ENCOUNTERwithMATHEMATICS番外編

MiniWorkshop on Symplectic Foliations

• 2018 年 3 月 9 日（金）-- 3 月 10 日（土）
  於中央大学理工学部　５号館３階５３３４号室
• 講演予定者： Mélanie Bertelson (Université Libre de Bruxelles), 森　淳秀（大阪歯科大学），粕谷　直彦（京都産業大学），三松　佳彦（中央大学）

• Date:   March 9 (Fri.) -- March 10 (Sat.)
• Venue:   Room: 5334, 3rd floor, Building No. 5,
  Faculty of Science and Engineering, Chuo University,
  1-13-27, Kasuga, Bunkyo-ku, 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)
     14:00-15:30 Yoshi MITSUMATSU
     16:00-17:30 Mélanie BERTELSON-1
    March 10 (Saturday)
     10:30-12:00 Naohiko KASUYA
     -lunch break-
     14:00-15:30 Mélanie BERTELSON-2
     16:00-17:30 Atsuhide MORI
• Titles:
  Yoshi MITSUMATSU
    Construction of leafwise symplectic foliations on the 5-sphere and the convexity
  Mélanie BERTELSON-1
    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 BERTELSON-2
    Is there such a thing as Piecewise Linear symplectic geometry?
  Atsuhide MORI
    Symplectic foliations associated with certain open-book decompositions
  
• Abstracts:
  

  Yoshi MITSUMATSU
    Title: Construction of leafwise symplectic foliations on the 5-sphere 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 BERTELSON-1
    Title: Old results and new questions about existence of leafwise symplectic structures
    Abstract:
  An h-principle 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 BERTELSON-2
    Title: Is there such a thing as Piecewise Linear symplectic geometry?
    Abstract:
  The answer to the above-raised 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 open-book decompositions
    Abstract:
  In the present understanding, the topology of symplectic foliation has relations with those of Lefschetz fibration and open-book decomposition (typically into Milnor fibers) from different points of view. As for codimension-one foliations of 5-manifolds, 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 non-trivial example of symplectic foliation associated with an open-book decomposition. A few new results in these directions will be explained.

連絡先：三松　佳彦 (Yoshihiko Mitsumatsu)
TEL:03-3817-1749
E-MAIL:yoshiATmath.chuo-u.ac.jp