Speakers・Titles・Abstracts: |
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Quo-Shin Chi (Washington U in St Louis), I |
"A new look at Condition A" |
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In this talk, I will first quickly review the recent
progress on the classification of isoparametric hypersurfaces in spheres,
which leaves open only the four exceptional cases of four principal curvatures
with multiplicity pairs (4,5), (3,4), (7,8), (6,9). Ozeki and Takeuchi
introduced Conditions A and B to construct inhomogeneous examples of
isoparametric hypersurfaces with four principal curvatures of multiplicity
pairs (3,4r) and (7,8r) in spheres. Later Dorfmeister and Neher showed
that Condition A alone implies the isoparametric hypersurfaces is one of
the examples constructed by Ferus, Karcher and Munzner that generalized
those of Ozeki and Takeuchi. It appears Condition A may hold the key
to the classification of the multiplicity pairs (3,4) and (7,8).
Dorfmeister and Neher's method is algebraic in nature and their
proof for the multiplicity pairs (3,4) and (7,8) relies on the
classification result of McCrimmon about composition triples. We will present
a fairly short and straightforward classification proof of the result of
Dormeister and Neher based on more geometric considerations, in which the
octonian algebra plays a decisive role.
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Quo-Shin Chi (Washington U.in St. Louis), II |
"On a problem of Kuiper" |
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Kuiper raised the question whether a taut submanifold in
Euclidean space is algebraic, i.e., is an open subset of an irreducible
component of a real algebraic variety in the ambient Euclidean space. I
will show the answer is affirmative.
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Josef Dorfmeister (Muenchen TU) |
"Planar CMC 4-noids of constant mean curvature" |
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There are two parts to this talk:
The first part discusses Fuchsian equations
from the point of view of H.A.Schwarz.
This means to consider a fundamental system u,v of solutions to a second
order Fuchsian ODE
and to discuss the polygon in the extended complex plane obtained as
boundary curve to the
image of the upper half-plane under the quotient map u/v. This polygon
consists of circular arcs.
We will characterize what it means that all monodromy matrices of the
Fuchsian equations are unitary.
In the second part we will apply ideas of Hilb and associate with the
circular arcs of the Schwarz polygon
planes intersecting the sphere in those circular arcs. Consequently, arcs
meeting at some vertex create some axis
via the the intersection of planes. We will characterize in terms of
intersecting axes and the sign of some coefficient
in some normalized Fuchsian equation what it means that all monodromy
matrices are unitary.
As a final application we will discuss what this means for the construction
of planar CMC 4-noids.
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長谷川浩司 Koji Hasegawa (Tohoku U.) |
"Quantizing the discrete Painleve VI equation" |
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Painleve equations have rich symmetry known as
"Baecklund transformations" which in fact generate
affine Weyl groups. In the VIth case, the group is of
type D_4^(1) and there is a symmetry-preserving
time discretization by Jimbo and Sakai. We will quantize
this, i.e. construct a non-commutative version of their
discrete VIth equation. Two ways to quantize: the symmetry
point of view and the monodromy-preserving point of view.
It turns out that these two provides the same equation.
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Hui Ma (Tsinghua U. OCAMI) |
"Hamiltonian stability of the Gauss images of homogeneous isoparametric" |
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The volume minimizing problem of Lagrangian submanifolds in Kaehler
manifolds under Hamiltonian deformations arises as a constraint variational problem
in the intersection of Riemannian Geometry and Symplectic Geometry.
As a generalization of minimal submanifolds and usual stability,
it defines Hamiltonian minimal submanifolds and Hamiltonian stability.
It is interesting to study the construction of Hamiltonian minimal submanifolds in specific Kaehler manifolds
and their Hamiltonian stability.
In this talk, we focus on minimal Lagrangian submanifolds
in complex hyperquadrics, obtained from Gauss images of isoparametric hypersurfaces
in unit spheres. We shall discuss the Hamiltonian stability in the
homogenous case.
