Speaker: Cristina Manolache

Title: A method for comparing Gromov-Witten-like invariants.
Abstract: For a (special) variety X we can construct several compact spaces of curves on X which are nice enough to allow us do intersection theory on them. Intersection theory on these different compactifications gives rise to several types of invariants: Gromov-Witten invariants, stable quotient invariants, stable quasi-maps invariants, etc. Very roughly (and naively), we might think of a Gromov-Witten invariant, or a stable quotient invariant, etc, as the number of curves on X of fixed genus, fixed degree and which intersect some given subvarieties of X. In particular, we might expect the above invariants to be equal. There are by now several theorems and conjectures which relate these different types of invariants. In this seminar I will define Gromov-Witten invariants and stable quotient invariants and prove that they are equal. If time allows I will also discuss some features which appear in the more general picture.