Speaker	：Toshihiro Shoda ( Dept. of Math., Saga Univ. )
Title	：Minimal surfaces and algebraic curves
	（Abstract）
Date	：March 14 (Wed.) 14：40～16：10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yukio Otsu (Kyushu University, Dept. of Math.)
Title	：On quantum statistical mechanics of harmonic oscillators of random nets
	（Abstract）
Date	：February 21 (Wed.) 14：40～16：10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Hajime Ono ( Dept. of Math., Tokyo Inst. Tec. )
Title	：The existence and uniqueness of toric Sasaki-Einstein metrics
	（Abstract）
Date	：February 7 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Hiroshi Takai (Tokyo Metropolitan University)
Title	：Moduli Spaces of Instantons on Noncommutative 4-Manifolds
	（Abstract）
Date	：February 7 (Wed.) 13:00～14:30
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yoshitake Hashimoto ( Dept. of Math., Osaka City Univ. )
Title	：On "D. Joyce, Configurations in abelian categories"
	（Abstract）
Date	：January 31 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Naoyuki Koike ( Dept. of Math., Tokyo Univ. Sci. )
Title	：Complexification of a pseudo-Riemannian manifold and anti-Kaehler geometry
	（Abstract）
Date	：January 27 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Hisayoshi Muroya ( Dept. of Math., Osaka City Univ. )
Title	：Quasiconformal harmonic maps and the universal Teichm\"{u}ller space
	（Abstract）
Date	：January 17 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Naoki Hamamoto ( Dept. of Math., Osaka City Univ. )
Title	：Solutions of Einstein's field equations under the Kerr-Shild ansatz
	（Abstract）
Date	：December 20 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yasuyuki Nagatomo ( Faculty of Math., Kyushu Univ. )
Title	：Harmonic map into Grassmannian manifolds
	（Abstract）
Date	：December 6 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Takashi Otofuji ( Fac. of Tech., Nihon Univ. )
Title	：Geodesics of Hofer's metric on the space of Lagrangian submanifolds
	（Abstract）
Date	：November 15 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Akira Asada (Former: Shinshu University)
Title	：Integrable connections and loop group bundels
	（Abstract）
Date	：November 8 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：David Brander (Kobe University, JSPS researcher )
Title	：Isometric immersions of space forms as pluriharmonic maps
	（Abstract）
Date	：October 18 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Nobutaka Boumuki (Osaka City University Advanced MathematicalInstitute )
Title	：Real simple Lie groups and pseudo-kaehlerian homogeneous spaces
	（Abstract）
Date	：October 11 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yoshihiro Ohnita (Osaka City University)
Title	：Lagrangian Submanifolds in Complex Hyperquadrics and Isoparametric Hypersurfaces in Spheres
	（Abstract）
Date	：October 4 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Takefumi Kondo ( Department of Mathematics, Kyoto University )
Title	：Fixed-point property of random groups
	（Abstract）
Date	：July 19 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Hiroshi Sawai ( Department of Mathematics, Osaka University )
Title	：Locally conformal K\"ahler structures on compact nilmanifolds with left-invariant complex structures
	（Abstract）
Date	：June 28 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Norio Ejiri ( Department of Mathematics, Meijo University )
Title	：Minimal Surfaces in Tori
	（Abstract）
Date	：June 14 (Thu.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Ryoichi Kobayashi ( Nagoya University)
Title	：The Gauss map of algebraic minimal surfaces - toward Nevanlinna-Galois theory -
	（Abstract）
Date	：June 7 (Thu.) 16:00～17:30
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Hiroyuki Tasaki 　(Graduate School of Pure and Applied Sciences, University of Tsukuba)
Title	：Geometry of reflective submanifolds
	（Abstract）
Date	：May 19 (Fri.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Sumio Yamada ( Graduate School of Science, Tohoku University )
Title	：On existence of singular minimal subvarieties
	（Abstract）
Date	：May 18 (Thu.) 10:40～12:10
Place	：Dept. of Mathematics, Sci. Bldg., 2068
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Speaker	：Nobutaka Boumuki 　(Osaka City University Advanced MathematicalInstitute )
Title	：Pseudo-hermitian symmetric spaces and elliptic adjoint orbits
	（Abstract）
Date	：May 10 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Takashi Sakai (Osaka City University)
Title	：Weakly reflective submanifolds and austere submanifolds
	（Abstract）
Date	：April 19 (Wed.) 14:40～16:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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It is well-known that a conformal minimal immersion from a compact Riemann surface into a flat torus factors through the Jacobian variety. So, this fact suggests that there is some correlation between the theory of minimal surfaces and that of algebraic curves. In this talk, I will talk about the theory of minimal surfaces in terms of that of algebraic curves.

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We can approximate an compact Riemannian manifold by a set of random points, which we call random net. By considering random net as finite graph, we can define discrete Laplacian, which converges to continuum one by proper scaling. In this talk, we formulate quantum statistical mechanics of harmonic oscillators by regarding the values of function on net as canonical coordinates and Dirichlet integral as potential energy. Then we investigate its application to geometry.