This talk is based on the joint work with Prof. Yoshihiro Ohnita. |
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井ノ口順一 Jun-ichi Inoguchi (Yamagata U.) |
"Constant mean curvature surfaces in hyperbolic 3-space" |
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I will discuss a generalised Weierstrass representation
for constant mean curvature surfaces in hyperbolic 3-space
with mean curvature less than 1.
This is a joint work with Josef Dorfmeister and Shimpei Kobayashi.
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川上 裕 Yu Kawakami (Kyushu U.) |
"On the upper bound of the number of exceptional values of
the hyperbolic Gauss map" |
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In this talk, we will give the upper bound of the number of
exceptional values of the hyperbolic Gauss map of algebraic
CMC-1 surfaces and flat fronts with regular ends in the
hyperbolic three-space and discuss the sharpness of the estimates.
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小林真平 Shimpei Kobayashi (Hirosaki U.) |
"Harmonic trinoids in complex projective spaces" |
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I shall give a talk about a construction of harmonic maps
from a thrice punctured Riemann sphere into complex
projective spaces using loop group techniques and theory of
ordinary differential equations.
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野原雄一 Yuichi Nohara (Tohoku U.) |
"Toric degenerations of Gelfand-Cetlin systems and potential functions" |
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The Gelfand-Cetlin system is a completely integrable system
on a flag manifold of type A, whose moment polytope is called
the Gelfand-Cetlin polytope. It is also known that the flag
manifold has a degeneration into a toric variety corresponding
to the Gelfand-Cetlin polytope. We show that the Gelfand-Cetlin
system can be deformed into a moment map of a torus action on
the toric variety. We also discuss an application to mirror symmetry.
This is based on a joint work with T. Nishinou and K. Ueda.
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山田澄生 Sumio Yamada (Tohoku U.) |
"Weil-Petersson geometry of Teichmuller-Coxeter complex" |
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The Weil-Petersson metric on a Teichmuller space is well known to be
incomplete. We construct a geodesic
completion of the Teichmuller space, with help of the Coxeter complex
formalism, where
each copy of the Teichmuller space acts as a simplex. We deduce a
finite rank property
from such a construction. |
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Wayne Rossman (Kobe U.) |
"Discrete flat and linear Weingarten surfaces in
hyperbolic 3-space" |
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This is a joint work with Tim Hoffmann (Munich
Technical University), Takeshi Sasaki and Masaaki
Yoshida. Previous works have led to definitions
of discrete minimal surfaces in Euclidean 3-space
(Bobenko and Pinkall) and discrete CMC 1 surfaces
in hyperbolic 3-space (Hertrich-Jeromin). Taking
inspiration from those works, and from works by
Galves-Martinez-Milan and Kokubu-Umehara-Yamada
which give representations for smooth flat and smooth
linear Weingarten surfaces in hyperbolic 3-space,
we find discretizations for those surfaces. We
will present some resulting theorems that justify
our choice of definitions, and we will examine notions
of singularities and caustics on discrete flat
surfaces.
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酒井高司 Takashi Sakai (Tohoku Metrop. U.) |
"Tight Lagrangian surfaces in S^2×S^2" |
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In 1991, Y.-G. Oh introduced the notion of tightness of closed
Lagrangian submanifolds in Hermitian symmetric spaces. It is known that
any real forms in a compact Hermitian symmetric space are tight. In
this talk, we determine all tight Lagrangian surfaces in S^2×S^2. Latter, we shall discuss global tightness of real forms in
Hermitian symmetric spaces. In particular, we will show that globally
tight Lagrangian surfaces in S^2×S^2 are nothing but real
forms. This talk is based on a joint work with Hiroshi Iriyeh.
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宇田川 誠一 Seiichi Udagawa (Nihon U.) |
"Affine spheres of finite type and Symes method" |
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We construct an extended framing for Blaschke immersion of affine spheres in A^3 and may give all Blaschke immersions of finite type by Symes method. Moreover, DPW-method also gives a Weierstrass-Kenmotsu type representation for Blaschke immersions of affine spheres. This is a joint work with J. Inoguchi.
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