Speaker	：Markus Schmies (TU Berlin)
Title	：Numerical methods for Schottky uniformization
	（Abstract）
Date	：January 25 (Wed.) 15：20～16：20
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Christoph Bohle (TU Berlin)
Title	：Constrained Willmore surfaces
	（Abstract）
Date	：January 25 (Wed.) 14：15～15：15
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Shimpei Kobayashi (Tokyo Denki University)
Title	：Coarse classification of constant mean curvature cylinders
	（Abstract）
Date	：December 7 (Wed.) 2：40～4:10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Martin A. Guest (Tokyo Metropolitan University)
Title	：Quantum cohomology and harmonic maps
	（Abstract）
Date	：December 7 (Wed.) 10：40～12：10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Tadashi Taniguchi (Sendai National College of Technology)
Title	：SUSY Instanton Bundles on Super Twistor Space
	（Abstract）
Date	：November 30 (Wed.) 14：40～16：10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Akhil Ranjan (Indian Institute of Technology)
Title	：Proof of Lichnerowicz conjecture in the simply connected compact case
	（Abstract）
Date	：November 16 (Wed.) 14：40～16：10
Place	：Dept. of Mathematics, Sci. Bldg., Seminar room 1
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Speaker	：Yasuo Matsushita (Shiga Prefecture University)
Title	：The existence of indefinite metrics of signature (+ + - -) and two kinds of almost complex structures in dimension four
	（Abstract）
Date	：November 9 (Wed.) 14：40～16：10
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yoshihiro Ohnita (Osaka City University)
Title	：On Hamitonian stability of certain Lagrangian submanifolds in K\"ahler manifolds
	（Abstract）
Date	：October 26 (Wed.) 14：30～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Tomonori Noda (Osaka City University Advanced Mathematical Institute)
Title	：Stability of harmonic foliations and complex surfaces
	（Abstract）
Date	：October 19 (Wed.) 14：30～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Futoshi Takahashi (Osaka City University)
Title	：Multiple solutions of H-systems on some multiply-connected domains
	（Abstract）
Date	：October 12 (Wed.) 14：30～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Yoshihiro Ohnita (Osaka City University)
Title	：On moduli spaces of special Lagrangian submanifolds
	（Abstract）
Date	：October 5 (Wed.) 14：30～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Akira　Asada (Former: Sinsyu University)
Title	：Regularized volume of the sphere of a Hilbert space with the determinant bundle
	（Abstract）
Date	：July 6 (Wed.) 15：00～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Speaker	：Sergei　Ketov（Tokyo Metropolitan University, Physics）
Title	：Non-anti-commutativity in quantum field theory and strings
	（Abstract）
Date	：June 22(Wed.) 15：00～16：00
Place	：Dept. of Mathematics, Sci. Bldg., 3040
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Riemann surfaces of higher genus have many applications but their numerical treatment is challenging. Using Schottky uniformization to represent Riemann surfaces, differentials and integrals can be explicitly expressed as Poincar\'e theta series. I explain how this used to achieve efficient numerical methods and apply these to compute solutions of the KP2 equation, which is a standard example from the theory of integrable systems.

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Constrained Willmore surfaces are the critical points of the Willmore functional with respect to conformal variations of compact support. Examples include all CMC-surfaces in space forms. In my talk I will derive the Euler-Lagrange equations and discuss low genus examples.

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This is joint work with Josef Dorfmeister at TU Munich. We give a coarse classification of constant mean curvature ({\sc CMC}) immersions of cylinders into $\R3$ via the loop group method. We particularly, for this purpose, generalize {\sc CMC}-immersions into double loop groups and introduce a new type of meromorphic 1-forms corresponding to {\sc CMC}-immersions on Riemann surfaces.

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The quantum cohomology of a space corresponds to a flat connection, and this flat connection corresponds to a pluriharmonic map. We shall give some concrete examples of this correspondence, including the interesting case of Calabi-Yau manifolds, which is related to mirror symmetry.

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Let $R^{4\vert 4N}$ be a $4\vert 4N$ dimensional super Euclidean supace.
The super twistor space of $R^{4\vert 4N}$ is the complex super projective space $P^{3\vert N}$. We showed that there is a one-to-one correspondence between N=2 Supersymmetric Yang-Mills instantons over $R^{4\vert 8}$ and certain holomorphic super vector bundles over $P^{3\vert 2}$, it so called Super Penrose-Ward correspondence. So the problem of describing all supersymmetric instantons is reduced to the description of holomorphic super vectror bundles over $P^{3\vert 3}$. In this framework the solutions are obtained from a super monad over $P^{3\vert 2}, and then the super Penrose-Ward correspondence is used to pass back to $R^{4\vert 8}$.

