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PROFILE
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・・*・  NAME  ・*・・ Toshiki Mabuchi
・・*・  Keyward  ・*・・ Complex Geometry
・・*・  association  ・*・・ Department of Mathematics
・・*・  Position  ・*・・ Professor
・・*・  Mathematical Society  ・*・・ The Mathematical Society of Japan
・・*・  constellation  ・*・・ Pisces


Complex Geometry
Kaehler manifolds and projective algebraic manifolds are my prime research interests. We study these algebraic geometric objects from differential geometric viewpoints. Related to the moduli spaces of such manifolds, actions of reductive algebraic groups are often considered by using symplectic reduction. Let me give an example of a theme I am working on. The Hitchin-Kobayashi correspondence for vector bundles, established by Kobayashi, Donaldson and Uhlenbeck-Yau, states that an indecomposable holomorphic vector bundle is stable in the sense of Mumford-Takemoto if and only if the vector bundle admits a Hermitian-Einstein metric. I am working on its analogue in the case of manifolds.