Cycles on the moduli space of curves. Part 1

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).