ENCOUNTERwithMATHEMATICS”ÔŠO•Ò
MiniWorkshop on Symplectic Foliations

2018 ”N 3 ŒŽ 9 “úi‹àj 3 ŒŽ 10 “úi“yj
‰—’†‰›‘åŠw—HŠw•”@‚T†ŠÙ‚RŠK‚T‚R‚R‚S†Žº  u‰‰—\’èŽÒF Mélanie Bertelson (Université Libre de Bruxelles), X@~Gi‘åãŽ•‰È‘åŠwjC””’J@’¼•Fi‹ž“sŽY‹Æ‘åŠwjCŽO¼@‰À•Fi’†‰›‘åŠwj
 Date: March 9 (Fri.)  March 10 (Sat.)
 Venue:
Room: 5334, 3rd floor, Building No. 5,
Faculty of Science and Engineering, Chuo University,
11327, Kasuga, Bunkyoku, Tokyo, Japan  Speakers: Mélanie Bertelson (Université Libre de Bruxelles), Atsuhide Mori (Osaka Dental Univ.), Naohiko Kasuya (Kyoto Sangyo Univ.), Yoshihiko Mitsumatsu (Chuo Univ.)
 Schedule:
March 9 (Friday)
14:0015:30 Yoshi MITSUMATSU
16:0017:30 Mélanie BERTELSON1
March 10 (Saturday)
10:3012:00 Naohiko KASUYA
lunch break
14:0015:30 Mélanie BERTELSON2
16:0017:30 Atsuhide MORI  Titles:
Yoshi MITSUMATSU
Construction of leafwise symplectic foliations on the 5sphere and the convexity
Mélanie BERTELSON1
Old results and new questions about existence of leafwise symplectic structures
Naohiko KASUYA
The contact boundary of the Milnor fiber of a cusp singularity
Mélanie BERTELSON2
Is there such a thing as Piecewise Linear symplectic geometry?
Atsuhide MORI
Symplectic foliations associated with certain openbook decompositions
 Abstracts:
Yoshi MITSUMATSU
Title: Construction of leafwise symplectic foliations on the 5sphere and the convexity
Abstract:
The basic technology of construction of leafwise symplectic foliations from Milnor's fibration is explained. In general the Milnor fibre has a symplectically convex end which is not suitable for a modification into leaves of foliations. How and under which circumstance this obstacle is resolved are discussed. If the time and situation allow, the relation with Lefschetz fibrations is also mentioned.
Mélanie BERTELSON1
Title: Old results and new questions about existence of leafwise symplectic structures
Abstract:
An hprinciple for open relations invariant under leaf preserving isotopies will be recalled alongside with obstructions to existence of leafwise symplectic structures. These suggest to explore the question of which open manifolds could possibly be a leaf in leafwise symplectic foliation on a closed manifold.
Naohiko KASUYA
Title: The contact boundary of the Milnor fiber of a cusp singularity
Abstract:
The hypersurface singularity in C^3 defined by x^p+y^q+z^r+xyz=0 is called a cusp singularity (resp. a simple elliptic singularity) when 1/p+1/q+1/r<1 (resp. when 1/p+1/q+1/r=1). We consider the Milnor fibration of a cusp singularity or a simple elliptic singularity. The axis of the fibration is the link of the singularity, which is known to be diffeomorphic to a T^2 bundle over S^1. On the link, a contact structure is canonically induced by the complex tangency. We introduce a method to detect the link topology and the contact structure on it by using the moment polytope of S^5. This method is also useful for understanding of the topology of the Milnor fiber, which will be explained in Mori's talk.
Mélanie BERTELSON2
Title: Is there such a thing as Piecewise Linear symplectic geometry?
Abstract:
The answer to the aboveraised question is as yet unclear. Our explorations of the reasons why will be described in the talk. This is a joint work with Julie Distexhe and Yasha Eliashberg.Atsuhide MORI
Title: Symplectic foliations associated with certain openbook decompositions
Abstract:
In the present understanding, the topology of symplectic foliation has relations with those of Lefschetz fibration and openbook decomposition (typically into Milnor fibers) from different points of view. As for codimensionone foliations of 5manifolds, these points of view seem close to each other. Our collaboration with Yoshihiko Mitsumatsu and Naohiko Kasuya is now investigating their overlap as well as developing the topological understanding of a certain Milnor fiber. Simultaneously, we are trying to find a higher dimensional nontrivial example of symplectic foliation associated with an openbook decomposition. A few new results in these directions will be explained.
˜A—æFŽO¼@‰À•F (Yoshihiko Mitsumatsu)
TEL:0338171749
EMAIL:yoshiATmath.chuou.ac.jp