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Staff Introduction
My main research area is theoretical physics related to the gravitation theory, and I have been engaged in the following research projects in this area.
(1) Mathematical aspects of general relativity
The gravitation theory, the general relativity constructed by Einstein, is a theory that governs the dynamics of the spacetime. The basic equation of this theory is the Einstein equation, which is the set of partial differential equations for the spacetime metric. To elucidate mathematical properties of this equation, I studied construction methods of exact and numerical solutions of this equation, and also studied basic properties of those solutions such as stability against linear and nonlinear perturbations.
(2) Modified gravity theories and cosmology
Gravitation theories constructed by introducing various modifications to the general relativity are called modified gravity theories, and influences of those modifications to properties of gravitation and cosmological evolution have been attracting interest. Within this context, I examined how to explain the accelerated expansion of our universe based on the modifications, and also studied influences to the gravitational wave propagation and shock formation phenomena caused by it.
(3) Applications to dynamical phenomena in elementary particle physics
The string theory, a candidate of the theory that unites the elementary particle theory and the gravitation theory, predicts that these two theories are connected by a duality with which we can study phenomena in one theory by studying corresponding phenomena in the other theory. Using this duality, I studied dynamical phenomena and chaotic behavior in elementary particle physics setup employing techniques to study the dynamics of gravitation theory.
The above studies are intimately related to studies on mathematical analysis, geometry, fluid dynamics, dynamical system and chaos. Combining mathematical techniques in these research fields and my experiences in the past researches, I will try to extend studies on the above research topics and also try to apply my research techniques to problems in other research fields.
Keywords  Gravitation, Mathematical Physics, Numerical analysis, Nonlinear Phenomenology 

Faculty , Department  Institute of Mathematics for Industry , Advanced Mathematics Technology 
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