KASUYA Naohiko Associate Professor

Geometry

Organization
Department of Mathematics
Research Interest
Differential topology
Keywords
Contact structure, complex surface, strongly pseudoconvex boundary, strongly pseudoconcave boundary, Milnor fiber, singularity link

Research Activities

The main theme of my research is complex surfaces and their boundary contact structures. Stein surfaces and their strongly pseudoconvex boundary are the most typical examples. Especially, I am interested in the Milnor fiber and the link of a complex hypersurface singularity, called a cusp singularity, and studying them based on the knowledge of differential topology, contact geometry and symplectic geometry. I am also interested in non-Kahler complex surfaces and complex surfaces with strongly pseudoconcave boundaries, and constructed complex structures on the 4-dimensional Euclidean space which have both properties, based on the knowledge of 4-dimensional topology.

Papers:

  • N. Kasuya,
    The canonical contact structure on the link of a cusp singularity,
    Tokyo Journal of Mathematics, Vol.37, No.1 (2014), 1-20.
  • N. Kasuya,
    An obstruction for codimension two contact embeddings in the odd dimensional Euclidean spaces,
    Journal of the Mathematical Society of Japan, Vol.68, No.2 (2016), 737-743.
  • A. J. Di Scala, N. Kasuya and D. Zuddas,
    Non-Kahler complex structures on $\mathbb{R}^4$,
    Geometry & Topology, Vol.21, Issue 4 (2017), 2461-2473.
  • N. Kasuya and M. Takase,
    Knots and links of complex tangents,
    Transactions of the American Mathematical Society 370 (2018), 2023-2038.
  • A. J. Di Scala, N. Kasuya and D. Zuddas,
    Non-Kahler complex structures on $\mathbb{R}^4$,II
    Journal of Symplectic Geometry, Vol.16, No.3 (2018), 631-644.

contact

nkasuya（at）math.sci.hokudai.ac.jp