Categorical compactifications and master equations for moduli spaces of curves -- CANCELLED --

We will discuss categorical construction of the moduli spaces of curves and various compactifications.
This involves the operations of push-forward of functors or Kan extensions and W-constructions in the
framework of Feynman categories. We also show that there is a tower of compactifications that
is naturally available though the master equation and canonical blow-downs. This is joint work with
Clemens Berger and Javier Zuniga.