Mathematics Colloquia and Seminars

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The Weil-Petersson metric on Teichmuller space unifies the complex and hyperbolic natures of a Riemann surface of negative Euler characteristic. We introduce a coarse combinatorial description of the Weil-Petersson metric using familiar pair-of-pants decompositions of surfaces. As a consequence, we show that the volume of the convex core of the quasi-Fuchsian hyperbolic 3-manifold Q(X,Y) is comparable to the Weil-Petersson distance d_{WP}(X,Y) between X and Y. We will focus on the simple combinatorics of pairs of pants and its connection to hyperbolic volume.