Cohomology of moduli spaces of stable curves

Abstract: The cohomology rings of moduli spaces often have distinguished classes called tautological classes. This talk is about the special situation when all cohomology classes on a moduli space are tautological. I will start with the example of projective space. Then I'll introduce the moduli spaces M_{g,n}-bar of n-poined, stable genus g curves, using the example M_{2,0}-bar as a guide. At the end, I'll present several new small values (g, n) where we have proven that all classes on M_{g,n}-bar are tautological. This is joint work with Samir Canning.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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