（北海道大学大学院理学研究院）
- タイトル：Generalized Schur operators on the vector space spaned by
rooted planar binary trees
- アブストラクト：
- We introduce new families of operators on the vector
space spaned by rooted planar binary trees. We show that they are
generalized Schur operators.
野田 尚廣（名古屋大学大学院多元数理科学研究科）
- タイトル：Geometry of tangential distribution (接分布の幾何学)
- アブストラクト：
- Distributions on manifolds are studied by many
researcher. In particular, Goursat and Cartan studied some distributions
deeply using differential system and Lie algebra. In this talk, we
explain results on geometric structure associated with distributions.
深澤 知（早稲田大学理工学術院/日本学術振興会）
- タイトル：The generic smoothness of the Gauss map and the reflexivity
for a projective variety
- アブストラクト：
- The Gauss map is a rational map from a projective variety to the Grassmannian which assigns to a smooth point its projective tangent space. In this presentation, we study the Gauss map from the viewpoint of positive characteristic geometry. We discuss the relationship between the generic smoothness of the Gauss map and the reflexivity with respect to projective duality.
藤井 忍（広島大学大学院理学研究科）
- タイトル：Moment maps of isotropy representations of Hermitian symmetric
spaces and the isoparametric hypersurfaces in spheres （Hermite対称空間
の等方表現の運動量写像と球面内の等径超曲面）
- アブストラクト：
- The isotropy representations of real Grassmannian
manifolds of rank two are Hamiltonian actions. In this talk, we explain
that (weighted) square norms of their moment maps are isoparametric
functions. We expect that isoparametric hypersurfaces with four distinct
principal curvatures in spheres are related to moment maps of group actions.
宮本 安人（東京工業大学大学院理工学研究科）
- タイトル：On the shape of the stable patterns for activator-inhibitor
systems in a disk
- アブストラクト：
- It is well-known that all the inhomogeneous steady
states to a scalar reaction-diffusion equation on a convex domain in R^n
are unstable. Hence if a steady state is stable, then it should be
constant. When the domain is an interval, if a steady state of a shadow
system of activator-inhibitor type is stable, then it should be monotone
or constant. However, the shape of stable steady state of shadow systems
seems to be unknown in the case of high-dimensional domains. We study
the shape when the domain is a disk.
村田 駿祐（筑波大学大学院数理物質科学研究科）
- タイトル：Some relations in universal enveloping algebras of three
dimensional Lie algebras
- アブストラクト：
- We let L be a three dimensional Lie algebra which
generated by two elements x, y. And the universal enveloping algebra of
L is denoted by U(L). When L is the spaclal linear Lie algebra $sl_2$ or
the Heisenberg Lie algebra $H$ it has been proved that a concrete basis
of U(L) is given by some $x^iy^jx^k$. We explain several relations to
obtain a similar basis when L is neither $sl_2$ nor $H$. Then we also
show certain characterizations of $sl_2$ and $H$.
四ツ谷 直仁（名古屋大学大学院多元数理科学研究科）
- タイトル：The plethystic program
- アブストラクト：
- The Plethystic Program is an efficient methhod of
counting single-trace and multi-trace gauge invariant operators (GIO) of
gauge theory proposed by Hanany et al. Systematically,there are three
ways to count GIO, if Calabi-Yau (CY) manifold is given.The key to this
program is the map called "The Plethystic Exponential " and its inverse
map "The Plethystic Logarithm".This program also includes fascinating
mathematical structures ;Syzygies ,Young Tableaux and Hilbert scheames.
若狭 有光（北海道大学大学院工学研究科）
- タイトル：Study of neoclassical transport of LHD plasmas using the
DCOM/NNW neoclassical transport database
- アブストラクト：
- We have developed a neoclassical transport database for
LHD plasmas, DCOM/NNW. The mono-energetic diffusion coefficients are
evaluated based on the Monte Carlo method by DCOM code and the
mono-energetic diffusion coefficient database is constructed using a
neural network technique. In this study, the database construction
related to the plasma beta is investigated. The improved DCOM/NNW
database is applied finite beta LHD plasma, and the neoclassical
transport coefficients and the ambipolar radial electric field are
evaluated.
澤野 嘉宏（首都大学東京大学院理学研究科）
- タイトル：An introduction of the theory of reproducing kernel Hilbert spaces
- アブストラクト：
- This talk is oriented to the theory of reproducing
kernel Hilbert spaces. First, I shall present the definition of Hilbert
spaces and then I will develop a brief theory of the reproducing kernel
Hilbert spaces. Some elementary examples are presented in this talk. If
time permits, I will allude to my own results.
甲斐 千舟（金沢大学大学院自然科学研究科）
- タイトル：A distinguished bounded realization and a symmetry characterization of homogeneous bounded domains
- アブストラクト：
- Stefan Bergman defined the Bergman mappings for bounded
domains, which give the Riemann mappings in the one-dimensional case. We
show that if a bounded domain is homogeneous, its Bergman mapping works
very well. As an application, we prove that a homogeneous bounded domain
is symmetric if and only if the image of the Bergman mapping is convex.