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In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a pro...
The paper initiates a systematic study of M¨obius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is M¨obius equivalent to the boun...
Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a K¨ahler group on the real hyperbolic space of dimension at least 3 factors through a homom...
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classi cation of modular compacti cations of Mg;n, and t...
We define and count lattice points in the moduli spaceMg,n of stable genus g curves with n labeled points.
In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under pertu...

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