## University of Sydney Algebra Seminar

# Ezra Getzler (Northwestern University)

## Friday 2nd October, 12.05-12.55pm, Carslaw 375

### Topological field theory in two dimensions and a filtration of Deligne-Mumford moduli spaces

Deligne-Mumford moduli spaces are moduli spaces for projective curves with mild (normal crossing) singularities. They are important tools in mathematics and mathematical physics (their volumes are related to the KdV hierarchy, and they were used by de Jong in his famous theorem on the existence of smooth alterations). In this talk, I explain a way in which they resemble polyhedra: they carry a filtration such that the inclusion of the k'th filtrand is a k-homotopy equivalence.