Title: The moduli space of stable quotients.

Abs: I will talk about a new moduli space of stable quotients of the trivial
sheaf on stable curves. Over nonsingular curves, the moduli space is
Grothendieck's Quot scheme. Over nodal curves, a relative construction is made
to keep the torsion of the quotient away from the singularities. New
compactifications of classical spaces arise naturally: a nonsingular,
irreducible, and modular compactification of the moduli of maps from genus 1
curves to projective space is obtained. The moduli space of stable quotients
carries a canonical 2-term obstruction theory and thus a virtual class. I will
discuss the resulting theory in several toric and CY cases. Questions about the
behavior of stable quotients for arbitrary targets will be raised.
Joint work with A. Marian and D. Oprea.