In this thesis we will extend the study of Teichmüller spaces in two relatively unexplored new directions. First, beginning with the Teichmüller space of the flat 2- torus, rather than increasing the genus, we will explore higher dimensional tori. This yields Riemannian symmetric spaces with very different, yet analogous, behavior to classically studied Teichmüller spaces of hyperbolic surfaces. Second, in the setting of hyperbolic surfaces, we study a certain kind of rigidity for maps between different Teichmüller spaces. We will classify most of the possible cases of holomorphic isometric submersions between Teichmüller spaces of finite-type hyperbolic surfaces and begin exploration in the case of infinite-type.

Mark's advisor is Lizhen Ji.

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https://umich.zoom.us/j/94865577229 Speaker(s): Mark Greenfield (UM)