### Homotopy theory of compactified moduli spaces. (Søren Galatius)

### Abstract:

The Pontrjagin-Thom construction defines a map from the moduli space
M_g of Riemann surfaces to a certain Thom spectrum, and the
Madsen-Weiss theorem tells us that the map is a homology equivalence
in a range. In many applications, not the moduli space M_g itself,
but its compactification (the Deligne-Mumford compactification) is
relevant. In this talk I will define a Thom spectrum with a natural
map from the compactified moduli space, and describe progress towards
a "compactified Madsen-Weiss theorem". This is joint work with
Y. Eliashberg.