 Richard Sharp (mathematician)

Richard Sharp works on the geometry of Anosov flows. His Abelian Livšic theorems for Anosov flows by Richard Sharp gives two short proofs of an earlier abelian Livšic theorem and extends the framework to positive-density sets of null-homologous periodic orbits and amenable covers.^[ref]

The abelian formulation separates a derivative along the flow from a contribution carried by a closed differential form. Integrals over periodic orbits record the obstruction to representing a function entirely as such a derivative. This makes orbit data into information about cohomology and explains why restricting to null-homologous orbits changes the formulation.^[ref]