Researcher's Information

Associate Professor

TARAMA, Daisuke

Mathematics

Theory of integrable systems, geometric mechanics, dynamical systems theory, and related geometries

The researches of Daisuke Tarama focus on dynamical systems, geometric mechanics, and related geometries, such as differential geometry, particularly symplectic geometry and Poisson geometry, as well as algebraic and complex analytic geometry. 
Daisuke Tarama has mainly been studying the finite-dimensional integrable systems, particularly (generalized) free rigid body dynamics, or equivalently the integrable geodesic flows on Lie groups with respect to a left-invariant metric of a large class. Through the symmetry and the singularities of the systems, one sees their interesting aspects in relation to not only dynamical systems theory and Lie theory, but also such different mathematical disciplines as symplectic geometry, Poisson geometry, and, algebraic and complex analytic geometry, as well as mathematical analysis of differential operators, when one considers corresponding quantum systems. For such finite-dimensional integrable systems, he has investigated the dynamical behavior around the equilibria (singularities), the analysis of (quantum) differential operators with Lie group symmetry, and the associated algebraic varieties, such as elliptic fibrations and K3 surfaces. 
Daisuke Tarama also aims at expanding his research scope towards applied mathematics and physics in symmetry and singularities, trying to carrying out geometrical and globally analytical studies on wider phenomena in such areas as natural sciences, data science, and engineering.