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Geometry-Topology Seminar

Thursday, November 30, 2017 - 4:30pm

Tarik Aougab

Brown University


University of Pennsylvania


This is the second of two Geometry-Topology talks today.

In low-dimensional topology, there are many problems that can be studied with a combination of geometric, combinatorial, dynamical, and algebraic tools. In this talk, we'll focus on a particular concept from geometry and dynamics, a geodesic current, which is a generalization of a closed geodesic on a hyperbolic surface. We'll apply the theory of currents to attack problems in both group theory and in combinatorics, specifically:
(1) equipping the moduli space of graphs with a metric resembling the classical Weil-Petersson metric, and using its geometry to study the outer automorphism group of the free group (joint work with Matt Clay and Yo'av Rieck);  
(2) counting mapping class group orbits of closed curves on a surface of negative Euler characteristic, and relating these counts to geometric features of the Teichmuller space (joint work with Juan Souto).