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This talk is based on a joint work with A. Futaki and G. Wang.
We consider the following problem: Let M be a compact``transversely Fano" Sasaki manifold. Then is there a Sasaki-Einstein metric on M? And if it exists, is it unique up to automorphisms? We show that if M is toric then there exists a ``unique" toric Sasaki-Einstein metric on M.

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Studied is the instanton moduli spaces on noncommutative 4-manifolds. Especially given a principal bundle over a compact spin toric 4-manifold with its fibres to be a compact connected Lie group and its noncommutative one, then its associated module derived from noncommutative smooth sections with a hightest weight has the instanton moduli space whose geometric feature is a locally smooth manifold with its dimension determined by its highest weight as well as spin structure. This can be generalized for any compact toric 4-manifold. As their applications, we apply our main results to typical two examples which could be explained in detail.

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I shall review D. Joyce, Configurations in abelian categories, I-IV, math.AG/0312190, 0503029, 0410267, 0410268 and related topics.
Joyce conjectured the existence of a new invariant of Calabi-Yau 3-folds in On counting special Lagrangian homology 3-spheres, hep-th/9907013, and to construct it he presented series of papers Special Lagrangian submanifolds with isolated conical singularities, I-V and the series in the title of this talk. This invariant is given by counting special Lagrangian submanifolds, and is conjectured to correspond to the Donaldson-Thomas invariant (a complex analogue of the Casson invarant) by the Mirror Symmetry.

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It is known that the complexification $M_g^{\bf c}$ of a $C^{\omega}$-pseudo-Riemannian manifold $(M,g)$ is defined as a tubular neighborhod (equipped with the complex structure $J^g$ arising from $g$) of the zero section ($=M$) of the tangent bundle $TM$ of $M$. First we define the complexification $f^{\bf c}:M_g^{\bf c}\to\tilde M_{\tilde g}^{\bf c}$ of a $C^{\omega}$-map $f:(M,g)\to(\tilde M,\tilde g)$ and show that $f^{\bf c}$ is the holomorphic extension of $f$, where $(M,g)$ and $(\tilde M,\tilde g)$ are pseudo-Riemannian manifolds. Next we state that an anti-Kaehler metric $g_A$ on $M_g^{\bf c}$ is defined in a natural manner. We show that, for a $C^{\omega}$-isometric immersion $f:(M,g)\hookrightarrow(\tilde M,\tilde g)$, its complexification $f^{\bf c}:(M_g^{\bf c},g_A)\to(\tilde M_{\tilde g}^{\bf c},\tilde g_A)$ is a holomorphic isometric immersion on a tubular neighborhood of $M$. Also, we state the dual of a $C^{\omega}$-pseudo-Riemannian manifold at each point, a complex Jacobi field along a complex geodesic and a complex focal radius of an anti-Kaehler submanifold.

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The universal Teichm\{"}uller space is defined by equivarent classes of quasi-conformal maps between Poincare disks. We shall introduce some known results about quasiconformal harmonic maps and the universal Teichm\{"}uller space.

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A study to find a solution of an Einstein equation expressed in Kerr-Shild form is pushed forward flourishingly. In the case of 4 dimension, the solutions which is expressed by a Kerr-Shild form are completely known. The most generalized solution is high-dimensional Kerr-NUT-AdS now; Riemann curvature tensor by this solution is found to be D type by a calculation. If time remains, I speak a definition of parallel transport of a vector without a definition of vector bundle.

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Theorem of Takahashi on a minimal immersion of a Riemannian manifold into a sphere is generalized to a harmonic map into a Grassmannian manifold. We describe harmonic maps from a compact symmetric space into a Grassmannian manifold which have constant energy densities. Finally, we introduce a ``Penrose transform" between a harmonic map from a 4-dimensional sphere into a complex Grassmannian manofold which satisfies a differential equation of the first order and a holomorphic map from a 3-dimensional complex projective space into a complex Grassmannian manifold.

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We study geodesics of Hofer's metric on the space of Lagrangian submanifolds in arbitrary symplectic manifolds from the variational point of view. We give a characterization of length-critical paths with respect to this metric.

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Let $A$ be an integrable connection on a manifold $M$, then $trA^{2p-1}$ is a closed form and with suitable normalization, its de Rham class $b^p$ is an integral class if $A$ is written as $g^{-1}dg$ on $M$ and vanishes if the logarithm of $g$ exists on $M$. Obstruction to the global existence of logarithm of $g$ on $M$ is obtained as the loop group bundel $B(g)$ constructed from $g$. $b^p, p>1$ is written by using curvature and connection of $B(g)$. $b2$ is the so called string class and the obstruction to the lift of the structure group of $B(g)$ to the central extension of the loop group.

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Pluriharmonic maps from an n-dimensional complex manifold into a symmetric space are known to have a loop group formulation, that is they come in families parametererized by a spectral parameter in the unit circle. For the case n=1, it is well known that these have interpretations as special surfaces, depending on the symmetric space involved. In higher dimensions, the applications to special submanifolds appear to be unexplored.

