Differential operators on supercircle: conformally equivariant   quantization and symbol calculus
  We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist. 
Hichem Gargoubi (IPEIT), Najla Mellouli (ICJ), Valentin Ovsienko (ICJ)