KAWASAKI Morimichi Associate Professor

Geometry

Organization
Department of Mathematics
Research Interest
Symplectic Geometry
Keywords
Symplectic manifold, The group of Hamiltonian diffeomorphisms, (Partial) quasi-morphism, Hofer metric, Conjugation-invariant norm, Oh--Schwarz spectral invariant

Research Activities

My main reseaerch interest is symplectic geometry. Symplectic geometry has historical roots in Hamiltonian systems in classical mechanics and has gained recent attention for its connections with various other fields.
I am particularly interested in studying the metric and group structures of the group of Hamiltonian diffeomorphisms, which is one of the transformation groups of symplectic manifolds. Additionally, I research their applications, such as non-displaceable fibers in integrable systems, and I am also interested in applying group-theoretic arguments used to study the group of Hamiltonian diffeomorphisms to other transformation groups like the contact diffeomorphism group and the diffeomorphism group.

Papers

  • Relative quasimorphisms and stably unbounded norms on the group of symplectomorphisms of the Euclidean spaces, J. Symplectic Geom. 14 (2016), no. 1, 297–304.
  • Rigid fibers of integrable systems on cotangent bundles(joint work with Ryuma Orita), J. Math. Soc. Japan 74 (2022), no. 3, 829–847.
  • Ĝ-invariant quasimorphisms and symplectic geometry of surfaces (joint work with Mitsuaki Kimura), Israel J. Math. 247 (2022), no. 2, 845–871.
  • Commuting symplectomorphisms on a surface and the flux homomorphism, online published in Geom. Funct. Anal.

WebPage

Link

contact

kawasaki（at）math.sci.hokudai.ac.jp