Abstract:Moduli spaces are a geometer's obsession. A celebrated example in algebraic geometry is the space M̄ g,n of stable n-pointed algebraic curves of genus g, due to Deligne—Mumford and Knudsen. It has a d...Moduli spaces are a geometer's obsession. A celebrated example in algebraic geometry is the space M̄ g,n of stable n-pointed algebraic curves of genus g, due to Deligne—Mumford and Knudsen. It has a delightful combinatorial structure based on weighted graphs.Recent papers of Branetti, Melo, Viviani and of Caporaso defined an entirely different moduli space of tropical curves, which are weighted metrized graphs. It also has a delightful combinatorial structure based on weighted graphs.One is led to ask whether there is a geometric connection between these moduli spaces. In joint work [1] with Caporaso and Payne, we exhibit a connection, which passes through a third type of geometry — nonarchimedean analytic geometry.KeywordsModulus SpaceRiemann SurfaceElliptic CurveElliptic CurfWeighted GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.Read More