On the number and location of short geodesics on moduli space,  with D. Margalit
 

abstract A closed Teichmüller geodesic in the moduli space M_g of Riemann surfaces of genus g is called L-short, if it has length at most L/g. We show that for any L > 0 there exist ε₁ > ε₁ > 0, independent of g, so that the L-short geodesics in M_g all lie in the intersection of the ε₁-thick part and the ε₂-thin part. We also estimate the number of L-short geodesics in M_g, bounding this from above and below by polynomials in g whose degrees depend on L and tend to infinity as L does.