The strata of k-differentials are spaces parametrizing stable curves with n markings admitting a k-log differential with prescribed zeroes and poles. A natural question to ask is whether there is an explicit formula in the Chow ring of M_{g,n}(bar) of the Chow class of these spaces. When k and all the zeroes and poles are odd numbers we can define the so-called "spin refinement" of this problem. In this talk we will investigate the approach via (spin) Double ramification cycles on the computation of these strata which reduces the problem to the case of holomorphic (spin) strata of 1-differentials. Finally, we sketch the computation of holomorphic spin strata of 1-differentials which gives a complete answer to the aforementioned problem.
This is joint work with Adrien Sauvaget and David Holmes. | 
