Hodge integrals and tautological classes
on the moduli space of curves


Carel Faber

Oklahoma State University



Room 2-190

4:30 p.m., Thursday, March 30, 2000


Abstract:   By virtue of its universal property, the moduli space of curves carries a collection of algebraic intersection classes, the tautological or Mumford-Morita-Miller classes. It is important to understand the relations between these classes. According to the (conjectural) picture that is emerging, the subalgebras of tautological classes satisfy a form of Poincaré duality.

Hodge integrals are intersection numbers of tautological classes.  All these can be recursively computed by the work of Witten and Kontsevich, but this doesn't yield explicit formulas. Recent joint work with R. Pandharipande focuses on obtaining explicit ormulas for certain Hodge integrals via Gromov-Witten theory.

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