We show that pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold correspond to isometric immersions with flat normal bundle between space forms, which had already been given a loop group formulation by Ferus and Pedit. Conversely, we can show, using a technique from loop groups, that every such isometric immersion can be extended to such a pluriharmonic map.

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Let G be a connected real Lie group, and let H be a connected, closed subgroup of G. Then, the coset space G/H is said to be a symplectic homogeneous space if there exists an invariant symplectic form on G/H. In particular, it is said to be a pseudo-kaehlerian homogeneous space if there also exists an invariant complex structure on G/H which is compatible with its symplectic form. The main purpose of our talk is to give a necessary and sufficient condition for symplectic homogeneous space G/H to be pseudo-kaehlerian, in the case where G is simple.

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This talk is based on my joint work with Hui Ma (Hsinghua University, P.~R.~China).　In this talk we begin with basic propeties of Lagrangian submanifolds in Kaehler manifolds and their Hamiltonian deformations and give a characterzation of Hamiltonian deformations in terms of a notion of isomonodromy deformations. We shall give our attention to Lagrangian submanifolds in complex hyperquadrics, which is a compact Hermitian symmetric space of rank 2. The relationship of Lagrangian submanifolds in complex hyperquadrics with Hypersurafce Geometry in Spheres will be discussed via the Gauss maps recalling B.Palmer's results.　We shall provide a classification of compact homogeneous Lagrangian submanifolds, i.~e.~Lagrangian orbits of compact Lie groups, in complex hyperquadrics from the viewpoint of homogeneous isoparametric hypersurfaces.　Moreover we shall discuss Hamiltonian stability of minimal Lagrangian submanifolds obtained as Gauss images of isoparametric hypersurfaces in spheres and obtain new examples of compact Hamiltonian stable minimal Lagrangian submanifolds in complex hyperquadrics．

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(Joint work with Izeki-Nayatani) Given a discrete group and its isometric action on a CAT(0) space, Izeki and Nayatani formulated a criterion for the action to have a global fixed point. Combining generalized version of this result with a result of Zuk, we conclude that a random group with "many" relations of length three has a strong fixed-point property. We explain the relation of our result to the nonlinearity problem.

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Let $(M,g,J)$ be a compact Hermitian manifold and $\Omega$ the fundamental $2$-form of $(g,J)$. A Hermitian manifold $(M,g,J)$ is called a locally conformal K\"ahler manifold if there exists a closed $1$-form $\alpha$ such that $d\Omega=\alpha\wedge\Omega$. The purpose of this talk is to give a complete classification of locally conformal K\"ahler nilmanifolds with left-invariant complex structures. In addition, we mention locally conformal K\"ahler structures on compact solvmanifolds.

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We give the fundamental construction of complex submanifolds and Lagrange submanifolds associated with the moduli space of minimal surfaces in tori. In paticular, for holomorphic curves, we know the difference between tori of dimension ≦ 6 and dimension ≧ 8.

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The invariant $R$ introduced in the colloquium talk is a very interesting object to study in the value distribution theory. We introduce the fundamental framework for the Nevanlinna theory of the Gauss map of algebraic minimal surfaces lifted to the universal cover, i.e., the disk. Because of the presence of the Galois group action, such mathematics may be called the Nevanlinna-Galois theory. We will explain the present status of the project toward understanding the Nevanlinna-Galois theory.

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We consider an extension of Crofton formula of plane curves to an integral formula of submanifolds in Riemannian symmetric spaces. We use reflective submanifolds in this integral formula. A reflective submanifold is the fixed point set of an involutive isometry. The set of reflective submanifolds has a sturucture of symmetric space, an invariant pseudo-Riemannian metric and an invariant measure. We establish a coarea formula with respect to a pseudo-Riemannian metrics and by the use of this coarea formula we can extend Crofton formula in the case of Riemannian symmetric spaces.

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The key idea of solution by J. Douglas, of the Plateau problem was to use harmonic map in order to show the existence of minimal surfaces spanned by a Jordan curve. In this talk new results concerning existence of singular minimal subvarieties, motivated by geometric measure theory, in particular (M, epsilon, delta)-minimal sets, will be presented. (Joint work with C. Mese)

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Irreducible pseudo-hermitian symmetric spaces belong to the category of affine symmetric spaces and of elliptic adjoint orbits. Hence, it is possible to realize them as elliptic adjoint orbits. In this talk, we will realize a pseudo-hermitian symmetric space $E_{6(-14)} / (SO^*(10)\times T)$ as an elliptic adjoint orbit.

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This talk is based on a joint work with H. Tasaki and O. Ikawa. We introduce a notion of weakly reflective submanifolds in a Riemannian manifold, which is a generalization of reflective submanifold. We will discuss some fundamental properties of weakly reflective submanifolds and relationship to austere submanifolds. Moreover, we will give the classification of austere orbits and weakly reflective orbits of isotropy representations of irreducible symmetric spaces.

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