Résume | Many modern geometric constructions yield natural classes on the moduli space of curves. How can we compute these classes? The genus 0 cases are the simplest and are often governed by essentially closed formulas. To make the jump from genus 0 to higher genus, a new route via the study of semisimple Cohomological Field Theories (CohFTs) and the Givental-Teleman classification can be used. I will discuss how the CohFT results lead to complete calculations in several cases (related to r-spin curves, Verlinde bundles, and Gromov-Witten theories). The talk represents joint work with several authors: F. Janda, A. Marian, D. Oprea, A. Pixton, H.-H. Tseng, and D. Zvonkine. |