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We show that the energy of harmonic maps f: M ----> S (Riemann surface varying along Teichmüller geodesic in Teichmüller space) is quasi-convex along Teichmüller geodesics generalizing previously known result about the length of closed geodesics. The asymptotic growth of the…

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Random geometric graphs hide geometric structure inside an otherwise random-looking network: each vertex has a latent position on a high-dimensional sphere, and edges are formed between vertices that are sufficiently close. When can this hidden geometry be detected from the graph alone? In this…

Abstract

Abstract

TBA

Abstract