Speaker: Clara Dolfen (Columbia University)

Title: Degenerations in enumerative geometry

Abstract: In order to study stable maps to singular targets Jun Li developed the theory of relative Gromov-Witten invariants. These invariants count stable maps to the stack of expanded relative pairs. Using a degeneration formula, one can recover the GW invariants of the singular target. A similar construction holds in Donaldson-Thomas theory. In this talk we discuss the construction of the building blocks of the stack of expanded degenerations and the stack of expanded relative pairs. If time permits we will introduce the notion of admissible ideal sheaves, which are the objects counted in relative Donaldson-Thomas theory.