People

Ryushi GOTO

Email	goto(@math.sci.osaka-u.ac.jp)
Research	Differential geometry, complex geometry
Keywords	Calabi-Yau manifolds, Hyper Kähler manifolds, G2, Spin(7)-structures, Generalized Geometry
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My research interest is mostly in complex and differential geometry, which are closely related with algebraic geometry and theoretical physics. My own research started with special geometric structures such as Calabi-Yau, hyperKaehler, G2 and Spin(7) structures. These four structures exactly correspond to special holonomy groups which give rise to Ricci-flat Einstein metrics on manifolds. It is intriguing that these moduli spaces are smooth manifolds on which local Torelli type theorem holds. In order to understand these phenomena, I introduce a notion of geometric structures defined by a system of closed differential forms and establish a criterion of unobstructed deformations of structures. When we apply this approach to Calabi-Yau, hyperKaehler, G2 and Spin(7) structures, we obtain a unified construction of these moduli spaces. At present I also explore other interesting geometric structures and their moduli spaces.