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.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/5312