# Tautological classes on moduli of curves

## Seminar/Forum

213
Peter Hall
For a natural number $$g>1$$ the moduli space $$M_g$$ classifies smooth projective curves of genus $$g$$. In 1969 Deligne and Mumford proved that this space is irreducible and studied some of its fundamental properties. The geometry of moduli spaces of curves have been studied extensively since then by people from different perspectives. Many questions about the geometry of moduli of curves involve the so called tautological classes. In this talk I will review well-known facts and conjectures about tautological classes. I will also discuss recent progress and developments.