I will give two lectures on the intersection theory of the moduli space of curves: tautological classes, relations, integral calculus, and cycle formulas. The role of the virtual fundamental class of the moduli of stable maps will be highlighted. In the second lecture, I will discuss the recent proof of Pixton's formula for double ramification cycles (joint work with Janda, Pixton, and Zvonkine).
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/AT2015