IZUMIYA, Shyuichi

IZUMIYA, Shyuichi
Research Field
Specially Appointed Professor
Department of Mathematics
Research Interest
Geometry; Singularities of Differentiable Mappings
Research Activities

I am interested in the following subjects:

1)Applications of the theory of singularities to classical differential Geometries (i.e., Euclidean Geometry, Hyperbolic Geometry, Lorentz geometry etc)

2)Singularities appearing in the various models of horizon in General relativity theory

3)Caustics appearing in the brane world scenario

4)Singularities of special surfaces (i.e., flat surfaces, ruled surfaces etc) in space forms (i.e., Euclidean space, Sphere, Hyperbolic space, Minkowski space, de Sitter space or anti de Sitter space)

5)Gravitaional lensings

6)Singularities of solutions for non-linear partial differential equations I applied the theory of Legendrian or Lagrangian singularities to the above subjects and have discovered some interesting geometric invariants

1)Legendrian dualities and spacelike hypersurfaces in the lightcone
Shyuichi Izumiya
Moscow Mathematical Journal 9(2) 325-357, April, 2009

2)Geometric Singularities for Solutions of Single Conservation Laws
Shyuichi Izumiya and Georgios T. Kossioris
Arch. Rational Mech. Anal. 139 255-290, 1997

3)Perestroikas of optical wave fronts and graphlike Legedrian unfoldings
Shyuichi Izumiya
Journal of Differential Geometry 38 485-500, 1993

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