Stratifications of the moduli space of curves and related questions

Abstract

We discuss results and open problem on the geometry of the moduli space of complex curves, with special emphasis on vanishing results in cohomology and in the tautological ring. The focus is on the techniques, namely algebraic stratifications, transversely real foliations and q-convex exhaustion functions. A selection of related problems in the field is also quickly mentioned.

Keywords

• riemann surfaces
• moduli space of curves
• tautological ring
• stratifications
• translation surfaces
• abelian differentials