Abstract:we (try to) give a friendly guide for shearing between hyperbolic surfaces in as ``efficient" a manner as possible. On the way, we'll see Teichmueller spaces, Thurston's earthquake theorem, and a novel metric on Teichmueller space called the earthquake metric which has surprising connections to both the Thurston metric and the Weil-Petersson metric. This is work in collaboration with K...
Abstract：The moduli spaces of points on n-spheres carry natural actions of braid groups. For n=0, 1, and 3, we prove that these symmetries extend to actions of mapping class groups of certain positive genus surfaces, through exceptional isomorphisms with certain moduli of local systems. Moreover, the isomorphisms map the Coxeter invariants of points on spheres to the boundary monodromy of the ...
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