IZUMIYA, Shyuichi
 Research Field
 Geometry
 Position
 Specially Appointed Professor
 Organization
 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 nonlinear partial differential equations I applied the theory of Legendrian or Lagrangian singularities to the above subjects and have discovered some interesting geometric invariants
 Papers:
 1）Legendrian dualities and spacelike hypersurfaces in the lightcone
Shyuichi Izumiya
Moscow Mathematical Journal 9(2) 325357, April, 2009  2）Geometric Singularities for Solutions of Single Conservation Laws
Shyuichi Izumiya and Georgios T. Kossioris
Arch. Rational Mech. Anal. 139 255290, 1997  3）Perestroikas of optical wave fronts and graphlike Legedrian unfoldings
Shyuichi Izumiya
Journal of Differential Geometry 38 485500, 1993  Keywords
 Brane world, Caustics, Classical Differntial Geometry, Gravitation Lensing, Gravitation Theory, Hyperbolic Geometry, Lagrangian Singularities, Legendrian Singularities, Line congruences, Loentzian Geometry, Nonlinear PDE, Ruled surfaces, Singularities, Vision Theory
 WebPage
 http://researchmap.jp/izumiya/?lang=english