Several classes of co-homologies on $\bar M_{g,n}$ computed by means of the classification of semisimple cohomology field theories

I will give several examples of natural cohomology classes on the moduli space of stable curves and formulas for them. All these formulas are similar in form, and this is not accidental: they are all obtained using the same classification of semisimple cohomological field theories developed by Givental and Telemann.