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In 1944 Lichnerowicz defined a class of Riemannian spaces called 'harmonic spaces ' and showed that in dimensions up to four they are all rank one symmetric. He cojectured this to be true in all dimensions. In 1990, Z I Szabo proved the conjecture for compact harmonic spaces with finite fundamental groups. We will present a simplified version of his proof in this talk.

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The existence of a neutral metric (+ + - -) on a 4-manifold is equivalent to the existence of a 2-plane field on the 4-manifold. The condition for a 4-manifold to admit a 2-plane field is a fundamental result of Hirzebruch and Hopf (1958). It is reported (1991) that a 4-manifold with a 2-plane field admits two kinds of almost complex structures. On the basis of these existence conditions of a neutral metric, a 2-plane field and two kinds of almost complex structures, we can exhibit various interesting results on 4-manifolds.

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A Lagrangian submanifold in a K\"ahler manifold is called Hamiltonian minimal if the first variation of the volume vanishes under every Hamiltonian variation. Moreover, a Hamiltonian minimal Lagrangian submanifold is called Hamiltonian stable if the second variation of the volume is non-negative under every Hamiltonian variation. So many Hamiltonian stable Lagrangian submanifolds are not known yet. It is not so well-investigated what kinds of Lagrangian submanifolds are Hamiltonian stable. In this talk we discuss the Hamiltonian stability of compact Lagrangian submanifolds embedded in complex space forms with parallel second fundamental form and the existence of a compact homogeneous Hamitonian stable minimal Lagrangian submanifold in 3-dimensional complex projective space whose second fundamental form is not parallel.

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Harmonicity for foliations was defined by Kamber-Tondeur and various notions for harmonic maps were shifted to notions in theory of foliations. In this talk, stability for harmonic foliations is discussed and sufficient conditions are given. Moreover, stability for harmonic foliations on compact complex surfaces without Kaehler structures are treated.

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We study the multiple existence of solutions of H-systems, which are systems of elliptic equations satisfied by conformal parametrisation of surfaces of constant mean curvature, under the homogeneous Dirichlet boundary condition.

In 1970's, H. Wente proved the followings:

If the domain is simply-connected, the only solution is a trivial one. On the other hand, if the domain is an annulus, there exists at least one non-trivial solution.

In this talk, we consider the problem on some (K+1)-ply connected domain (which has K holes) and prove that there exist at least K distinct non-trivial solutions. Our proof is based on the infinite-dimensional Morse theory.

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Recently the theory of moduli spaces of special Lagrangian submanifolds with conical singularities in Calabi-Yau manifolds are discussed by D.Joyce in a series of his many papers.
In this seminar I want to explain briefly his ideas and results in the theory and to state my recent results on stability of special Lagrangian cones.

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Calculi on an infinite dimensional space H often meet the problem of divergence. When H is the Hilbert space over a compact Riemannian manifold X, we fix a non-degenerate selfadjoint elliptic operator D on X and use the spectral zeta function Z(D,s) to overcome this difficulty.
Applying analytic continuation of Z(D,s), we can regularize integrals on H and give a mathematical justification of the appearence of the Ray-Singer determinant in the calculation of Gaussian path integral. But in this regularization, we need to add one dimension to H, which can be viewed as the determinant bundle.
 Rewriting this regularization by using polar coordinate of H, we obtain regularized volume form and volume of the sphere in H with the determinant bunlde, They take same forms as the volume forms and voluems of finite dimensional spheres, but the regularized volume form has singularities on the sphere of H. So unless adding the determinant bundel, we can not obtain regularized volume form of the sphere.

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In this talk I would like to introduce a new notion of non-anti-commutativity in supersymmetric field theory. This talk is designed for mathematicians, so no physical applications will be discussed. Instead, a simple introduction into a mathematical structure of quantum theory will be given, from the first principles.I briefly review the mathematical structure of classical mechanics,  quantum mechanics and quantum field theory. The physical notions of spin, statistics, and supersymmetry are defined in formal terms. Then a short discussion of a spacetime non-commutativity follows. Finally, a non-anti-commutativity is introduced in superspace. When the time allows, a connection to string theory will be shortly discussed too.

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