Weil-Petersson analogs for graphs

Geometry & Topology
Event time: 
Tuesday, April 9, 2019 - 4:15pm
DL 431
Tarik Aougab
Speaker affiliation: 
Brown University
Event description: 

The Weil-Petersson metric is a Riemannian metric on the Teichmuller space which comes from and reflects the geometry of the hyperbolic metrics on the underlying surface. Motivated by foundational work of McMullen, Pollicott-Sharp (and later Kao) proposed an analogous metric for the moduli space of metrics on a fixed graph. We study this metric and completely characterize its completion in the case of a rose, showing that it resembles the completion of the classical WP metric. This represents joint work with Matt Clay and Yo’av Rieck. 

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