Colloquium（2009）

Last Modified on 2011.3.31

Speaker:Miyuki KOISO ( Nara Women's University & PRESTO, JST )
Title:Global analysis on variational problems for surfaces and its applications
Date: Feb. 10 (Wed.) 2010, 16：30～17：30
Place: Dept. of Mathematics, Sci.Bldg., 3040
Abstract:
We consider variational problems for surfaces with constraint. An equilibrium surface is said to be stable if the second variation of the energy functional is nonnegative for all admissible variations. We discuss stability and bifurcations of solutions. We will give general methods and their applications to some concrete examples which may be interesting from both mathematical and physical point of view.

Speaker: Takuro MOCHIZUKI ( Kyoto University )
Title: On wild harmonic bundles
Date: Oct. 6 (Tue.) 2009, 16:30～17:30
Place: Dept. of Mathematics, Sci.Bldg., 3040
Abstract:
We will give an overview of the study on wild harmonic bundles. Very briefly, the results for tame harmonic bundles are generalized for wild harmonic bundles, and we obtain Hard Lefschetz Theorem for semisimple (non-regular) holonomic D-modules. There are several interesting phenomena and difficulties which do not appear in the tame (regular) case. For example, the existence of turning points, very bad singularity for meromorphic flat bundles over higher dimensional varieties, was a serious stumbling block. We also need to study Stokes structure. We would like to describe more recent results, if it is possible.

Speaker: Atsushi ICHINO ( Osaka City University )
Title: Representation theory and arithmetic invariants
Date: Oct. 6 (Tue.) 2009, 15:00～16:00
Place: Dept. of Mathematics, Sci.Bldg., 3040
Abstract:
The local Langlands conjecture relates the representation theory of reductive groups over local fields to arithmetic objects. Based on this conjecture, it is interesting to study how representation-theoretic invariants relate to arithmetic invariants. We explain this in the case of formal degrees.

Speaker: Kaoru ONO ( Hokkaido University )
Title: An analogous question to the flux conjecture concerning Lagrangian submanifolds
Date: July 29 (Wed.) 2009, 16：30～17：30
Place: Dept. of Mathematics, Sci.Bldg., 3040
Abstract:
A few years ago, I applied the Floer theory to prove the C^1-flux conjecture, which states that the group of Hamiltonian diffeomorphisms is closed in the identity component of the group of symplectomorphisms with respect to the C^1-topology. (Here we assume that the symplectic manifold is compact without boundary.) I would like to discuss its analog concerning Lagrangian submanifolds. Namely, the question is whether the quotient space of the space of Lagrangian submanifolds isotopic to a fixed one by the action of the group of Hamiltonian diffeomorphisms is Hausdorff or not. Although it is known that the answer is negative in general, we can show the following. If a closed Lagrangian submanifold has trivial Maslov class and is unobstructed in the sense of FOOO theory, its orbit by the action of the group of Hamiltonian diffeomorphisms is closed with respect to the C^1-topology.

Speaker: Prof. Jozef Zajac (the State University of Applied Science in Chelm)
Title: Teichmller spaces of a Jordan curve
Date: Apr. 22 (Wed.) 2009, 16：30～17：30
Place: Dept. of Mathematics, Sci.Bldg., 3040
Abstract:
In this presentation we will discuss the problem of introducing the group and metric structure to the family of all admissible parametrization functions of a given oriented Jordan curve on the extended complex plane. Introducing special number uniquely characterizing each parametrization function and then using Teichmuller metric we will show that it is bringing the construction to the Teichmuller space of a given oriented Jordan curve. Moreover, if additionally, the Jordan curve is a quasicircle then one may associate two conjugated Teichmuller spaces of a given quasicircle. One may show that the distance function between these conjugated spaces is determined uniquely by a constant characterizing the quasicircle.