People

Shinpei BABA

Email	baba(@math.sci.osaka-u.ac.jp)
Research	Geometry and topology
Keywords	hyperbolic geometry, Riemann surface, holonomy, Teichmüller Theory, measured lamination
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My research is mainly on certain structures on a Riemann surface, and their relation to representations of the fundamental group of the surface into a Lie group.

A complex projective structure is a geometric structure on a Riemann surface, and it has a holonomy representation which is not necessarily discrete. Projective structures give geometric meaning to non-discrete representations. Projective structures are analytic objects, and their holonomy representations are algebraic. In addition, each projective structure corresponds to a mapping from the universal cover of the surface into hyperbolic three-space equivariant w.r.t. a holonomy representation. I am excited to explore relations between different aspects of projective structures.